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trunk/esys2/escript/py_src/linearPDEs.py revision 142 by jgs, Mon Jul 25 05:28:20 2005 UTC trunk/escript/py_src/linearPDEs.py revision 1787 by artak, Mon Sep 15 01:36:34 2008 UTC
# Line 1  Line 1 
1    #
2  # $Id$  # $Id$
3    #
4  ## @file linearPDEs.py  #######################################################
5    #
6    #           Copyright 2003-2007 by ACceSS MNRF
7    #       Copyright 2007 by University of Queensland
8    #
9    #                http://esscc.uq.edu.au
10    #        Primary Business: Queensland, Australia
11    #  Licensed under the Open Software License version 3.0
12    #     http://www.opensource.org/licenses/osl-3.0.php
13    #
14    #######################################################
15    #
16    
17  """  """
18  Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
19    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
20    solver capabilities in itself but hands the PDE over to
21    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
22    The general interface is provided through the L{LinearPDE} class. The
23    L{AdvectivePDE} which is derived from the L{LinearPDE} class
24    provides an interface to PDE dominated by its advective terms. The L{Poisson},
25    L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
26    classs which are also derived form the L{LinearPDE} class should be used
27    to define of solve these sepecial PDEs.
28    
29    @var __author__: name of author
30    @var __copyright__: copyrights
31    @var __license__: licence agreement
32    @var __url__: url entry point on documentation
33    @var __version__: version
34    @var __date__: date of the version
35  """  """
36    
37    import math
38  import escript  import escript
39  import util  import util
40  import numarray  import numarray
41    
42    __author__="Lutz Gross, l.gross@uq.edu.au"
43    __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
44                        http://www.access.edu.au
45                    Primary Business: Queensland, Australia"""
46    __license__="""Licensed under the Open Software License version 3.0
47                 http://www.opensource.org/licenses/osl-3.0.php"""
48    __url__="http://www.iservo.edu.au/esys"
49    __version__="$Revision$"
50    __date__="$Date$"
51    
52    
53  def _CompTuple2(t1,t2):  class IllegalCoefficient(ValueError):
54       """
55       raised if an illegal coefficient of the general ar particular PDE is requested.
56     """     """
57     Compare two tuples     pass
58    
59     \param t1 The first tuple  class IllegalCoefficientValue(ValueError):
    \param t2 The second tuple  
60     """     """
61       raised if an incorrect value for a coefficient is used.
62       """
63       pass
64    
65     dif=t1[0]+t1[1]-(t2[0]+t2[1])  class IllegalCoefficientFunctionSpace(ValueError):
66     if dif<0: return 1     """
67     elif dif>0: return -1     raised if an incorrect function space for a coefficient is used.
68     else: return 0     """
   
 def ELMAN_RAMAGE(P):  
     return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
   
 def SIMPLIFIED_BROOK_HUGHES(P):  
     c=(P-3.).whereNegative()  
     return P/6.*c+1./2.*(1.-c)  
69    
70  def HALF(P):  class UndefinedPDEError(ValueError):
71      return escript.Scalar(0.5,P.getFunctionSpace())     """
72       raised if a PDE is not fully defined yet.
73       """
74       pass
75    
76  class PDECoefficient:  class PDECoefficient(object):
77      """      """
78      A class for PDE coefficients      A class for describing a PDE coefficient
79    
80        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
81        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
82        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
83        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
84        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
85        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
86        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
87        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
88        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
89        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
90        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
91        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
92        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
93        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
94    
95      """      """
     # identifier for location of Data objects defining COEFFICIENTS  
96      INTERIOR=0      INTERIOR=0
97      BOUNDARY=1      BOUNDARY=1
98      CONTACT=2      CONTACT=2
99      CONTINUOUS=3      SOLUTION=3
100      # identifier in the pattern of COEFFICIENTS:      REDUCED=4
101      # the pattern is a tuple of EQUATION,SOLUTION,DIM where DIM represents the spatial dimension, EQUATION the number of equations and SOLUTION the      BY_EQUATION=5
102      # number of unknowns.      BY_SOLUTION=6
103      EQUATION=3      BY_DIM=7
104      SOLUTION=4      OPERATOR=10
105      DIM=5      RIGHTHANDSIDE=11
106      # indicator for what is altered if the coefficient is altered:      BOTH=12
107      OPERATOR=5      INTERIOR_REDUCED=13
108      RIGHTHANDSIDE=6      BOUNDARY_REDUCED=14
109      BOTH=7      CONTACT_REDUCED=15
110      def __init__(self,where,pattern,altering):  
111        def __init__(self, where, pattern, altering):
112         """         """
113         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
114    
115           @param where: describes where the coefficient lives
116           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
117                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
118           @param pattern: describes the shape of the coefficient and how the shape is build for a given
119                  spatial dimension and numbers of equation and solution in then PDE. For instance,
120                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
121                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
122                  on a 2-dimensional domain. In the case of single equation and a single solution component
123                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
124                  the example would be read as (2,).
125           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
126           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
127           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
128           @param reduced: indicates if reduced
129           @type reduced: C{bool}
130         """         """
131           super(PDECoefficient, self).__init__()
132         self.what=where         self.what=where
133         self.pattern=pattern         self.pattern=pattern
134         self.altering=altering         self.altering=altering
# Line 68  class PDECoefficient: Line 140  class PDECoefficient:
140         """         """
141         self.value=escript.Data()         self.value=escript.Data()
142    
143      def getFunctionSpace(self,domain):      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
144         """         """
145         defines the FunctionSpace of the coefficient on the domain         defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
146    
147         @param domain:         @param domain: domain on which the PDE uses the coefficient
148         """         @type domain: L{Domain<escript.Domain>}
149         if self.what==self.INTERIOR: return escript.Function(domain)         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
150         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)         @type reducedEquationOrder: C{bool}
151         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
152         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         @type reducedSolutionOrder: C{bool}
153           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
154           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
155           """
156           if self.what==self.INTERIOR:
157                return escript.Function(domain)
158           elif self.what==self.INTERIOR_REDUCED:
159                return escript.ReducedFunction(domain)
160           elif self.what==self.BOUNDARY:
161                return escript.FunctionOnBoundary(domain)
162           elif self.what==self.BOUNDARY_REDUCED:
163                return escript.ReducedFunctionOnBoundary(domain)
164           elif self.what==self.CONTACT:
165                return escript.FunctionOnContactZero(domain)
166           elif self.what==self.CONTACT_REDUCED:
167                return escript.ReducedFunctionOnContactZero(domain)
168           elif self.what==self.SOLUTION:
169                if reducedEquationOrder and reducedSolutionOrder:
170                    return escript.ReducedSolution(domain)
171                else:
172                    return escript.Solution(domain)
173           elif self.what==self.REDUCED:
174                return escript.ReducedSolution(domain)
175    
176      def getValue(self):      def getValue(self):
177         """         """
178         returns the value of the coefficient:         returns the value of the coefficient
179    
180           @return:  value of the coefficient
181           @rtype:  L{Data<escript.Data>}
182         """         """
183         return self.value         return self.value
184        
185      def setValue(self,newValue):      def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
        """  
        set the value of the coefficient to new value  
186         """         """
187           set the value of the coefficient to a new value
188    
189           @param domain: domain on which the PDE uses the coefficient
190           @type domain: L{Domain<escript.Domain>}
191           @param numEquations: number of equations of the PDE
192           @type numEquations: C{int}
193           @param numSolutions: number of components of the PDE solution
194           @type numSolutions: C{int}
195           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
196           @type reducedEquationOrder: C{bool}
197           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
198           @type reducedSolutionOrder: C{bool}
199           @param newValue: number of components of the PDE solution
200           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
201           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
202           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
203           """
204           if newValue==None:
205               newValue=escript.Data()
206           elif isinstance(newValue,escript.Data):
207               if not newValue.isEmpty():
208                  if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
209                    try:
210                      newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
211                    except:
212                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
213           else:
214               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
215           if not newValue.isEmpty():
216               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
217                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
218         self.value=newValue         self.value=newValue
219        
220      def isAlteringOperator(self):      def isAlteringOperator(self):
221          """          """
222      return true if the operator of the PDE is changed when the coefficient is changed          checks if the coefficient alters the operator of the PDE
223    
224            @return:  True if the operator of the PDE is changed when the coefficient is changed
225            @rtype:  C{bool}
226      """      """
227          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
228              return not None              return not None
# Line 102  class PDECoefficient: Line 231  class PDECoefficient:
231    
232      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
233          """          """
234      return true if the right hand side of the PDE is changed when the coefficient is changed          checks if the coefficeint alters the right hand side of the PDE
235    
236        @rtype:  C{bool}
237            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
238      """      """
239          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
240              return not None              return not None
241          else:          else:
242              return None              return None
243    
244      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
245         """         """
246         tries to estimate the number of equations in a given tensor shape for a given spatial dimension dim         tries to estimate the number of equations and number of solutions if the coefficient has the given shape
247    
248         @param shape:         @param domain: domain on which the PDE uses the coefficient
249         @param dim:         @type domain: L{Domain<escript.Domain>}
250           @param shape: suggested shape of the coefficient
251           @type shape: C{tuple} of C{int} values
252           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
253                     If no appropriate numbers could be identified, C{None} is returned
254           @rtype: C{tuple} of two C{int} values or C{None}
255         """         """
256           dim=domain.getDim()
257         if len(shape)>0:         if len(shape)>0:
258             num=max(shape)+1             num=max(shape)+1
259         else:         else:
260             num=1             num=1
261         search=[]         search=[]
262         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
263            for e in range(num):            for u in range(num):
264               search.append((e,u))               for e in range(num):
265         search.sort(_CompTuple2)                  search.append((e,u))
266         for item in search:            search.sort(self.__CompTuple2)
267               s=self.buildShape(item[0],item[1],dim)            for item in search:
268                 s=self.getShape(domain,item[0],item[1])
269               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
270                   return (1,1)                   return (1,1)
271               else:               else:
272                   if s==shape: return item                   if s==shape: return item
273           elif self.definesNumEquation():
274              for e in range(num,0,-1):
275                 s=self.getShape(domain,e,0)
276                 if len(s)==0 and len(shape)==0:
277                     return (1,None)
278                 else:
279                     if s==shape: return (e,None)
280    
281           elif self.definesNumSolutions():
282              for u in range(num,0,-1):
283                 s=self.getShape(domain,0,u)
284                 if len(s)==0 and len(shape)==0:
285                     return (None,1)
286                 else:
287                     if s==shape: return (None,u)
288         return None         return None
289        def definesNumSolutions(self):
290           """
291           checks if the coefficient allows to estimate the number of solution components
292    
293      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
294          """         @rtype: C{bool}
295      builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
296           for i in self.pattern:
297                 if i==self.BY_SOLUTION: return True
298           return False
299    
300      @param e:      def definesNumEquation(self):
301      @param u:         """
302      @param dim:         checks if the coefficient allows to estimate the number of equations
303      """  
304          s=()         @return: True if the coefficient allows an estimate of the number of equations
305          for i in self.pattern:         @rtype: C{bool}
306               if i==self.EQUATION:         """
307                  if e>1: s=s+(e,)         for i in self.pattern:
308               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
309                  if u>1: s=s+(u,)         return False
310    
311        def __CompTuple2(self,t1,t2):
312          """
313          Compare two tuples of possible number of equations and number of solutions
314    
315          @param t1: The first tuple
316          @param t2: The second tuple
317    
318          """
319    
320          dif=t1[0]+t1[1]-(t2[0]+t2[1])
321          if dif<0: return 1
322          elif dif>0: return -1
323          else: return 0
324    
325        def getShape(self,domain,numEquations=1,numSolutions=1):
326           """
327           builds the required shape of the coefficient
328    
329           @param domain: domain on which the PDE uses the coefficient
330           @type domain: L{Domain<escript.Domain>}
331           @param numEquations: number of equations of the PDE
332           @type numEquations: C{int}
333           @param numSolutions: number of components of the PDE solution
334           @type numSolutions: C{int}
335           @return: shape of the coefficient
336           @rtype: C{tuple} of C{int} values
337           """
338           dim=domain.getDim()
339           s=()
340           for i in self.pattern:
341                 if i==self.BY_EQUATION:
342                    if numEquations>1: s=s+(numEquations,)
343                 elif i==self.BY_SOLUTION:
344                    if numSolutions>1: s=s+(numSolutions,)
345               else:               else:
346                  s=s+(dim,)                  s=s+(dim,)
347          return s         return s
348    
349  class LinearPDE:  class LinearPDE(object):
350     """     """
351     Class to handle a linear PDE     This class is used to define a general linear, steady, second order PDE
352         for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
    class to define a linear PDE of the form  
353    
354     \f[     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
      -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i  
    \f]  
355    
356     with boundary conditons:     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
357    
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
358    
359     and contact conditions     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
360       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
361       The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
362       L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
363       L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
364       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
365       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
366    
367     \f[     The following natural boundary conditions are considered:
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i  
    \f]  
368    
369     and constraints:     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
370    
371     \f[     where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
    u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
372    
    """  
    TOL=1.e-13  
    DEFAULT_METHOD=util.DEFAULT_METHOD  
    DIRECT=util.DIRECT  
    CHOLEVSKY=util.CHOLEVSKY  
    PCG=util.PCG  
    CR=util.CR  
    CGS=util.CGS  
    BICGSTAB=util.BICGSTAB  
    SSOR=util.SSOR  
    GMRES=util.GMRES  
    PRES20=util.PRES20  
    ILU0=util.ILU0  
    JACOBI=util.JACOBI  
373    
374     def __init__(self,domain,numEquations=0,numSolutions=0):     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
      """  
      initializes a new linear PDE.  
375    
376       @param args:     M{u=r}  where M{q>0}
377       """  
378       # COEFFICIENTS can be overwritten by subclasses:     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
379       self.COEFFICIENTS={     The constraints override any other condition set by the PDE or the boundary condition.
380         "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
381         "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     The PDE is symmetrical if
382         "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION,PDECoefficient.DIM),PDECoefficient.OPERATOR),  
383         "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
384         "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),  
385         "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     For a system of PDEs and a solution with several components the PDE has the form
386         "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
387         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
388         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,PDECoefficient.SOLUTION),PDECoefficient.OPERATOR),  
389         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
390         "r"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),     The natural boundary conditions take the form:
391         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.SOLUTION,),PDECoefficient.BOTH)}  
392       M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
393    
394    
395       The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
396    
397       Constraints take the form
398    
399       M{u[i]=r[i]}  where  M{q[i]>0}
400    
401       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
402    
403       The system of PDEs is symmetrical if
404    
405            - M{A[i,j,k,l]=A[k,l,i,j]}
406            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
407            - M{B[i,j,k]=C[k,i,j]}
408            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
409            - M{D[i,k]=D[i,k]}
410            - M{D_reduced[i,k]=D_reduced[i,k]}
411            - M{d[i,k]=d[k,i]}
412            - M{d_reduced[i,k]=d_reduced[k,i]}
413    
414       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
415       discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
416       defined as
417    
418       M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
419    
420       For the case of single solution component and single PDE M{J} is defined
421    
422       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
423    
424       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
425       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
426       the contact condition takes the form
427    
428       M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
429    
430       where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
431       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
432       L{jump<util.jump>}.
433       The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
434       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
435       In case of a single PDE and a single component solution the contact condition takes the form
436    
437       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
438    
439       In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
440    
441       @cvar DEFAULT: The default method used to solve the system of linear equations
442       @cvar DIRECT: The direct solver based on LDU factorization
443       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
444       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
445       @cvar CR: The conjugate residual method
446       @cvar CGS: The conjugate gardient square method
447       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
448       @cvar TFQMR: Transport Free Quasi Minimal Residual method.
449       @cvar MINRES: Minimum residual method.
450       @cvar SSOR: The symmetric overrealaxtion method
451       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
452       @cvar ILUT: The incomplete LU factorization preconditioner with will in
453       @cvar JACOBI: The Jacobi preconditioner
454       @cvar GMRES: The Gram-Schmidt minimum residual method
455       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
456       @cvar LUMPING: Matrix lumping.
457       @cvar NO_REORDERING: No matrix reordering allowed
458       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
459       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
460       @cvar PASO: PASO solver package
461       @cvar SCSL: SGI SCSL solver library
462       @cvar MKL: Intel's MKL solver library
463       @cvar UMFPACK: the UMFPACK library
464       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
465       @cvar ITERATIVE: The default iterative solver
466       @cvar AMG: algebraic multi grid
467       @cvar RILU: recursive ILU
468    
469       """
470       DEFAULT= 0
471       DIRECT= 1
472       CHOLEVSKY= 2
473       PCG= 3
474       CR= 4
475       CGS= 5
476       BICGSTAB= 6
477       SSOR= 7
478       ILU0= 8
479       ILUT= 9
480       JACOBI= 10
481       GMRES= 11
482       PRES20= 12
483       LUMPING= 13
484       NO_REORDERING= 17
485       MINIMUM_FILL_IN= 18
486       NESTED_DISSECTION= 19
487       SCSL= 14
488       MKL= 15
489       UMFPACK= 16
490       ITERATIVE= 20
491       PASO= 21
492       AMG= 22
493       RILU = 23
494       TRILINOS = 24
495       NONLINEAR_GMRES = 25
496       TFQMR = 26
497       MINRES = 27
498    
499       SMALL_TOLERANCE=1.e-13
500       __PACKAGE_KEY="package"
501       __METHOD_KEY="method"
502       __SYMMETRY_KEY="symmetric"
503       __TOLERANCE_KEY="tolerance"
504       __PRECONDITIONER_KEY="preconditioner"
505    
506    
507       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
508         """
509         initializes a new linear PDE
510    
511         @param domain: domain of the PDE
512         @type domain: L{Domain<escript.Domain>}
513         @param numEquations: number of equations. If numEquations==None the number of equations
514                              is exracted from the PDE coefficients.
515         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
516                              is exracted from the PDE coefficients.
517         @param debug: if True debug informations are printed.
518    
519         """
520         super(LinearPDE, self).__init__()
521         #
522         #   the coefficients of the general PDE:
523         #
524         self.__COEFFICIENTS_OF_GENEARL_PDE={
525           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
526           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
527           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
528           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
529           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
530           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
531           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
532           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
533           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
535           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
536           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
537           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
538           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
540           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
541           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
542           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
543           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
544           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
545           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
546           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
547    
548         # COEFFICIENTS can be overwritten by subclasses:
549         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
550         self.__altered_coefficients=False
551       # initialize attributes       # initialize attributes
552       self.__debug=None       self.__debug=debug
553       self.__domain=domain       self.__domain=domain
554       self.__numEquations=numEquations       self.__numEquations=numEquations
555       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
556       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
557    
558       # set some default values:       # set some default values:
559       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
560       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
561       self.__tolerance=1.e-8       self.__tolerance=1.e-8
562       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
563       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
564         self.__preconditioner=self.DEFAULT
565         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
566       self.__sym=False       self.__sym=False
      self.__lumping=False  
567    
568     def createCoefficient(self, name):       self.resetCoefficients()
569         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
570       # =============================================================================
571       #    general stuff:
572       # =============================================================================
573       def __str__(self):
574         """
575         returns string representation of the PDE
576    
577         @return: a simple representation of the PDE
578         @rtype: C{str}
579         """
580         return "<LinearPDE %d>"%id(self)
581       # =============================================================================
582       #    debug :
583       # =============================================================================
584       def setDebugOn(self):
585       """       """
586       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
587       """       """
588       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
589    
590     def __del__(self):     def setDebugOff(self):
      pass  
   
    def getCoefficient(self,name):  
591       """       """
592       return the value of the parameter name       switches off debugging
593         """
594         self.__debug=None
595    
596       @param name:     def trace(self,text):
597         """
598         print the text message if debugging is swiched on.
599         @param text: message
600         @type text: C{string}
601       """       """
602       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
603    
604     def getCoefficientOfPDE(self,name):     # =============================================================================
605       # some service functions:
606       # =============================================================================
607       def getDomain(self):
608       """       """
609       return the value of the coefficient name of the general PDE.       returns the domain of the PDE
      This method is called by the assembling routine it can be  
      overwritten to map coefficients of a particualr PDE to the general PDE.  
610    
611       @param name:       @return: the domain of the PDE
612         @rtype: L{Domain<escript.Domain>}
613       """       """
614       return self.getCoefficient(name)       return self.__domain
615    
616     def hasCoefficient(self,name):     def getDim(self):
617        """       """
618        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
619    
620        @param name:       @return: the spatial dimension of the PDE domain
621        """       @rtype: C{int}
622        return self.COEFFICIENTS.has_key(name)       """
623         return self.getDomain().getDim()
624    
625     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
626       """       """
627       return true if the test functions should use reduced order       returns the number of equations
628    
629         @return: the number of equations
630         @rtype: C{int}
631         @raise UndefinedPDEError: if the number of equations is not be specified yet.
632       """       """
633       return self.__row_function_space       if self.__numEquations==None:
634             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
635         else:
636             return self.__numEquations
637    
638     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
639       """       """
640       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
641    
642         @return: the number of unknowns
643         @rtype: C{int}
644         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
645       """       """
646       return self.__column_function_space       if self.__numSolutions==None:
647            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
648         else:
649            return self.__numSolutions
650    
651     def setValue(self,**coefficients):     def reduceEquationOrder(self):
652        """       """
653        sets new values to coefficients       return status for order reduction for equation
654    
655        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
656        """       @rtype: L{bool}
657        self.__setValue(**coefficients)       """
658               return self.__reduce_equation_order
659    
660     def cleanCoefficients(self):     def reduceSolutionOrder(self):
661       """       """
662       resets all coefficients to default values.       return status for order reduction for the solution
663    
664         @return: return True is reduced interpolation order is used for the represenation of the solution
665         @rtype: L{bool}
666       """       """
667       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
668    
669     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
670       """       """
671       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
672    
673         @return: representation space of equation
674         @rtype: L{FunctionSpace<escript.FunctionSpace>}
675       """       """
676       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
677                   return escript.ReducedSolution(self.getDomain())
678         else:
679             return escript.Solution(self.getDomain())
680    
681     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
682       """       """
683       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
684    
685       @param name:       @return: representation space of solution
686         @rtype: L{FunctionSpace<escript.FunctionSpace>}
687       """       """
688       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
689          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
690       else:       else:
691          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
692    
693     def getFunctionSpaceForCoefficient(self,name):  
694       def getOperator(self):
695       """       """
696       return the atoms of the coefficient name       provides access to the operator of the PDE
697    
698       @param name:       @return: the operator of the PDE
699         @rtype: L{Operator<escript.Operator>}
700       """       """
701       if self.hasCoefficient(name):       m=self.getSystem()[0]
702          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
703             return self.copyConstraint(1./m)
704       else:       else:
705          raise ValueError,"Solution coefficient %s requested"%name           return m
706    
707     def alteredCoefficient(self,name):     def getRightHandSide(self):
708       """       """
709       announce that coefficient name has been changed       provides access to the right hand side of the PDE
710         @return: the right hand side of the PDE
711         @rtype: L{Data<escript.Data>}
712         """
713         r=self.getSystem()[1]
714         if self.isUsingLumping():
715             return self.copyConstraint(r)
716         else:
717             return r
718    
719       @param name:     def applyOperator(self,u=None):
720       """       """
721       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
722          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
723          if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()       @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
724                   the current solution is used.
725         @type u: L{Data<escript.Data>} or None
726         @return: image of u
727         @rtype: L{Data<escript.Data>}
728         """
729         if u==None:
730            return self.getOperator()*self.getSolution()
731       else:       else:
732          raise ValueError,"unknown coefficient %s requested"%name          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
733    
734     # ===== debug ==============================================================     def getResidual(self,u=None):
735     def setDebugOn(self):       """
736         """       return the residual of u or the current solution if u is not present.
737    
738         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
739                   the current solution is used.
740         @type u: L{Data<escript.Data>} or None
741         @return: residual of u
742         @rtype: L{Data<escript.Data>}
743         """
744         return self.applyOperator(u)-self.getRightHandSide()
745    
746       def checkSymmetry(self,verbose=True):
747          """
748          test the PDE for symmetry.
749    
750          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
751          @type verbose: C{bool}
752          @return:  True if the PDE is symmetric.
753          @rtype: L{Data<escript.Data>}
754          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
755          """
756          verbose=verbose or self.__debug
757          out=True
758          if self.getNumSolutions()!=self.getNumEquations():
759             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
760             out=False
761          else:
762             A=self.getCoefficientOfGeneralPDE("A")
763             if not A.isEmpty():
764                tol=util.Lsup(A)*self.SMALL_TOLERANCE
765                if self.getNumSolutions()>1:
766                   for i in range(self.getNumEquations()):
767                      for j in range(self.getDim()):
768                         for k in range(self.getNumSolutions()):
769                            for l in range(self.getDim()):
770                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
771                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
772                                   out=False
773                else:
774                   for j in range(self.getDim()):
775                      for l in range(self.getDim()):
776                         if util.Lsup(A[j,l]-A[l,j])>tol:
777                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
778                            out=False
779             B=self.getCoefficientOfGeneralPDE("B")
780             C=self.getCoefficientOfGeneralPDE("C")
781             if B.isEmpty() and not C.isEmpty():
782                if verbose: print "non-symmetric PDE because B is not present but C is"
783                out=False
784             elif not B.isEmpty() and C.isEmpty():
785                if verbose: print "non-symmetric PDE because C is not present but B is"
786                out=False
787             elif not B.isEmpty() and not C.isEmpty():
788                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
789                if self.getNumSolutions()>1:
790                   for i in range(self.getNumEquations()):
791                       for j in range(self.getDim()):
792                          for k in range(self.getNumSolutions()):
793                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
794                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
795                                  out=False
796                else:
797                   for j in range(self.getDim()):
798                      if util.Lsup(B[j]-C[j])>tol:
799                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
800                         out=False
801             if self.getNumSolutions()>1:
802               D=self.getCoefficientOfGeneralPDE("D")
803               if not D.isEmpty():
804                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
805                 for i in range(self.getNumEquations()):
806                    for k in range(self.getNumSolutions()):
807                      if util.Lsup(D[i,k]-D[k,i])>tol:
808                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
809                          out=False
810               d=self.getCoefficientOfGeneralPDE("d")
811               if not d.isEmpty():
812                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
813                 for i in range(self.getNumEquations()):
814                    for k in range(self.getNumSolutions()):
815                      if util.Lsup(d[i,k]-d[k,i])>tol:
816                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
817                          out=False
818               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
819               if not d_contact.isEmpty():
820                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
821                 for i in range(self.getNumEquations()):
822                    for k in range(self.getNumSolutions()):
823                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
824                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
825                          out=False
826             # and now the reduced coefficients
827             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
828             if not A_reduced.isEmpty():
829                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
830                if self.getNumSolutions()>1:
831                   for i in range(self.getNumEquations()):
832                      for j in range(self.getDim()):
833                         for k in range(self.getNumSolutions()):
834                            for l in range(self.getDim()):
835                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
836                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
837                                   out=False
838                else:
839                   for j in range(self.getDim()):
840                      for l in range(self.getDim()):
841                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
842                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
843                            out=False
844             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
845             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
846             if B_reduced.isEmpty() and not C_reduced.isEmpty():
847                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
848                out=False
849             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
850                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
851                out=False
852             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
853                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
854                if self.getNumSolutions()>1:
855                   for i in range(self.getNumEquations()):
856                       for j in range(self.getDim()):
857                          for k in range(self.getNumSolutions()):
858                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
859                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
860                                  out=False
861                else:
862                   for j in range(self.getDim()):
863                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
864                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
865                         out=False
866             if self.getNumSolutions()>1:
867               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
868               if not D_reduced.isEmpty():
869                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
870                 for i in range(self.getNumEquations()):
871                    for k in range(self.getNumSolutions()):
872                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
873                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
874                          out=False
875               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
876               if not d_reduced.isEmpty():
877                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
878                 for i in range(self.getNumEquations()):
879                    for k in range(self.getNumSolutions()):
880                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
881                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
882                          out=False
883               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
884               if not d_contact_reduced.isEmpty():
885                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
886                 for i in range(self.getNumEquations()):
887                    for k in range(self.getNumSolutions()):
888                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
889                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
890                          out=False
891          return out
892    
893       def getSolution(self,**options):
894         """         """
895         self.__debug=not None         returns the solution of the PDE. If the solution is not valid the PDE is solved.
896    
897     def setDebugOff(self):         @return: the solution
898           @rtype: L{Data<escript.Data>}
899           @param options: solver options
900           @keyword verbose: True to get some information during PDE solution
901           @type verbose: C{bool}
902           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
903                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
904           @keyword iter_max: maximum number of iteration steps allowed.
905           @keyword drop_tolerance: threshold for drupping in L{ILUT}
906           @keyword drop_storage: maximum of allowed memory in L{ILUT}
907           @keyword truncation: maximum number of residuals in L{GMRES}
908           @keyword restart: restart cycle length in L{GMRES}
909         """         """
910           if not self.__solution_isValid:
911              mat,f=self.getSystem()
912              if self.isUsingLumping():
913                 self.__solution=self.copyConstraint(f*mat)
914              else:
915                 options[self.__TOLERANCE_KEY]=self.getTolerance()
916                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
917                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
918                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
919                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
920                 self.trace("PDE is resolved.")
921                 self.trace("solver options: %s"%str(options))
922                 self.__solution=mat.solve(f,options)
923              self.__solution_isValid=True
924           return self.__solution
925    
926       def getFlux(self,u=None):
927         """
928         returns the flux M{J} for a given M{u}
929    
930         M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
931    
932         or
933    
934         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
935    
936         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
937         @type u: L{Data<escript.Data>} or None
938         @return: flux
939         @rtype: L{Data<escript.Data>}
940         """
941         if u==None: u=self.getSolution()
942         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
943               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
944               -util.self.getCoefficientOfGeneralPDE("X") \
945               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
946               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
947               -util.self.getCoefficientOfGeneralPDE("X_reduced")
948       # =============================================================================
949       #   solver settings:
950       # =============================================================================
951       def setSolverMethod(self,solver=None,preconditioner=None):
952         """         """
953         self.__debug=None         sets a new solver
954    
955           @param solver: sets a new solver method.
956           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{TFQMR}, L{MINRES}, L{PRES20}, L{LUMPING}, L{AMG}
957           @param preconditioner: sets a new solver method.
958           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
959           """
960           if solver==None: solver=self.__solver_method
961           if preconditioner==None: preconditioner=self.__preconditioner
962           if solver==None: solver=self.DEFAULT
963           if preconditioner==None: preconditioner=self.DEFAULT
964           if not (solver,preconditioner)==self.getSolverMethod():
965               self.__solver_method=solver
966               self.__preconditioner=preconditioner
967               self.__checkMatrixType()
968               self.trace("New solver is %s"%self.getSolverMethodName())
969    
970     def debug(self):     def getSolverMethodName(self):
971         """         """
972         returns true if the PDE is in the debug mode         returns the name of the solver currently used
973    
974           @return: the name of the solver currently used.
975           @rtype: C{string}
976         """         """
        return self.__debug  
977    
978     #===== Lumping ===========================         m=self.getSolverMethod()
979     def setLumpingOn(self):         p=self.getSolverPackage()
980        """         method=""
981        indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
982        """         elif m[0]==self.DIRECT: method= "DIRECT"
983        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
984           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
985           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
986           self.__lumping=True         elif m[0]==self.TFQMR: method= "TFQMR"
987           elif m[0]==self.MINRES: method= "MINRES"
988           elif m[0]==self.CR: method= "CR"
989           elif m[0]==self.CGS: method= "CGS"
990           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
991           elif m[0]==self.SSOR: method= "SSOR"
992           elif m[0]==self.GMRES: method= "GMRES"
993           elif m[0]==self.PRES20: method= "PRES20"
994           elif m[0]==self.LUMPING: method= "LUMPING"
995           elif m[0]==self.AMG: method= "AMG"
996           if m[1]==self.DEFAULT: method+="+DEFAULT"
997           elif m[1]==self.JACOBI: method+= "+JACOBI"
998           elif m[1]==self.ILU0: method+= "+ILU0"
999           elif m[1]==self.ILUT: method+= "+ILUT"
1000           elif m[1]==self.SSOR: method+= "+SSOR"
1001           elif m[1]==self.AMG: method+= "+AMG"
1002           elif m[1]==self.RILU: method+= "+RILU"
1003           if p==self.DEFAULT: package="DEFAULT"
1004           elif p==self.PASO: package= "PASO"
1005           elif p==self.MKL: package= "MKL"
1006           elif p==self.SCSL: package= "SCSL"
1007           elif p==self.UMFPACK: package= "UMFPACK"
1008           elif p==self.TRILINOS: package= "TRILINOS"
1009           else : method="unknown"
1010           return "%s solver of %s package"%(method,package)
1011    
    def setLumpingOff(self):  
       """  
       switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
1012    
1013     def setLumping(self,flag=False):     def getSolverMethod(self):
1014        """         """
1015        set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
1016    
1017     def isUsingLumping(self):         @return: the solver method currently be used.
1018        """         @rtype: C{int}
1019                 """
1020        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
1021    
1022     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
1023         """         """
1024         sets a new solver         sets a new solver package
1025    
1026           @param package: sets a new solver method.
1027           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1028         """         """
1029         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
1030             self.__solver_method=solver         if not package==self.getSolverPackage():
1031             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__solver_package=package
1032             self.__checkMatrixType()             self.__checkMatrixType()
1033               self.trace("New solver is %s"%self.getSolverMethodName())
1034    
1035     def getSolverMethod(self):     def getSolverPackage(self):
1036         """         """
1037         returns the solver method         returns the package of the solver
1038    
1039           @return: the solver package currently being used.
1040           @rtype: C{int}
1041         """         """
1042         return self.__solver_method         return self.__solver_package
1043    
1044       def isUsingLumping(self):
1045          """
1046          checks if matrix lumping is used a solver method
1047    
1048          @return: True is lumping is currently used a solver method.
1049          @rtype: C{bool}
1050          """
1051          return self.getSolverMethod()[0]==self.LUMPING
1052    
    #============ tolerance business =========================================================  
1053     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1054         """         """
1055         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1056    
1057           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1058    
1059           defines the stopping criterion.
1060    
1061           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1062                       the system will be resolved.
1063           @type tol: positive C{float}
1064           @raise ValueError: if tolerance is not positive.
1065         """         """
1066         if not tol>0:         if not tol>0:
1067             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1068         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1069         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1070         self.__tolerance=tol         self.__tolerance=tol
1071         return         return
1072    
1073     def getTolerance(self):     def getTolerance(self):
1074         """         """
1075         returns the tolerance set for the solution         returns the tolerance set for the solution
1076    
1077           @return: tolerance currently used.
1078           @rtype: C{float}
1079         """         """
1080         return self.__tolerance         return self.__tolerance
1081    
1082     #===== symmetry  flag ==========================     # =============================================================================
1083       #    symmetry  flag:
1084       # =============================================================================
1085     def isSymmetric(self):     def isSymmetric(self):
1086        """        """
1087        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1088    
1089          @return: True is a symmetric PDE is indicated, otherwise False is returned
1090          @rtype: C{bool}
1091        """        """
1092        return self.__sym        return self.__sym
1093    
1094     def setSymmetryOn(self):     def setSymmetryOn(self):
1095        """        """
1096        sets the symmetry flag to true        sets the symmetry flag.
1097        """        """
1098        if not self.isSymmetric():        if not self.isSymmetric():
1099           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1100           self.__sym=True           self.__sym=True
1101           self.__checkMatrixType()           self.__checkMatrixType()
1102    
1103     def setSymmetryOff(self):     def setSymmetryOff(self):
1104        """        """
1105        sets the symmetry flag to false        removes the symmetry flag.
1106        """        """
1107        if self.isSymmetric():        if self.isSymmetric():
1108           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1109           self.__sym=False           self.__sym=False
1110           self.__checkMatrixType()           self.__checkMatrixType()
1111    
1112     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1113       """        """
1114       sets the symmetry flag to flag        sets the symmetry flag to flag
1115    
1116       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1117       """        @type flag: C{bool}
1118       if flag:        """
1119          self.setSymmetryOn()        if flag:
1120       else:           self.setSymmetryOn()
1121          self.setSymmetryOff()        else:
1122             self.setSymmetryOff()
1123    
1124     #===== order reduction ==========================     # =============================================================================
1125       # function space handling for the equation as well as the solution
1126       # =============================================================================
1127     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1128       """       """
1129       switches to on reduced order       switches on reduced order for solution and equation representation
1130    
1131         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1132       """       """
1133       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1134       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1135    
1136     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1137       """       """
1138       switches to full order       switches off reduced order for solution and equation representation
1139    
1140         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1141       """       """
1142       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1143       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1144    
1145     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1146       """       """
1147       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1148         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1149       @param flag:                    if flag is not present order reduction is switched off
1150         @type flag: C{bool}
1151         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1152       """       """
1153       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1154       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1155    
1156     #===== order reduction solution ==========================  
1157     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1158       """       """
1159       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1160    
1161         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1162       """       """
1163       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1164       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1165           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1166           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1167           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1168             self.__resetSystem()
1169    
1170     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1171       """       """
1172       switches to full order to interpolate solution       switches off reduced order for solution representation
1173    
1174         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1175       """       """
1176       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1177       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1178           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1179           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1180           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1181             self.__resetSystem()
1182    
1183     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1184       """       """
1185       sets order for test functions according to flag       sets order for test functions according to flag
1186    
1187       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1188                      if flag is not present order reduction is switched off
1189         @type flag: C{bool}
1190         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1191       """       """
1192       if flag:       if flag:
1193          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1194       else:       else:
1195          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1196                                                                                                                                                              
    #===== order reduction equation ==========================  
1197     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1198       """       """
1199       switches to reduced order for test functions       switches on reduced order for equation representation
1200    
1201         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1202       """       """
1203       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1204       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1205           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1206           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1207           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1208             self.__resetSystem()
1209    
1210     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1211       """       """
1212       switches to full order for test functions       switches off reduced order for equation representation
1213    
1214         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1215       """       """
1216       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1217       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1218           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1219           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1220           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1221             self.__resetSystem()
1222    
1223     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1224       """       """
1225       sets order for test functions according to flag       sets order for test functions according to flag
1226    
1227       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1228                      if flag is not present order reduction is switched off
1229         @type flag: C{bool}
1230         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1231       """       """
1232       if flag:       if flag:
1233          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1234       else:       else:
1235          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1236                                                                                                                                                              
1237     # ==== initialization =====================================================================     # =============================================================================
1238       # private method:
1239       # =============================================================================
1240       def __checkMatrixType(self):
1241         """
1242         reassess the matrix type and, if a new matrix is needed, resets the system.
1243         """
1244         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1245         if not new_matrix_type==self.__matrix_type:
1246             self.trace("Matrix type is now %d."%new_matrix_type)
1247             self.__matrix_type=new_matrix_type
1248             self.__resetSystem()
1249       #
1250       #   rebuild switches :
1251       #
1252       def __invalidateSolution(self):
1253           """
1254           indicates the PDE has to be resolved if the solution is requested
1255           """
1256           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1257           self.__solution_isValid=False
1258    
1259       def __invalidateOperator(self):
1260           """
1261           indicates the operator has to be rebuilt next time it is used
1262           """
1263           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1264           self.__invalidateSolution()
1265           self.__operator_is_Valid=False
1266    
1267       def __invalidateRightHandSide(self):
1268           """
1269           indicates the right hand side has to be rebuild next time it is used
1270           """
1271           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1272           self.__invalidateSolution()
1273           self.__righthandside_isValid=False
1274    
1275       def __invalidateSystem(self):
1276           """
1277           annonced that everthing has to be rebuild:
1278           """
1279           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1280           self.__invalidateSolution()
1281           self.__invalidateOperator()
1282           self.__invalidateRightHandSide()
1283    
1284       def __resetSystem(self):
1285           """
1286           annonced that everthing has to be rebuild:
1287           """
1288           self.trace("New System is built from scratch.")
1289           self.__operator=escript.Operator()
1290           self.__operator_is_Valid=False
1291           self.__righthandside=escript.Data()
1292           self.__righthandside_isValid=False
1293           self.__solution=escript.Data()
1294           self.__solution_isValid=False
1295       #
1296       #    system initialization:
1297       #
1298     def __getNewOperator(self):     def __getNewOperator(self):
1299         """         """
1300           returns an instance of a new operator
1301         """         """
1302           self.trace("New operator is allocated.")
1303         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1304                             self.getNumEquations(), \                             self.getNumEquations(), \
1305                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1307  class LinearPDE:
1307                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1308                             self.__matrix_type)                             self.__matrix_type)
1309    
1310     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1311         """         """
1312           returns an instance of a new right hand side
1313         """         """
1314         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1315         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1316             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1317         else:         else:
1318             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1319    
1320     def __getNewSolution(self):     def __getNewSolution(self):
1321         """         """
1322           returns an instance of a new solution
1323         """         """
1324         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1325         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1326             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1327         else:         else:
1328             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1329    
1330       def __makeFreshSolution(self):
1331           """
1332           makes sure that the solution is instantiated and returns it initialized by zeros
1333           """
1334           if self.__solution.isEmpty():
1335               self.__solution=self.__getNewSolution()
1336           else:
1337               self.__solution*=0
1338               self.trace("Solution is reset to zero.")
1339           return self.__solution
1340    
1341       def __makeFreshRightHandSide(self):
1342           """
1343           makes sure that the right hand side is instantiated and returns it initialized by zeros
1344           """
1345           if self.__righthandside.isEmpty():
1346               self.__righthandside=self.__getNewRightHandSide()
1347           else:
1348               self.__righthandside.setToZero()
1349               self.trace("Right hand side is reset to zero.")
1350           return self.__righthandside
1351    
1352     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1353         """         """
1354           makes sure that the operator is instantiated and returns it initialized by zeros
1355         """         """
1356         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1357             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1358         else:         else:
1359             self.__operator.setValue(0.)             self.__operator.resetValues()
1360             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1361         return self.__operator         return self.__operator
1362    
1363     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1364     def getDomain(self):         """
1365           applies the constraints defined by q and r to the system
1366           """
1367           if not self.isUsingLumping():
1368              q=self.getCoefficientOfGeneralPDE("q")
1369              r=self.getCoefficientOfGeneralPDE("r")
1370              if not q.isEmpty() and not self.__operator.isEmpty():
1371                 # q is the row and column mask to indicate where constraints are set:
1372                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1373                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1374                 u=self.__getNewSolution()
1375                 if r.isEmpty():
1376                    r_s=self.__getNewSolution()
1377                 else:
1378                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1379                 u.copyWithMask(r_s,col_q)
1380                 if not self.__righthandside.isEmpty():
1381                    self.__righthandside-=self.__operator*u
1382                    self.__righthandside=self.copyConstraint(self.__righthandside)
1383                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1384       # =============================================================================
1385       # function giving access to coefficients of the general PDE:
1386       # =============================================================================
1387       def getCoefficientOfGeneralPDE(self,name):
1388         """
1389         return the value of the coefficient name of the general PDE.
1390    
1391         @note: This method is called by the assembling routine it can be overwritten
1392               to map coefficients of a particular PDE to the general PDE.
1393         @param name: name of the coefficient requested.
1394         @type name: C{string}
1395         @return: the value of the coefficient  name
1396         @rtype: L{Data<escript.Data>}
1397         @raise IllegalCoefficient: if name is not one of coefficients
1398                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1399                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1400       """       """
1401       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1402            return self.getCoefficient(name)
1403         else:
1404            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1405    
1406       def hasCoefficientOfGeneralPDE(self,name):
1407       """       """
1408       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1409    
1410         @param name: name of the coefficient enquired.
1411         @type name: C{string}
1412         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1413         @rtype: C{bool}
1414    
    def getDim(self):  
1415       """       """
1416       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1417    
1418       def createCoefficientOfGeneralPDE(self,name):
1419       """       """
1420       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1421    
1422     def getNumEquations(self):       @param name: name of the coefficient requested.
1423         @type name: C{string}
1424         @return: a coefficient name initialized to 0.
1425         @rtype: L{Data<escript.Data>}
1426         @raise IllegalCoefficient: if name is not one of coefficients
1427                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1428                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1429       """       """
1430       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1431            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1432         else:
1433            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1434    
1435       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1436       """       """
1437       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1438           return self.__numEquations  
1439         @param name: name of the coefficient enquired.
1440         @type name: C{string}
1441         @return: the function space to be used for coefficient name
1442         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1443         @raise IllegalCoefficient: if name is not one of coefficients
1444                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1445                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1446         """
1447         if self.hasCoefficientOfGeneralPDE(name):
1448            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1449       else:       else:
1450           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1451    
1452     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1453       """       """
1454       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1455    
1456         @param name: name of the coefficient enquired.
1457         @type name: C{string}
1458         @return: the shape of the coefficient name
1459         @rtype: C{tuple} of C{int}
1460         @raise IllegalCoefficient: if name is not one of coefficients
1461                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1462                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1463       """       """
1464       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1465          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1466       else:       else:
1467          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1468    
1469       # =============================================================================
1470       # functions giving access to coefficients of a particular PDE implementation:
1471       # =============================================================================
1472       def getCoefficient(self,name):
1473         """
1474         returns the value of the coefficient name
1475    
1476     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1477        """       @type name: C{string}
1478        returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.       @return: the value of the coefficient name
1479        """       @rtype: L{Data<escript.Data>}
1480        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1481        out=True       """
1482        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1483           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1484           out=False       else:
1485        else:          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
          A=self.getCoefficientOfPDE("A")  
          if not A.isEmpty():  
             tol=util.Lsup(A)*self.TOL  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                   for j in range(self.getDim()):  
                      for k in range(self.getNumSolutions()):  
                         for l in range(self.getDim()):  
                             if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:  
                                if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)  
                                out=False  
             else:  
                for j in range(self.getDim()):  
                   for l in range(self.getDim()):  
                      if util.Lsup(A[j,l]-A[l,j])>tol:  
                         if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)  
                         out=False  
          B=self.getCoefficientOfPDE("B")  
          C=self.getCoefficientOfPDE("C")  
          if B.isEmpty() and not C.isEmpty():  
             if verbose: print "non-symmetric PDE because B is not present but C is"  
             out=False  
          elif not B.isEmpty() and C.isEmpty():  
             if verbose: print "non-symmetric PDE because C is not present but B is"  
             out=False  
          elif not B.isEmpty() and not C.isEmpty():  
             tol=(util.Lsup(B)+util.Lsup(C))*self.TOL/2.  
             if self.getNumSolutions()>1:  
                for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          if util.Lsup(B[i,j,k]-C[k,i,j])>tol:  
                               if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)  
                               out=False  
             else:  
                for j in range(self.getDim()):  
                   if util.Lsup(B[j]-C[j])>tol:  
                      if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)  
                      out=False  
          if self.getNumSolutions()>1:  
            D=self.getCoefficientOfPDE("D")  
            if not D.isEmpty():  
              tol=util.Lsup(D)*self.TOL  
              for i in range(self.getNumEquations()):  
                 for k in range(self.getNumSolutions()):  
                   if util.Lsup(D[i,k]-D[k,i])>tol:  
                       if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)  
                       out=False  
               
       return out  
1486    
1487     def getFlux(self,u):     def hasCoefficient(self,name):
1488         """       """
1489         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1490    
1491         \f[       @param name: name of the coefficient enquired.
1492         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1493         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1494         @rtype: C{bool}
1495         """
1496         return self.COEFFICIENTS.has_key(name)
1497    
1498         @param u: argument of the operator     def createCoefficient(self, name):
1499         """       """
1500         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1501    
1502     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1503         """       @rtype: L{Data<escript.Data>}
1504         applies the operator of the PDE to a given solution u in weak from       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1505         """
1506         if self.hasCoefficient(name):
1507            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1508         else:
1509            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1510    
1511         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1512         """       """
1513         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        return the residual of u in the weak from  
1514    
1515         @param u:       @param name: name of the coefficient enquired.
1516         """       @type name: C{string}
1517         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1518         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1519         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1520         """
1521         if self.hasCoefficient(name):
1522            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1523         else:
1524            raise ValueError,"unknown coefficient %s requested"%name
1525       def getShapeOfCoefficient(self,name):
1526         """
1527         return the shape of the coefficient name
1528    
1529         @param name: name of the coefficient enquired.
1530         @type name: C{string}
1531         @return: the shape of the coefficient name
1532         @rtype: C{tuple} of C{int}
1533         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1534         """
1535         if self.hasCoefficient(name):
1536            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1537         else:
1538            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1539    
1540       def resetCoefficients(self):
1541         """
1542         resets all coefficients to there default values.
1543         """
1544         for i in self.COEFFICIENTS.iterkeys():
1545             self.COEFFICIENTS[i].resetValue()
1546    
1547       def alteredCoefficient(self,name):
1548         """
1549         announce that coefficient name has been changed
1550    
1551         @param name: name of the coefficient enquired.
1552         @type name: C{string}
1553         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1554         @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1555         """
1556         if self.hasCoefficient(name):
1557            self.trace("Coefficient %s has been altered."%name)
1558            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1559               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1560               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1561         else:
1562            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1563    
1564       def copyConstraint(self,u):
1565          """
1566          copies the constraint into u and returns u.
1567    
1568          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1569          @type u: L{Data<escript.Data>}
1570          @return: the input u modified by the constraints.
1571          @rtype: L{Data<escript.Data>}
1572          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1573          """
1574          q=self.getCoefficientOfGeneralPDE("q")
1575          r=self.getCoefficientOfGeneralPDE("r")
1576          if not q.isEmpty():
1577             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1578             if r.isEmpty():
1579                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1580             else:
1581                 r=escript.Data(r,u.getFunctionSpace())
1582             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1583          return u
1584    
1585     def __setValue(self,**coefficients):     def setValue(self,**coefficients):
1586        """        """
1587        sets new values to coefficient        sets new values to coefficients
1588    
1589        @param coefficients:        @param coefficients: new values assigned to coefficients
1590          @keyword A: value for coefficient A.
1591          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1592          @keyword A_reduced: value for coefficient A_reduced.
1593          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1594          @keyword B: value for coefficient B
1595          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1596          @keyword B_reduced: value for coefficient B_reduced
1597          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1598          @keyword C: value for coefficient C
1599          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1600          @keyword C_reduced: value for coefficient C_reduced
1601          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1602          @keyword D: value for coefficient D
1603          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1604          @keyword D_reduced: value for coefficient D_reduced
1605          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1606          @keyword X: value for coefficient X
1607          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1608          @keyword X_reduced: value for coefficient X_reduced
1609          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1610          @keyword Y: value for coefficient Y
1611          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1612          @keyword Y_reduced: value for coefficient Y_reduced
1613          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1614          @keyword d: value for coefficient d
1615          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1616          @keyword d_reduced: value for coefficient d_reduced
1617          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1618          @keyword y: value for coefficient y
1619          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1620          @keyword d_contact: value for coefficient d_contact
1621          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1622          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1623          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1624          @keyword y_contact: value for coefficient y_contact
1625          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1626          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1627          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1628          @keyword r: values prescribed to the solution at the locations of constraints
1629          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1630                   depending of reduced order is used for the solution.
1631          @keyword q: mask for location of constraints
1632          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1633                   depending of reduced order is used for the representation of the equation.
1634          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1635        """        """
1636        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1637        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1638           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1639              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1640        # if the number of unknowns or equations is still unknown we try to estimate them:        # if the number of unknowns or equations is still unknown we try to estimate them:
1641        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1642           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1643              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1644                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1648  class LinearPDE:
1648                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1649              if s!=None:              if s!=None:
1650                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1651                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1652                  if res==None:                  if res==None:
1653                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1654                  else:                  else:
1655                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1656                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1657        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1658        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1659        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1660        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1661          if d==None:          try:
1662               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),
1663          elif isinstance(d,escript.Data):                                           self.getNumEquations(),self.getNumSolutions(),
1664               if d.isEmpty():                                           self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1665                  d2=d             self.alteredCoefficient(i)
1666               else:          except IllegalCoefficientFunctionSpace,m:
1667                  d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              # if the function space is wrong then we try the reduced version:
1668          else:              i_red=i+"_reduced"
1669                d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1670          if not d2.isEmpty():                  try:
1671             if not self.getShapeOfCoefficient(i)==d2.getShape():                      self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1672                 raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())                                                        self.getNumEquations(),self.getNumSolutions(),
1673          # overwrite new values:                                                        self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1674          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i                      self.alteredCoefficient(i_red)
1675          self.COEFFICIENTS[i].setValue(d2)                  except IllegalCoefficientValue,m:
1676          self.alteredCoefficient(i)                      raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1677                          except IllegalCoefficientFunctionSpace,m:
1678        # reset the HomogeneousConstraintFlag:                      raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1679        self.__setHomogeneousConstraintFlag()              else:
1680        if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()                  raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1681            except IllegalCoefficientValue,m:
1682     def __setHomogeneousConstraintFlag(self):             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1683        """        self.__altered_coefficients=True
1684        checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.        # check if the systrem is inhomogeneous:
1685        """        if len(coefficients)>0 and not self.isUsingLumping():
1686        self.__homogeneous_constraint=True           q=self.getCoefficientOfGeneralPDE("q")
1687        q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1688        r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1689        if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1690           if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False               if util.Lsup(q*r)>0.:
1691        if self.debug():                 self.trace("Inhomogeneous constraint detected.")
1692             if self.__homogeneous_constraint:                 self.__invalidateSystem()
                print "PDE Debug: Constraints are homogeneous."  
            else:  
                print "PDE Debug: Constraints are inhomogeneous."  
   
   
    # ==== rebuild switches =====================================================================  
    def __rebuildSolution(self,deep=False):  
        """  
        indicates the PDE has to be reolved if the solution is requested  
        """  
        if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."  
        self.__solution_isValid=False  
        if deep: self.__solution=escript.Data()  
   
   
    def __rebuildOperator(self,deep=False):  
        """  
        indicates the operator has to be rebuilt next time it is used  
        """  
        if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__operator_isValid=False  
        if deep: self.__operator=escript.Operator()  
   
    def __rebuildRightHandSide(self,deep=False):  
        """  
        indicates the right hand side has to be rebuild next time it is used  
        """  
        if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__righthandside_isValid=False  
        if deep: self.__righthandside=escript.Data()  
   
    def __rebuildSystem(self,deep=False):  
        """  
        annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
      """  
      reassess the matrix type and, if needed, initiates an operator rebuild  
      """  
      new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())  
      if not new_matrix_type==self.__matrix_type:  
          if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type  
          self.__matrix_type=new_matrix_type  
          self.__rebuildOperator(deep=True)  
   
    #============ assembling =======================================================  
    def __copyConstraint(self):  
       """  
       copies the constrint condition into u  
       """  
       if not self.__righthandside.isEmpty():  
          q=self.getCoefficientOfPDE("q")  
          r=self.getCoefficientOfPDE("r")  
          if not q.isEmpty():  
              if r.isEmpty():  
                 r2=escript.Data(0,self.__righthandside.getShape(),self.__righthandside.getFunctionSpace())  
              else:  
                 r2=escript.Data(r,self.__righthandside.getFunctionSpace())  
              self.__righthandside.copyWithMask(r2,escript.Data(q,self.__righthandside.getFunctionSpace()))  
   
    def __applyConstraint(self):  
        """  
        applies the constraints defined by q and r to the system  
        """  
        q=self.getCoefficientOfPDE("q")  
        r=self.getCoefficientOfPDE("r")  
        if not q.isEmpty() and not self.__operator.isEmpty():  
           # q is the row and column mask to indicate where constraints are set:  
           row_q=escript.Data(q,self.getFunctionSpaceForEquation())  
           col_q=escript.Data(q,self.getFunctionSpaceForSolution())  
           u=self.__getNewSolution()  
           if r.isEmpty():  
              r_s=self.__getNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if self.isUsingLumping():  
              self.__operator.copyWithMask(escript.Data(1,q.getShape(),self.getFunctionSpaceForEquation()),row_q)  
           else:  
              if not self.__righthandside.isEmpty(): self.__righthandside-=self.__operator*u  
              self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
1693    
1694     def getSystem(self):     def getSystem(self):
1695         """         """
1696         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1697    
1698           @return: the discrete version of the PDE
1699           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1700         """         """
1701         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1702            if self.isUsingLumping():            if self.isUsingLumping():
1703                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1704                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1705                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1706                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1707                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1708                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1709                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient B in lumped matrix may not be present."
1710                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1711                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient C in lumped matrix may not be present."
1712                   if self.debug() : print "PDE Debug: New lumped operator is built."                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1713                   mat=self.__getNewOperator()                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1714                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1715                             self.getCoefficientOfPDE("A"), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1716                             self.getCoefficientOfPDE("B"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1717                             self.getCoefficientOfPDE("C"), \                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1718                             self.getCoefficientOfPDE("D"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1719                             escript.Data(), \                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1720                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1721                             self.getCoefficientOfPDE("d"), \                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1722                             escript.Data(),\                   D=self.getCoefficientOfGeneralPDE("D")
1723                             self.getCoefficientOfPDE("d_contact"), \                   d=self.getCoefficientOfGeneralPDE("d")
1724                             escript.Data())                   D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1725                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1726                   self.__applyConstraint()                   if not D.isEmpty():
1727                   self.__operator_isValid=True                       if self.getNumSolutions()>1:
1728                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1729                         else:
1730                            D_times_e=D
1731                     else:
1732                        D_times_e=escript.Data()
1733                     if not d.isEmpty():
1734                         if self.getNumSolutions()>1:
1735                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1736                         else:
1737                            d_times_e=d
1738                     else:
1739                        d_times_e=escript.Data()
1740          
1741                     if not D_reduced.isEmpty():
1742                         if self.getNumSolutions()>1:
1743                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1744                         else:
1745                            D_reduced_times_e=D_reduced
1746                     else:
1747                        D_reduced_times_e=escript.Data()
1748                     if not d_reduced.isEmpty():
1749                         if self.getNumSolutions()>1:
1750                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1751                         else:
1752                            d_reduced_times_e=d_reduced
1753                     else:
1754                        d_reduced_times_e=escript.Data()
1755    
1756                     self.__operator=self.__getNewRightHandSide()
1757                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1758                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1759                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1760                     else:
1761                        self.getDomain().addPDEToRHS(self.__operator, \
1762                                                     escript.Data(), \
1763                                                     D_times_e, \
1764                                                     d_times_e,\
1765                                                     escript.Data())
1766                        self.getDomain().addPDEToRHS(self.__operator, \
1767                                                     escript.Data(), \
1768                                                     D_reduced_times_e, \
1769                                                     d_reduced_times_e,\
1770                                                     escript.Data())
1771                     self.__operator=1./self.__operator
1772                     self.trace("New lumped operator has been built.")
1773                     self.__operator_is_Valid=True
1774                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1775                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1776                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1777                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1778                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1779                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1780                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1781                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1782                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1783                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1784                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1785                     self.trace("New right hand side as been built.")
1786                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1787            else:            else:
1788               if not self.__operator_isValid and not self.__righthandside_isValid:               if not self.__operator_is_Valid and not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New system is built."  
1789                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1790                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1791                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1792                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1793                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1794                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1795                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1796                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1797                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1798                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1799                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1800                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1801                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1806                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1808                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1809                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1810                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1811                   self.__applyConstraint()                   self.__applyConstraint()
1812                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1813                   self.__operator_isValid=True                   self.trace("New system has been built.")
1814                     self.__operator_is_Valid=True
1815                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1816               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1817                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1818                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1819                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1820                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1821                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1822                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1823                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1824                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1825                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1826                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1827                     self.__righthandside=self.copyConstraint(self.__righthandside)
1828                     self.trace("New right hand side has been built.")
1829                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1830               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1831                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1832                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1833                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1834                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1835                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1836                                escript.Data(), \
1837                                escript.Data(), \
1838                                self.getCoefficientOfGeneralPDE("d"), \
1839                                escript.Data(),\
1840                                self.getCoefficientOfGeneralPDE("d_contact"), \
1841                                escript.Data())
1842                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1843                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1844                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1845                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1846                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1847                              escript.Data(), \                              escript.Data(), \
1848                              escript.Data(), \                              escript.Data(), \
1849                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d_reduced"), \
1850                              escript.Data(),\                              escript.Data(),\
1851                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1852                              escript.Data())                              escript.Data())
1853                   self.__applyConstraint()                   self.__applyConstraint()
1854                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1855                     self.__operator_is_Valid=True
1856         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
   
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
   
    def solve(self,**options):  
       """  
       solve the PDE  
   
       @param options:  
       """  
       mat,f=self.getSystem()  
       if self.isUsingLumping():  
          out=f/mat  
       else:  
          options[util.TOLERANCE_KEY]=self.getTolerance()  
          options[util.METHOD_KEY]=self.getSolverMethod()  
          options[util.SYMMETRY_KEY]=self.isSymmetric()  
          if self.debug() : print "PDE Debug: solver options: ",options  
          out=mat.solve(f,options)  
       return out  
   
    def getSolution(self,**options):  
        """  
        returns the solution of the PDE  
   
        @param options:  
        """  
        if not self.__solution_isValid:  
            if self.debug() : print "PDE Debug: PDE is resolved."  
            self.__solution=self.solve(**options)  
            self.__solution_isValid=True  
        return self.__solution  
   
1857    
1858    
1859  def ELMAN_RAMAGE(P):  class Poisson(LinearPDE):
      """   """  
      return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))  
 def SIMPLIFIED_BROOK_HUGHES(P):  
      """   """  
      c=(P-3.).whereNegative()  
      return P/6.*c+1./2.*(1.-c)  
   
 def HALF(P):  
     """ """  
     return escript.Scalar(0.5,P.getFunctionSpace())  
   
 class AdvectivePDE(LinearPDE):  
1860     """     """
1861     Class to handle a linear PDE dominated by advective terms:     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
     
    class to define a linear PDE of the form  
   
    \f[  
    -(A_{ijkl}u_{k,l})_{,j} -(B_{ijk}u_k)_{,j} + C_{ikl}u_{k,l} +D_{ik}u_k = - (X_{ij})_{,j} + Y_i  
    \f]  
1862    
1863     with boundary conditons:     M{-grad(grad(u)[j])[j] = f}
1864    
1865     \f[     with natural boundary conditons
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
1866    
1867     and contact conditions     M{n[j]*grad(u)[j] = 0 }
   
    \f[  
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d^{contact}_{ik}[u_k] = - n_j*X_{ij} + y^{contact}_{i}  
    \f]  
1868    
1869     and constraints:     and constraints:
1870    
1871     \f[     M{u=0} where M{q>0}
1872     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1873     """     """
    def __init__(self,domain,numEquations=0,numSolutions=0,xi=ELMAN_RAMAGE):  
       LinearPDE.__init__(self,domain,numEquations,numSolutions)  
       self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def __calculateXi(self,peclet_factor,Z,h):  
        Z_max=util.Lsup(Z)  
        if Z_max>0.:  
           return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.TOL)  
        else:  
           return 0.  
1874    
1875     def setValue(self,**args):     def __init__(self,domain,debug=False):
1876         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       """
1877         self._LinearPDE__setValue(**args)       initializes a new Poisson equation
             
    def getXi(self):  
       if self.__Xi.isEmpty():  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          A=self.getCoefficient("A")  
          h=self.getDomain().getSize()  
          self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))  
          if not C.isEmpty() or not B.isEmpty():  
             if not C.isEmpty() and not B.isEmpty():  
                 Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       for i in range(self.getNumEquations()):  
                          for k in range(self.getNumSolutions()):  
                             for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2  
                    else:  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2  
                 else:  
                    if self.getNumSolutions()>1:  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2  
                    else:  
                       for l in range(self.getDim()): Z2+=(C[l]-B[l])**2  
                 length_of_Z=util.sqrt(Z2)  
             elif C.isEmpty():  
               length_of_Z=util.length(B)  
             else:  
               length_of_Z=util.length(C)  
1878    
1879              Z_max=util.Lsup(length_of_Z)       @param domain: domain of the PDE
1880              if Z_max>0.:       @type domain: L{Domain<escript.Domain>}
1881                 length_of_A=util.length(A)       @param debug: if True debug informations are printed.
                A_max=util.Lsup(length_of_A)  
                if A_max>0:  
                     inv_A=1./(length_of_A+A_max*self.TOL)  
                else:  
                     inv_A=1./self.TOL  
                peclet_number=length_of_Z*h/2*inv_A  
                xi=self.__xi(peclet_number)  
                self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)  
                print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)  
       return self.__Xi  
         
1882    
    def getCoefficientOfPDE(self,name):  
1883       """       """
1884       return the value of the coefficient name of the general PDE       super(Poisson, self).__init__(domain,1,1,debug)
1885         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1886                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1887                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1888         self.setSymmetryOn()
1889    
1890       @param name:     def setValue(self,**coefficients):
1891       """       """
1892       if not self.getNumEquations() == self.getNumSolutions():       sets new values to coefficients
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
1893    
1894       if name == "A" :       @param coefficients: new values assigned to coefficients
1895           A=self.getCoefficient("A")       @keyword f: value for right hand side M{f}
1896           B=self.getCoefficient("B")       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1897           C=self.getCoefficient("C")       @keyword q: mask for location of constraints
1898           if B.isEmpty() and C.isEmpty():       @type q: any type that can be casted to rank zeo L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1899              Aout=A                 depending of reduced order is used for the representation of the equation.
1900           else:       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1901              if A.isEmpty():       """
1902                 Aout=self.createNewCoefficient("A")       super(Poisson, self).setValue(**coefficients)
1903              else:  
1904                 Aout=A[:]     def getCoefficientOfGeneralPDE(self,name):
1905              Xi=self.getXi()       """
1906              if self.getNumEquations()>1:       return the value of the coefficient name of the general PDE
1907                  for i in range(self.getNumEquations()):       @param name: name of the coefficient requested.
1908                     for j in range(self.getDim()):       @type name: C{string}
1909                        for k in range(self.getNumSolutions()):       @return: the value of the coefficient  name
1910                           for l in range(self.getDim()):       @rtype: L{Data<escript.Data>}
1911                              if not C.isEmpty() and not B.isEmpty():       @raise IllegalCoefficient: if name is not one of coefficients
1912                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k])                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1913                              elif C.isEmpty():       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1914                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]       """
1915                              else:       if name == "A" :
1916                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]           return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1917              else:       elif name == "B" :
1918                  for j in range(self.getDim()):           return escript.Data()
1919                     for l in range(self.getDim()):       elif name == "C" :
1920                        if not C.isEmpty() and not B.isEmpty():           return escript.Data()
1921                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])       elif name == "D" :
1922                        elif C.isEmpty():           return escript.Data()
1923                            Aout[j,l]+=Xi*B[j]*B[l]       elif name == "X" :
1924                        else:           return escript.Data()
1925                            Aout[j,l]+=Xi*C[j]*C[l]       elif name == "Y" :
1926           return Aout           return self.getCoefficient("f")
1927       elif name == "B" :       elif name == "d" :
1928           B=self.getCoefficient("B")           return escript.Data()
1929           C=self.getCoefficient("C")       elif name == "y" :
1930           D=self.getCoefficient("D")           return escript.Data()
1931           if C.isEmpty() or D.isEmpty():       elif name == "d_contact" :
1932              Bout=B           return escript.Data()
          else:  
             Xi=self.getXi()  
             if B.isEmpty():  
                 Bout=self.createNewCoefficient("B")  
             else:  
                 Bout=B[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                   for p in range(self.getNumEquations()):  
                      tmp=Xi*D[p,k]  
                      for i in range(self.getNumEquations()):  
                         for j in range(self.getDim()):  
                            Bout[i,j,k]+=tmp*C[p,i,j]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
          return Bout  
      elif name == "C" :  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if B.isEmpty() or D.isEmpty():  
             Cout=C  
          else:  
             Xi=self.getXi()  
             if C.isEmpty():  
                 Cout=self.createNewCoefficient("C")  
             else:  
                 Cout=C[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                    for p in range(self.getNumEquations()):  
                       tmp=Xi*D[p,k]  
                       for i in range(self.getNumEquations()):  
                         for l in range(self.getDim()):  
                                  Cout[i,k,l]+=tmp*B[p,l,i]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
          return Cout  
      elif name == "D" :  
          return self.getCoefficient("D")  
      elif name == "X" :  
          X=self.getCoefficient("X")  
          Y=self.getCoefficient("Y")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):  
             Xout=X  
          else:  
             if X.isEmpty():  
                 Xout=self.createNewCoefficient("X")  
             else:  
                 Xout=X[:]  
             Xi=self.getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
             else:  
                  tmp=Xi*Y  
                  for j in range(self.getDim()):  
                     if not C.isEmpty() and not B.isEmpty():  
                        Xout[j]+=tmp*(C[j]-B[j])  
                     elif C.isEmpty():  
                        Xout[j]-=tmp*B[j]  
                     else:  
                        Xout[j]+=tmp*C[j]  
          return Xout  
      elif name == "Y" :  
          return self.getCoefficient("Y")  
      elif name == "d" :  
          return self.getCoefficient("d")  
      elif name == "y" :  
          return self.getCoefficient("y")  
      elif name == "d_contact" :  
          return self.getCoefficient("d_contact")  
1933       elif name == "y_contact" :       elif name == "y_contact" :
1934           return self.getCoefficient("y_contact")           return escript.Data()
1935       elif name == "r" :       elif name == "A_reduced" :
1936           return self.getCoefficient("r")           return escript.Data()
1937       elif name == "q" :       elif name == "B_reduced" :
1938             return escript.Data()
1939         elif name == "C_reduced" :
1940             return escript.Data()
1941         elif name == "D_reduced" :
1942             return escript.Data()
1943         elif name == "X_reduced" :
1944             return escript.Data()
1945         elif name == "Y_reduced" :
1946             return self.getCoefficient("f_reduced")
1947         elif name == "d_reduced" :
1948             return escript.Data()
1949         elif name == "y_reduced" :
1950             return escript.Data()
1951         elif name == "d_contact_reduced" :
1952             return escript.Data()
1953         elif name == "y_contact_reduced" :
1954             return escript.Data()
1955         elif name == "r" :
1956             return escript.Data()
1957         elif name == "q" :
1958           return self.getCoefficient("q")           return self.getCoefficient("q")
1959       else:       else:
1960           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1961    
1962    class Helmholtz(LinearPDE):
 class Poisson(LinearPDE):  
1963     """     """
1964     Class to define a Poisson equation problem:     Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1965    
1966     class to define a linear PDE of the form     M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1967     \f[  
1968     -u_{,jj} = f     with natural boundary conditons
1969     \f]  
1970       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
    with boundary conditons:  
   
    \f[  
    n_j*u_{,j} = 0  
    \f]  
1971    
1972     and constraints:     and constraints:
1973    
1974     \f[     M{u=r} where M{q>0}
1975     u=0 \quad \mathrm{where} \quad q>0  
    \f]  
1976     """     """
1977    
1978     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
1979         LinearPDE.__init__(self,domain,1,1)       """
1980         self.COEFFICIENTS={       initializes a new Poisson equation
1981         "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
1982         "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}       @param domain: domain of the PDE
1983         self.setSymmetryOn()       @type domain: L{Domain<escript.Domain>}
1984         self.setValue(f,q)       @param debug: if True debug informations are printed.
1985    
1986     def setValue(self,f=escript.Data(),q=escript.Data()):       """
1987         """set value of PDE parameters f and q"""       super(Helmholtz, self).__init__(domain,1,1,debug)
1988         self._LinearPDE__setValue(f=f,q=q)       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1989                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1993                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1994                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1995                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1996                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1997         self.setSymmetryOn()
1998    
1999     def getCoefficientOfPDE(self,name):     def setValue(self,**coefficients):
2000       """       """
2001       return the value of the coefficient name of the general PDE       sets new values to coefficients
2002    
2003       @param name:       @param coefficients: new values assigned to coefficients
2004         @keyword omega: value for coefficient M{S{omega}}
2005         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2006         @keyword k: value for coefficeint M{k}
2007         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2008         @keyword f: value for right hand side M{f}
2009         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2010         @keyword alpha: value for right hand side M{S{alpha}}
2011         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2012         @keyword g: value for right hand side M{g}
2013         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2014         @keyword r: prescribed values M{r} for the solution in constraints.
2015         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2016                   depending of reduced order is used for the representation of the equation.
2017         @keyword q: mask for location of constraints
2018         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2019                   depending of reduced order is used for the representation of the equation.
2020         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2021       """       """
2022       if name == "A" :       super(Helmholtz, self).setValue(**coefficients)
2023           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))  
2024       elif name == "B" :     def getCoefficientOfGeneralPDE(self,name):
2025           return escript.Data()       """
2026       elif name == "C" :       return the value of the coefficient name of the general PDE
2027    
2028         @param name: name of the coefficient requested.
2029         @type name: C{string}
2030         @return: the value of the coefficient  name
2031         @rtype: L{Data<escript.Data>}
2032         @raise IllegalCoefficient: if name is not one of coefficients
2033                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2034         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2035         """
2036         if name == "A" :
2037             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2038         elif name == "B" :
2039           return escript.Data()           return escript.Data()
2040       elif name == "D" :       elif name == "C" :
2041           return escript.Data()           return escript.Data()
2042       elif name == "X" :       elif name == "D" :
2043             return self.getCoefficient("omega")
2044         elif name == "X" :
2045           return escript.Data()           return escript.Data()
2046       elif name == "Y" :       elif name == "Y" :
2047           return self.getCoefficient("f")           return self.getCoefficient("f")
2048       elif name == "d" :       elif name == "d" :
2049             return self.getCoefficient("alpha")
2050         elif name == "y" :
2051             return self.getCoefficient("g")
2052         elif name == "d_contact" :
2053           return escript.Data()           return escript.Data()
2054       elif name == "y" :       elif name == "y_contact" :
2055           return escript.Data()           return escript.Data()
2056       elif name == "d_contact" :       elif name == "A_reduced" :
2057           return escript.Data()           return escript.Data()
2058       elif name == "y_contact" :       elif name == "B_reduced" :
2059             return escript.Data()
2060         elif name == "C_reduced" :
2061             return escript.Data()
2062         elif name == "D_reduced" :
2063             return escript.Data()
2064         elif name == "X_reduced" :
2065           return escript.Data()           return escript.Data()
2066       elif name == "r" :       elif name == "Y_reduced" :
2067             return self.getCoefficient("f_reduced")
2068         elif name == "d_reduced" :
2069           return escript.Data()           return escript.Data()
2070       elif name == "q" :       elif name == "y_reduced" :
2071            return self.getCoefficient("g_reduced")
2072         elif name == "d_contact_reduced" :
2073             return escript.Data()
2074         elif name == "y_contact_reduced" :
2075             return escript.Data()
2076         elif name == "r" :
2077             return self.getCoefficient("r")
2078         elif name == "q" :
2079           return self.getCoefficient("q")           return self.getCoefficient("q")
2080       else:       else:
2081           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2082    
2083  class LameEquation(LinearPDE):  class LameEquation(LinearPDE):
2084     """     """
2085     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2086    
2087     class to define a linear PDE of the form     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[k])[k])[j] = F_i -grad(S{sigma}[ij])[j] }
2088     \f[  
2089     -(\lambda (u_{i,j}+u_{j,i}))_{,j} - \mu u_{j,ji}} = F_i -\sigma_{ij,j}     with natural boundary conditons:
2090     \f]  
2091       M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
    with boundary conditons:  
   
    \f[  
    n_j(\lambda(u_{i,j}+u_{j,i})-sigma_{ij}) + n_i\mu u_{j,j} = f_i  
    \f]  
2092    
2093     and constraints:     and constraints:
2094    
2095     \f[     M{u[i]=r[i]} where M{q[i]>0}
2096     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
2097     """     """
2098    
2099     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2100         LinearPDE.__init__(self,domain,domain.getDim(),domain.getDim())        super(LameEquation, self).__init__(domain,\
2101         self.COEFFICIENTS={                                           domain.getDim(),domain.getDim(),debug)
2102         "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),        self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2103         "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2104         "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.DIM),PDECoefficient.RIGHTHANDSIDE),                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2105         "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,PDECoefficient.EQUATION),PDECoefficient.RIGHTHANDSIDE),                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2106         "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2107         "r"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH),                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2108         "q"            : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2109         self.setSymmetryOn()        self.setSymmetryOn()
2110    
2111     def setValue(self,lame_lambda=escript.Data(),lame_mu=escript.Data(),F=escript.Data(),sigma=escript.Data(),f=escript.Data(),r=escript.Data(),q=escript.Data()):     def setValues(self,**coefficients):
2112         """set value of PDE parameters"""       """
2113         self._LinearPDE__setValue(lame_lambda=lame_lambda, \       sets new values to coefficients
2114                                   lame_mu=lame_mu, \  
2115                                   F=F, \       @param coefficients: new values assigned to coefficients
2116                                   sigma=sigma, \       @keyword lame_mu: value for coefficient M{S{mu}}
2117                                   f=f, \       @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2118                                   r=r, \       @keyword lame_lambda: value for coefficient M{S{lambda}}
2119                                   q=q)       @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2120     def getCoefficientOfPDE(self,name):       @keyword F: value for internal force M{F}
2121         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2122         @keyword sigma: value for initial stress M{S{sigma}}
2123         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2124         @keyword f: value for extrenal force M{f}
2125         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2126         @keyword r: prescribed values M{r} for the solution in constraints.
2127         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2128                   depending of reduced order is used for the representation of the equation.
2129         @keyword q: mask for location of constraints
2130         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2131                   depending of reduced order is used for the representation of the equation.
2132         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2133         """
2134         super(LameEquation, self).setValues(**coefficients)
2135    
2136       def getCoefficientOfGeneralPDE(self,name):
2137       """       """
2138       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2139    
2140       @param name:       @param name: name of the coefficient requested.
2141         @type name: C{string}
2142         @return: the value of the coefficient  name
2143         @rtype: L{Data<escript.Data>}
2144         @raise IllegalCoefficient: if name is not one of coefficients
2145                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2146         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2147       """       """
2148       if name == "A" :       if name == "A" :
2149           A =self.createNewCoefficient("A")           out =self.createCoefficientOfGeneralPDE("A")
2150           for i in range(self.getDim()):           for i in range(self.getDim()):
2151             for j in range(self.getDim()):             for j in range(self.getDim()):
2152               out[i,i,j,j] += self.getCoefficient("lame_mu")               out[i,i,j,j] += self.getCoefficient("lame_lambda")
2153               out[i,j,j,i] += self.getCoefficient("lame_lambda")               out[i,j,j,i] += self.getCoefficient("lame_mu")
2154               out[i,j,i,j] += self.getCoefficient("lame_lambda")               out[i,j,i,j] += self.getCoefficient("lame_mu")
2155           return out           return out
2156       elif name == "B" :       elif name == "B" :
2157           return escript.Data()           return escript.Data()
2158       elif name == "C" :       elif name == "C" :
2159           return escript.Data()           return escript.Data()
2160       elif name == "D" :       elif name == "D" :
2161           return escript.Data()           return escript.Data()
2162       elif name == "X" :       elif name == "X" :
2163           return self.getCoefficient("sigma")           return self.getCoefficient("sigma")
2164       elif name == "Y" :       elif name == "Y" :
2165           return self.getCoefficient("F")           return self.getCoefficient("F")
2166       elif name == "d" :       elif name == "d" :
2167           return escript.Data()           return escript.Data()
2168       elif name == "y" :       elif name == "y" :
2169           return self.getCoefficient("f")           return self.getCoefficient("f")
2170       elif name == "d_contact" :       elif name == "d_contact" :
2171           return escript.Data()           return escript.Data()
2172       elif name == "y_contact" :       elif name == "y_contact" :
2173           return escript.Data()           return escript.Data()
2174       elif name == "r" :       elif name == "A_reduced" :
2175             return escript.Data()
2176         elif name == "B_reduced" :
2177             return escript.Data()
2178         elif name == "C_reduced" :
2179             return escript.Data()
2180         elif name == "D_reduced" :
2181             return escript.Data()
2182         elif name == "X_reduced" :
2183             return escript.Data()
2184         elif name == "Y_reduced" :
2185             return escript.Data()
2186         elif name == "d_reduced" :
2187             return escript.Data()
2188         elif name == "y_reduced" :
2189             return escript.Data()
2190         elif name == "d_contact_reduced" :
2191             return escript.Data()
2192         elif name == "y_contact_reduced" :
2193             return escript.Data()
2194         elif name == "r" :
2195           return self.getCoefficient("r")           return self.getCoefficient("r")
2196       elif name == "q" :       elif name == "q" :
2197           return self.getCoefficient("q")           return self.getCoefficient("q")
2198       else:       else:
2199           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2200    
2201  # $Log$  def LinearSinglePDE(domain,debug=False):
2202  # Revision 1.9  2005/07/25 05:28:13  jgs     """
2203  # Merge of development branch back to main trunk on 2005-07-25     defines a single linear PDEs
2204  #  
2205  # Revision 1.8  2005/06/09 05:37:59  jgs     @param domain: domain of the PDE
2206  # Merge of development branch back to main trunk on 2005-06-09     @type domain: L{Domain<escript.Domain>}
2207  #     @param debug: if True debug informations are printed.
2208  # Revision 1.7  2005/05/06 04:26:10  jgs     @rtype: L{LinearPDE}
2209  # Merge of development branch back to main trunk on 2005-05-06     """
2210  #     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2211  # Revision 1.1.2.24  2005/07/22 06:37:11  gross  
2212  # some extensions to modellib and linearPDEs  def LinearPDESystem(domain,debug=False):
2213  #     """
2214  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane     defines a system of linear PDEs
2215  # Fixed up some docstrings.  Moved module-level functions to top of file so  
2216  # that epydoc and doxygen can pick them up properly.     @param domain: domain of the PDE
2217  #     @type domain: L{Domain<escript.Domain>}
2218  # Revision 1.1.2.22  2005/05/12 11:41:30  gross     @param debug: if True debug informations are printed.
2219  # some basic Models have been added     @rtype: L{LinearPDE}
2220  #     """
2221  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2222  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of  
2223  # file so that the AdvectivePDE class is picked up by doxygen.  Some  class TransportPDE(object):
2224  # reformatting of docstrings.  Addition of code to make equations come out       """
2225  # as proper LaTeX.       Warning: This is still a very experimental. The class is still changing!
2226  #  
2227  # Revision 1.1.2.20  2005/04/15 07:09:08  gross       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2228  # some problems with functionspace and linearPDEs fixed.      
2229  #       u=r where q>0
2230  # Revision 1.1.2.19  2005/03/04 05:27:07  gross      
2231  # bug in SystemPattern fixed.       all coefficients are constant over time.
2232  #  
2233  # Revision 1.1.2.18  2005/02/08 06:16:45  gross       typical usage:
2234  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed  
2235  #           p=TransportPDE(dom)
2236  # Revision 1.1.2.17  2005/02/08 05:56:19  gross           p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2237  # Reference Number handling added           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2238  #           t=0
2239  # Revision 1.1.2.16  2005/02/07 04:41:28  gross           dt=0.1
2240  # some function exposed to python to make mesh merging running           while (t<1.):
2241  #                u=p.solve(dt)
2242  # Revision 1.1.2.15  2005/02/03 00:14:44  gross  
2243  # timeseries add and ESySParameter.py renames esysXML.py for consistence       """
2244  #       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2245  # Revision 1.1.2.14  2005/02/01 06:44:10  gross          self.__domain=domain
2246  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working          self.__num_equations=num_equations
2247  #          self.__useSUPG=useSUPG
2248  # Revision 1.1.2.13  2005/01/25 00:47:07  gross          self.__trace=trace
2249  # updates in the documentation          self.__theta=theta
2250  #          self.__matrix_type=0
2251  # Revision 1.1.2.12  2005/01/12 01:28:04  matt          self.__reduced=True
2252  # Added createCoefficient method for linearPDEs.          self.__reassemble=True
2253  #          if self.__useSUPG:
2254  # Revision 1.1.2.11  2005/01/11 01:55:34  gross             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2255  # a problem in linearPDE class fixed             self.__pde.setSymmetryOn()
2256  #             self.__pde.setReducedOrderOn()
2257  # Revision 1.1.2.10  2005/01/07 01:13:29  gross          else:
2258  # some bugs in linearPDE fixed             self.__transport_problem=self.__getNewTransportProblem()
2259  #          self.setTolerance()
2260  # Revision 1.1.2.9  2005/01/06 06:24:58  gross          self.__M=escript.Data()
2261  # some bugs in slicing fixed          self.__A=escript.Data()
2262  #          self.__B=escript.Data()
2263  # Revision 1.1.2.8  2005/01/05 04:21:40  gross          self.__C=escript.Data()
2264  # FunctionSpace checking/matchig in slicing added          self.__D=escript.Data()
2265  #          self.__X=escript.Data()
2266  # Revision 1.1.2.7  2004/12/29 10:03:41  gross          self.__Y=escript.Data()
2267  # bug in setValue fixed          self.__d=escript.Data()
2268  #          self.__y=escript.Data()
2269  # Revision 1.1.2.6  2004/12/29 05:29:59  gross          self.__d_contact=escript.Data()
2270  # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()          self.__y_contact=escript.Data()
2271  #          self.__r=escript.Data()
2272  # Revision 1.1.2.5  2004/12/29 00:18:41  gross          self.__q=escript.Data()
2273  # AdvectivePDE added  
2274  #       def trace(self,text):
2275  # Revision 1.1.2.4  2004/12/24 06:05:41  gross               if self.__trace: print text
2276  # some changes in linearPDEs to add AdevectivePDE       def getSafeTimeStepSize(self):
2277  #          if self.__useSUPG:
2278  # Revision 1.1.2.3  2004/12/16 00:12:34  gross              if self.__reassemble:
2279  # __init__ of LinearPDE does not accept any coefficient anymore                 h=self.__domain.getSize()
2280  #                 dt=None
2281  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs                 if not self.__A.isEmpty():
2282  # *** empty log message ***                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2283  #                    if dt == None:
2284  # Revision 1.1.2.1  2004/12/12 22:53:47  gross                       dt = dt2
2285  # linearPDE has been renamed LinearPDE                    else:
2286  #                       dt=1./(1./dt+1./dt2)
2287  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross                 if not self.__B.isEmpty():
2288  # GMRES added                    dt2=util.inf(h*self.__M/util.length(self.__B))
2289  #                    if dt == None:
2290  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross                       dt = dt2
2291  # options for GMRES and PRES20 added                    else:
2292  #                       dt=1./(1./dt+1./dt2)
2293  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross                 if not  self.__C.isEmpty():
2294  # some small changes                    dt2=util.inf(h*self.__M/util.length(self.__C))
2295  #                    if dt == None:
2296  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross                       dt = dt2
2297  # Finley solves 4M unknowns now                    else:
2298  #                       dt=1./(1./dt+1./dt2)
2299  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross                 if not self.__D.isEmpty():
2300  # poisson solver added                    dt2=util.inf(self.__M/util.length(self.__D))
2301  #                    if dt == None:
2302  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross                       dt = dt2
2303  # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry                    else:
2304  #                       dt=1./(1./dt+1./dt2)
2305  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross                 self.__dt = dt/2
2306  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed              return self.__dt
2307  #          else:
2308  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs              return self.__getTransportProblem().getSafeTimeStepSize()
2309  # initial import of project esys2       def getDomain(self):
2310  #          return self.__domain
2311  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs       def getTheta(self):
2312  # committing Lutz's and Paul's changes to brach jgs          return self.__theta
2313  #       def getNumEquations(self):
2314  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane          return self.__num_equations
2315  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.       def setReducedOn(self):
2316  #            if not self.reduced():
2317  # Revision 1.3  2004/09/23 00:53:23  jgs                if self.__useSUPG:
2318  # minor fixes                   self.__pde.setReducedOrderOn()
2319  #                else:
2320  # Revision 1.1  2004/08/28 12:58:06  gross                   self.__transport_problem=self.__getNewTransportProblem()
2321  # SimpleSolve is not running yet: problem with == of functionsspace            self.__reduced=True
2322  #       def setReducedOff(self):
2323  #            if self.reduced():
2324                  if self.__useSUPG:
2325                     self.__pde.setReducedOrderOff()
2326                  else:
2327                     self.__transport_problem=self.__getNewTransportProblem()
2328              self.__reduced=False
2329         def reduced(self):
2330             return self.__reduced
2331         def getFunctionSpace(self):
2332            if self.reduced():
2333               return escript.ReducedSolution(self.getDomain())
2334            else:
2335               return escript.Solution(self.getDomain())
2336    
2337         def setTolerance(self,tol=1.e-8):
2338            self.__tolerance=tol
2339            if self.__useSUPG:
2340                  self.__pde.setTolerance(self.__tolerance)
2341    
2342         def __getNewTransportProblem(self):
2343           """
2344           returns an instance of a new operator
2345           """
2346           self.trace("New Transport problem is allocated.")
2347           return self.getDomain().newTransportProblem( \
2348                                   self.getTheta(),
2349                                   self.getNumEquations(), \
2350                                   self.getFunctionSpace(), \
2351                                   self.__matrix_type)
2352              
2353         def __getNewSolutionVector(self):
2354             if self.getNumEquations() ==1 :
2355                    out=escript.Data(0.0,(),self.getFunctionSpace())
2356             else:
2357                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2358             return out
2359    
2360         def __getTransportProblem(self):
2361           if self.__reassemble:
2362                 self.__source=self.__getNewSolutionVector()
2363                 self.__transport_problem.reset()
2364                 self.getDomain().addPDEToTransportProblem(
2365                             self.__transport_problem,
2366                             self.__source,
2367                             self.__M,
2368                             self.__A,
2369                             self.__B,
2370                             self.__C,
2371                             self.__D,
2372                             self.__X,
2373                             self.__Y,
2374                             self.__d,
2375                             self.__y,
2376                             self.__d_contact,
2377                             self.__y_contact)
2378                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2379                 self.__reassemble=False
2380           return self.__transport_problem
2381         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2382                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2383                 if not M==None:
2384                      self.__reassemble=True
2385                      self.__M=M
2386                 if not A==None:
2387                      self.__reassemble=True
2388                      self.__A=A
2389                 if not B==None:
2390                      self.__reassemble=True
2391                      self.__B=B
2392                 if not C==None:
2393                      self.__reassemble=True
2394                      self.__C=C
2395                 if not D==None:
2396                      self.__reassemble=True
2397                      self.__D=D
2398                 if not X==None:
2399                      self.__reassemble=True
2400                      self.__X=X
2401                 if not Y==None:
2402                      self.__reassemble=True
2403                      self.__Y=Y
2404                 if not d==None:
2405                      self.__reassemble=True
2406                      self.__d=d
2407                 if not y==None:
2408                      self.__reassemble=True
2409                      self.__y=y
2410                 if not d_contact==None:
2411                      self.__reassemble=True
2412                      self.__d_contact=d_contact
2413                 if not y_contact==None:
2414                      self.__reassemble=True
2415                      self.__y_contact=y_contact
2416                 if not q==None:
2417                      self.__reassemble=True
2418                      self.__q=q
2419                 if not r==None:
2420                      self.__reassemble=True
2421                      self.__r=r
2422    
2423         def setInitialSolution(self,u):
2424                 if self.__useSUPG:
2425                     self.__u=util.interpolate(u,self.getFunctionSpace())
2426                 else:
2427                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2428    
2429         def solve(self,dt,**kwarg):
2430               if self.__useSUPG:
2431                    if self.__reassemble:
2432                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2433                        self.__reassemble=False
2434                    dt2=self.getSafeTimeStepSize()
2435                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2436                    dt2=dt/nn
2437                    nnn=0
2438                    u=self.__u
2439                    self.trace("number of substeps is %d."%nn)
2440                    while nnn<nn :
2441                        self.__setSUPG(u,u,dt2/2)
2442                        u_half=self.__pde.getSolution(verbose=True)
2443                        self.__setSUPG(u,u_half,dt2)
2444                        u=self.__pde.getSolution(verbose=True)
2445                        nnn+=1
2446                    self.__u=u
2447                    return self.__u
2448               else:
2449                   kwarg["tolerance"]=self.__tolerance
2450                   tp=self.__getTransportProblem()
2451                   return tp.solve(self.__source,dt,kwarg)
2452         def __setSUPG(self,u0,u,dt):
2453                g=util.grad(u)
2454                X=0
2455                Y=self.__M*u0
2456                X=0
2457                self.__pde.setValue(r=u0)
2458                if not self.__A.isEmpty():
2459                   X=X+dt*util.matrixmult(self.__A,g)
2460                if not self.__B.isEmpty():
2461                   X=X+dt*self.__B*u
2462                if not  self.__C.isEmpty():
2463                   Y=Y+dt*util.inner(self.__C,g)
2464                if not self.__D.isEmpty():
2465                   Y=Y+dt*self.__D*u
2466                if not self.__X.isEmpty():
2467                   X=X+dt*self.__X
2468                if not self.__Y.isEmpty():
2469                   Y=Y+dt*self.__Y
2470                self.__pde.setValue(X=X,Y=Y)
2471                if not self.__y.isEmpty():
2472                   self.__pde.setValue(y=dt*self.__y)
2473                if not self.__y_contact.isEmpty():
2474                   self.__pde.setValue(y=dt*self.__y_contact)
2475                self.__pde.setValue(r=u0)

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