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trunk/esys2/escript/py_src/linearPDEs.py revision 122 by jgs, Thu Jun 9 05:38:05 2005 UTC trunk/escript/py_src/linearPDEs.py revision 1513 by gross, Tue Apr 15 08:47:57 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 SSOR: The symmetric overrealaxtion method
449       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
450       @cvar ILUT: The incomplete LU factorization preconditioner with will in
451       @cvar JACOBI: The Jacobi preconditioner
452       @cvar GMRES: The Gram-Schmidt minimum residual method
453       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
454       @cvar LUMPING: Matrix lumping.
455       @cvar NO_REORDERING: No matrix reordering allowed
456       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
457       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
458       @cvar PASO: PASO solver package
459       @cvar SCSL: SGI SCSL solver library
460       @cvar MKL: Intel's MKL solver library
461       @cvar UMFPACK: the UMFPACK library
462       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
463       @cvar ITERATIVE: The default iterative solver
464       @cvar AMG: algebraic multi grid
465       @cvar RILU: recursive ILU
466    
467       """
468       DEFAULT= 0
469       DIRECT= 1
470       CHOLEVSKY= 2
471       PCG= 3
472       CR= 4
473       CGS= 5
474       BICGSTAB= 6
475       SSOR= 7
476       ILU0= 8
477       ILUT= 9
478       JACOBI= 10
479       GMRES= 11
480       PRES20= 12
481       LUMPING= 13
482       NO_REORDERING= 17
483       MINIMUM_FILL_IN= 18
484       NESTED_DISSECTION= 19
485       SCSL= 14
486       MKL= 15
487       UMFPACK= 16
488       ITERATIVE= 20
489       PASO= 21
490       AMG= 22
491       RILU = 23
492       TRILINOS = 24
493    
494       SMALL_TOLERANCE=1.e-13
495       __PACKAGE_KEY="package"
496       __METHOD_KEY="method"
497       __SYMMETRY_KEY="symmetric"
498       __TOLERANCE_KEY="tolerance"
499       __PRECONDITIONER_KEY="preconditioner"
500    
501    
502       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
503         """
504         initializes a new linear PDE
505    
506         @param domain: domain of the PDE
507         @type domain: L{Domain<escript.Domain>}
508         @param numEquations: number of equations. If numEquations==None the number of equations
509                              is exracted from the PDE coefficients.
510         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
511                              is exracted from the PDE coefficients.
512         @param debug: if True debug informations are printed.
513    
514         """
515         super(LinearPDE, self).__init__()
516         #
517         #   the coefficients of the general PDE:
518         #
519         self.__COEFFICIENTS_OF_GENEARL_PDE={
520           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
521           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
522           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
523           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
524           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
525           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
526           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
527           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
528           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
529           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
530           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
531           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
532           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
533           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
535           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
536           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
537           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
538           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
541           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
542    
543         # COEFFICIENTS can be overwritten by subclasses:
544         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
545         self.__altered_coefficients=False
546       # initialize attributes       # initialize attributes
547       self.__debug=None       self.__debug=debug
548       self.__domain=domain       self.__domain=domain
549       self.__numEquations=numEquations       self.__numEquations=numEquations
550       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
551       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  
552    
553       # set some default values:       # set some default values:
554       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
555       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
556       self.__tolerance=1.e-8       self.__tolerance=1.e-8
557       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
558       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
559         self.__preconditioner=self.DEFAULT
560         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
561       self.__sym=False       self.__sym=False
      self.__lumping=False  
562    
563     def createCoefficient(self, name):       self.resetCoefficients()
564         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
565       # =============================================================================
566       #    general stuff:
567       # =============================================================================
568       def __str__(self):
569         """
570         returns string representation of the PDE
571    
572         @return: a simple representation of the PDE
573         @rtype: C{str}
574         """
575         return "<LinearPDE %d>"%id(self)
576       # =============================================================================
577       #    debug :
578       # =============================================================================
579       def setDebugOn(self):
580       """       """
581       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
582       """       """
583       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
584    
585     def __del__(self):     def setDebugOff(self):
      pass  
   
    def getCoefficient(self,name):  
586       """       """
587       return the value of the parameter name       switches off debugging
588         """
589         self.__debug=None
590    
591       @param name:     def trace(self,text):
592         """
593         print the text message if debugging is swiched on.
594         @param text: message
595         @type text: C{string}
596       """       """
597       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
598    
599     def getCoefficientOfPDE(self,name):     # =============================================================================
600       # some service functions:
601       # =============================================================================
602       def getDomain(self):
603       """       """
604       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.  
605    
606       @param name:       @return: the domain of the PDE
607         @rtype: L{Domain<escript.Domain>}
608       """       """
609       return self.getCoefficient(name)       return self.__domain
610    
611     def hasCoefficient(self,name):     def getDim(self):
612        """       """
613        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
614    
615        @param name:       @return: the spatial dimension of the PDE domain
616        """       @rtype: C{int}
617        return self.COEFFICIENTS.has_key(name)       """
618         return self.getDomain().getDim()
619    
620     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
621       """       """
622       return true if the test functions should use reduced order       returns the number of equations
623    
624         @return: the number of equations
625         @rtype: C{int}
626         @raise UndefinedPDEError: if the number of equations is not be specified yet.
627       """       """
628       return self.__row_function_space       if self.__numEquations==None:
629             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
630         else:
631             return self.__numEquations
632    
633     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
634       """       """
635       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
636    
637         @return: the number of unknowns
638         @rtype: C{int}
639         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
640       """       """
641       return self.__column_function_space       if self.__numSolutions==None:
642            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
643         else:
644            return self.__numSolutions
645    
646     def setValue(self,**coefficients):     def reduceEquationOrder(self):
647        """       """
648        sets new values to coefficients       return status for order reduction for equation
649    
650        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
651        """       @rtype: L{bool}
652        self.__setValue(**coefficients)       """
653               return self.__reduce_equation_order
654    
655     def cleanCoefficients(self):     def reduceSolutionOrder(self):
656       """       """
657       resets all coefficients to default values.       return status for order reduction for the solution
658    
659         @return: return True is reduced interpolation order is used for the represenation of the solution
660         @rtype: L{bool}
661       """       """
662       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
663    
664     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
665       """       """
666       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
667    
668         @return: representation space of equation
669         @rtype: L{FunctionSpace<escript.FunctionSpace>}
670       """       """
671       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
672                   return escript.ReducedSolution(self.getDomain())
673         else:
674             return escript.Solution(self.getDomain())
675    
676     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
677       """       """
678       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
679    
680       @param name:       @return: representation space of solution
681         @rtype: L{FunctionSpace<escript.FunctionSpace>}
682       """       """
683       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
684          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
685       else:       else:
686          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
687    
688     def getFunctionSpaceForCoefficient(self,name):  
689       def getOperator(self):
690       """       """
691       return the atoms of the coefficient name       provides access to the operator of the PDE
692    
693       @param name:       @return: the operator of the PDE
694         @rtype: L{Operator<escript.Operator>}
695       """       """
696       if self.hasCoefficient(name):       m=self.getSystem()[0]
697          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
698             return self.copyConstraint(1./m)
699       else:       else:
700          raise ValueError,"Solution coefficient %s requested"%name           return m
701    
702     def alteredCoefficient(self,name):     def getRightHandSide(self):
703       """       """
704       announce that coefficient name has been changed       provides access to the right hand side of the PDE
705         @return: the right hand side of the PDE
706         @rtype: L{Data<escript.Data>}
707         """
708         r=self.getSystem()[1]
709         if self.isUsingLumping():
710             return self.copyConstraint(r)
711         else:
712             return r
713    
714       @param name:     def applyOperator(self,u=None):
715       """       """
716       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
717          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
718          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}
719                   the current solution is used.
720         @type u: L{Data<escript.Data>} or None
721         @return: image of u
722         @rtype: L{Data<escript.Data>}
723         """
724         if u==None:
725            return self.getOperator()*self.getSolution()
726       else:       else:
727          raise ValueError,"unknown coefficient %s requested"%name          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
728    
729     # ===== debug ==============================================================     def getResidual(self,u=None):
730     def setDebugOn(self):       """
731         """       return the residual of u or the current solution if u is not present.
732    
733         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
734                   the current solution is used.
735         @type u: L{Data<escript.Data>} or None
736         @return: residual of u
737         @rtype: L{Data<escript.Data>}
738         """
739         return self.applyOperator(u)-self.getRightHandSide()
740    
741       def checkSymmetry(self,verbose=True):
742          """
743          test the PDE for symmetry.
744    
745          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
746          @type verbose: C{bool}
747          @return:  True if the PDE is symmetric.
748          @rtype: L{Data<escript.Data>}
749          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
750          """
751          verbose=verbose or self.__debug
752          out=True
753          if self.getNumSolutions()!=self.getNumEquations():
754             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
755             out=False
756          else:
757             A=self.getCoefficientOfGeneralPDE("A")
758             if not A.isEmpty():
759                tol=util.Lsup(A)*self.SMALL_TOLERANCE
760                if self.getNumSolutions()>1:
761                   for i in range(self.getNumEquations()):
762                      for j in range(self.getDim()):
763                         for k in range(self.getNumSolutions()):
764                            for l in range(self.getDim()):
765                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
766                                   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)
767                                   out=False
768                else:
769                   for j in range(self.getDim()):
770                      for l in range(self.getDim()):
771                         if util.Lsup(A[j,l]-A[l,j])>tol:
772                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
773                            out=False
774             B=self.getCoefficientOfGeneralPDE("B")
775             C=self.getCoefficientOfGeneralPDE("C")
776             if B.isEmpty() and not C.isEmpty():
777                if verbose: print "non-symmetric PDE because B is not present but C is"
778                out=False
779             elif not B.isEmpty() and C.isEmpty():
780                if verbose: print "non-symmetric PDE because C is not present but B is"
781                out=False
782             elif not B.isEmpty() and not C.isEmpty():
783                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
784                if self.getNumSolutions()>1:
785                   for i in range(self.getNumEquations()):
786                       for j in range(self.getDim()):
787                          for k in range(self.getNumSolutions()):
788                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
789                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
790                                  out=False
791                else:
792                   for j in range(self.getDim()):
793                      if util.Lsup(B[j]-C[j])>tol:
794                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
795                         out=False
796             if self.getNumSolutions()>1:
797               D=self.getCoefficientOfGeneralPDE("D")
798               if not D.isEmpty():
799                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
800                 for i in range(self.getNumEquations()):
801                    for k in range(self.getNumSolutions()):
802                      if util.Lsup(D[i,k]-D[k,i])>tol:
803                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
804                          out=False
805               d=self.getCoefficientOfGeneralPDE("d")
806               if not d.isEmpty():
807                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
808                 for i in range(self.getNumEquations()):
809                    for k in range(self.getNumSolutions()):
810                      if util.Lsup(d[i,k]-d[k,i])>tol:
811                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
812                          out=False
813               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
814               if not d_contact.isEmpty():
815                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
816                 for i in range(self.getNumEquations()):
817                    for k in range(self.getNumSolutions()):
818                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
819                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
820                          out=False
821             # and now the reduced coefficients
822             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
823             if not A_reduced.isEmpty():
824                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
825                if self.getNumSolutions()>1:
826                   for i in range(self.getNumEquations()):
827                      for j in range(self.getDim()):
828                         for k in range(self.getNumSolutions()):
829                            for l in range(self.getDim()):
830                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
831                                   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)
832                                   out=False
833                else:
834                   for j in range(self.getDim()):
835                      for l in range(self.getDim()):
836                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
837                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
838                            out=False
839             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
840             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
841             if B_reduced.isEmpty() and not C_reduced.isEmpty():
842                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
843                out=False
844             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
845                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
846                out=False
847             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
848                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
849                if self.getNumSolutions()>1:
850                   for i in range(self.getNumEquations()):
851                       for j in range(self.getDim()):
852                          for k in range(self.getNumSolutions()):
853                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
854                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
855                                  out=False
856                else:
857                   for j in range(self.getDim()):
858                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
859                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
860                         out=False
861             if self.getNumSolutions()>1:
862               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
863               if not D_reduced.isEmpty():
864                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
865                 for i in range(self.getNumEquations()):
866                    for k in range(self.getNumSolutions()):
867                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
868                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
869                          out=False
870               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
871               if not d_reduced.isEmpty():
872                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
873                 for i in range(self.getNumEquations()):
874                    for k in range(self.getNumSolutions()):
875                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
876                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
877                          out=False
878               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
879               if not d_contact_reduced.isEmpty():
880                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
881                 for i in range(self.getNumEquations()):
882                    for k in range(self.getNumSolutions()):
883                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
884                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
885                          out=False
886          return out
887    
888       def getSolution(self,**options):
889         """         """
890         self.__debug=not None         returns the solution of the PDE. If the solution is not valid the PDE is solved.
891    
892     def setDebugOff(self):         @return: the solution
893           @rtype: L{Data<escript.Data>}
894           @param options: solver options
895           @keyword verbose: True to get some information during PDE solution
896           @type verbose: C{bool}
897           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
898                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
899           @keyword iter_max: maximum number of iteration steps allowed.
900           @keyword drop_tolerance: threshold for drupping in L{ILUT}
901           @keyword drop_storage: maximum of allowed memory in L{ILUT}
902           @keyword truncation: maximum number of residuals in L{GMRES}
903           @keyword restart: restart cycle length in L{GMRES}
904         """         """
905           if not self.__solution_isValid:
906              mat,f=self.getSystem()
907              if self.isUsingLumping():
908                 self.__solution=self.copyConstraint(f*mat)
909              else:
910                 options[self.__TOLERANCE_KEY]=self.getTolerance()
911                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
912                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
913                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
914                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
915                 self.trace("PDE is resolved.")
916                 self.trace("solver options: %s"%str(options))
917                 self.__solution=mat.solve(f,options)
918              self.__solution_isValid=True
919           return self.__solution
920    
921       def getFlux(self,u=None):
922         """
923         returns the flux M{J} for a given M{u}
924    
925         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]}
926    
927         or
928    
929         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
930    
931         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
932         @type u: L{Data<escript.Data>} or None
933         @return: flux
934         @rtype: L{Data<escript.Data>}
935         """
936         if u==None: u=self.getSolution()
937         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
938               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
939               -util.self.getCoefficientOfGeneralPDE("X") \
940               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
941               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
942               -util.self.getCoefficientOfGeneralPDE("X_reduced")
943       # =============================================================================
944       #   solver settings:
945       # =============================================================================
946       def setSolverMethod(self,solver=None,preconditioner=None):
947         """         """
948         self.__debug=None         sets a new solver
949    
950           @param solver: sets a new solver method.
951           @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{PRES20}, L{LUMPING}, L{AMG}
952           @param preconditioner: sets a new solver method.
953           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
954           """
955           if solver==None: solver=self.__solver_method
956           if preconditioner==None: preconditioner=self.__preconditioner
957           if solver==None: solver=self.DEFAULT
958           if preconditioner==None: preconditioner=self.DEFAULT
959           if not (solver,preconditioner)==self.getSolverMethod():
960               self.__solver_method=solver
961               self.__preconditioner=preconditioner
962               self.__checkMatrixType()
963               self.trace("New solver is %s"%self.getSolverMethodName())
964    
965     def debug(self):     def getSolverMethodName(self):
966         """         """
967         returns true if the PDE is in the debug mode         returns the name of the solver currently used
968    
969           @return: the name of the solver currently used.
970           @rtype: C{string}
971         """         """
        return self.__debug  
972    
973     #===== Lumping ===========================         m=self.getSolverMethod()
974     def setLumpingOn(self):         p=self.getSolverPackage()
975        """         method=""
976        indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
977        """         elif m[0]==self.DIRECT: method= "DIRECT"
978        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
979           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
980           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
981           self.__lumping=True         elif m[0]==self.CR: method= "CR"
982           elif m[0]==self.CGS: method= "CGS"
983           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
984           elif m[0]==self.SSOR: method= "SSOR"
985           elif m[0]==self.GMRES: method= "GMRES"
986           elif m[0]==self.PRES20: method= "PRES20"
987           elif m[0]==self.LUMPING: method= "LUMPING"
988           elif m[0]==self.AMG: method= "AMG"
989           if m[1]==self.DEFAULT: method+="+DEFAULT"
990           elif m[1]==self.JACOBI: method+= "+JACOBI"
991           elif m[1]==self.ILU0: method+= "+ILU0"
992           elif m[1]==self.ILUT: method+= "+ILUT"
993           elif m[1]==self.SSOR: method+= "+SSOR"
994           elif m[1]==self.AMG: method+= "+AMG"
995           elif m[1]==self.RILU: method+= "+RILU"
996           if p==self.DEFAULT: package="DEFAULT"
997           elif p==self.PASO: package= "PASO"
998           elif p==self.MKL: package= "MKL"
999           elif p==self.SCSL: package= "SCSL"
1000           elif p==self.UMFPACK: package= "UMFPACK"
1001           elif p==self.TRILINOS: package= "TRILINOS"
1002           else : method="unknown"
1003           return "%s solver of %s package"%(method,package)
1004    
    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  
1005    
1006     def setLumping(self,flag=False):     def getSolverMethod(self):
1007        """         """
1008        set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
1009    
1010     def isUsingLumping(self):         @return: the solver method currently be used.
1011        """         @rtype: C{int}
1012                 """
1013        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
1014    
1015     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
1016         """         """
1017         sets a new solver         sets a new solver package
1018    
1019           @param package: sets a new solver method.
1020           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1021         """         """
1022         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
1023             self.__solver_method=solver         if not package==self.getSolverPackage():
1024             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__solver_package=package
1025             self.__checkMatrixType()             self.__checkMatrixType()
1026               self.trace("New solver is %s"%self.getSolverMethodName())
1027    
1028     def getSolverMethod(self):     def getSolverPackage(self):
1029         """         """
1030         returns the solver method         returns the package of the solver
1031    
1032           @return: the solver package currently being used.
1033           @rtype: C{int}
1034         """         """
1035         return self.__solver_method         return self.__solver_package
1036    
1037       def isUsingLumping(self):
1038          """
1039          checks if matrix lumping is used a solver method
1040    
1041          @return: True is lumping is currently used a solver method.
1042          @rtype: C{bool}
1043          """
1044          return self.getSolverMethod()[0]==self.LUMPING
1045    
    #============ tolerance business =========================================================  
1046     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1047         """         """
1048         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1049    
1050           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1051    
1052           defines the stopping criterion.
1053    
1054           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1055                       the system will be resolved.
1056           @type tol: positive C{float}
1057           @raise ValueError: if tolerance is not positive.
1058         """         """
1059         if not tol>0:         if not tol>0:
1060             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1061         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1062         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1063         self.__tolerance=tol         self.__tolerance=tol
1064         return         return
1065    
1066     def getTolerance(self):     def getTolerance(self):
1067         """         """
1068         returns the tolerance set for the solution         returns the tolerance set for the solution
1069    
1070           @return: tolerance currently used.
1071           @rtype: C{float}
1072         """         """
1073         return self.__tolerance         return self.__tolerance
1074    
1075     #===== symmetry  flag ==========================     # =============================================================================
1076       #    symmetry  flag:
1077       # =============================================================================
1078     def isSymmetric(self):     def isSymmetric(self):
1079        """        """
1080        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1081    
1082          @return: True is a symmetric PDE is indicated, otherwise False is returned
1083          @rtype: C{bool}
1084        """        """
1085        return self.__sym        return self.__sym
1086    
1087     def setSymmetryOn(self):     def setSymmetryOn(self):
1088        """        """
1089        sets the symmetry flag to true        sets the symmetry flag.
1090        """        """
1091        if not self.isSymmetric():        if not self.isSymmetric():
1092           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1093           self.__sym=True           self.__sym=True
1094           self.__checkMatrixType()           self.__checkMatrixType()
1095    
1096     def setSymmetryOff(self):     def setSymmetryOff(self):
1097        """        """
1098        sets the symmetry flag to false        removes the symmetry flag.
1099        """        """
1100        if self.isSymmetric():        if self.isSymmetric():
1101           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1102           self.__sym=False           self.__sym=False
1103           self.__checkMatrixType()           self.__checkMatrixType()
1104    
1105     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1106       """        """
1107       sets the symmetry flag to flag        sets the symmetry flag to flag
1108    
1109       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1110       """        @type flag: C{bool}
1111       if flag:        """
1112          self.setSymmetryOn()        if flag:
1113       else:           self.setSymmetryOn()
1114          self.setSymmetryOff()        else:
1115             self.setSymmetryOff()
1116    
1117     #===== order reduction ==========================     # =============================================================================
1118       # function space handling for the equation as well as the solution
1119       # =============================================================================
1120     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1121       """       """
1122       switches to on reduced order       switches on reduced order for solution and equation representation
1123    
1124         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1125       """       """
1126       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1127       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1128    
1129     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1130       """       """
1131       switches to full order       switches off reduced order for solution and equation representation
1132    
1133         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1134       """       """
1135       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1136       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1137    
1138     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1139       """       """
1140       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1141         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1142       @param flag:                    if flag is not present order reduction is switched off
1143         @type flag: C{bool}
1144         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1145       """       """
1146       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1147       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1148    
1149     #===== order reduction solution ==========================  
1150     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1151       """       """
1152       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1153    
1154         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1155       """       """
1156       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1157       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1158           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1159           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1160           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1161             self.__resetSystem()
1162    
1163     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1164       """       """
1165       switches to full order to interpolate solution       switches off reduced order for solution representation
1166    
1167         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1168       """       """
1169       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1170       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1171           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1172           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1173           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1174             self.__resetSystem()
1175    
1176     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1177       """       """
1178       sets order for test functions according to flag       sets order for test functions according to flag
1179    
1180       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1181                      if flag is not present order reduction is switched off
1182         @type flag: C{bool}
1183         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1184       """       """
1185       if flag:       if flag:
1186          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1187       else:       else:
1188          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1189                                                                                                                                                              
    #===== order reduction equation ==========================  
1190     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1191       """       """
1192       switches to reduced order for test functions       switches on reduced order for equation representation
1193    
1194         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1195       """       """
1196       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1197       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1198           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1199           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1200           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1201             self.__resetSystem()
1202    
1203     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1204       """       """
1205       switches to full order for test functions       switches off reduced order for equation representation
1206    
1207         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1208       """       """
1209       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1210       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1211           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1212           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1213           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1214             self.__resetSystem()
1215    
1216     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1217       """       """
1218       sets order for test functions according to flag       sets order for test functions according to flag
1219    
1220       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1221                      if flag is not present order reduction is switched off
1222         @type flag: C{bool}
1223         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1224       """       """
1225       if flag:       if flag:
1226          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1227       else:       else:
1228          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1229                                                                                                                                                              
1230     # ==== initialization =====================================================================     # =============================================================================
1231       # private method:
1232       # =============================================================================
1233       def __checkMatrixType(self):
1234         """
1235         reassess the matrix type and, if a new matrix is needed, resets the system.
1236         """
1237         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1238         if not new_matrix_type==self.__matrix_type:
1239             self.trace("Matrix type is now %d."%new_matrix_type)
1240             self.__matrix_type=new_matrix_type
1241             self.__resetSystem()
1242       #
1243       #   rebuild switches :
1244       #
1245       def __invalidateSolution(self):
1246           """
1247           indicates the PDE has to be resolved if the solution is requested
1248           """
1249           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1250           self.__solution_isValid=False
1251    
1252       def __invalidateOperator(self):
1253           """
1254           indicates the operator has to be rebuilt next time it is used
1255           """
1256           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1257           self.__invalidateSolution()
1258           self.__operator_is_Valid=False
1259    
1260       def __invalidateRightHandSide(self):
1261           """
1262           indicates the right hand side has to be rebuild next time it is used
1263           """
1264           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1265           self.__invalidateSolution()
1266           self.__righthandside_isValid=False
1267    
1268       def __invalidateSystem(self):
1269           """
1270           annonced that everthing has to be rebuild:
1271           """
1272           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1273           self.__invalidateSolution()
1274           self.__invalidateOperator()
1275           self.__invalidateRightHandSide()
1276    
1277       def __resetSystem(self):
1278           """
1279           annonced that everthing has to be rebuild:
1280           """
1281           self.trace("New System is built from scratch.")
1282           self.__operator=escript.Operator()
1283           self.__operator_is_Valid=False
1284           self.__righthandside=escript.Data()
1285           self.__righthandside_isValid=False
1286           self.__solution=escript.Data()
1287           self.__solution_isValid=False
1288       #
1289       #    system initialization:
1290       #
1291     def __getNewOperator(self):     def __getNewOperator(self):
1292         """         """
1293           returns an instance of a new operator
1294         """         """
1295           self.trace("New operator is allocated.")
1296         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1297                             self.getNumEquations(), \                             self.getNumEquations(), \
1298                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1300  class LinearPDE:
1300                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1301                             self.__matrix_type)                             self.__matrix_type)
1302    
1303     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1304         """         """
1305           returns an instance of a new right hand side
1306         """         """
1307         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1308         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1309             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1310         else:         else:
1311             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1312    
1313     def __getNewSolution(self):     def __getNewSolution(self):
1314         """         """
1315           returns an instance of a new solution
1316         """         """
1317         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1318         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1319             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1320         else:         else:
1321             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1322    
1323       def __makeFreshSolution(self):
1324           """
1325           makes sure that the solution is instantiated and returns it initialized by zeros
1326           """
1327           if self.__solution.isEmpty():
1328               self.__solution=self.__getNewSolution()
1329           else:
1330               self.__solution*=0
1331               self.trace("Solution is reset to zero.")
1332           return self.__solution
1333    
1334       def __makeFreshRightHandSide(self):
1335           """
1336           makes sure that the right hand side is instantiated and returns it initialized by zeros
1337           """
1338           if self.__righthandside.isEmpty():
1339               self.__righthandside=self.__getNewRightHandSide()
1340           else:
1341               self.__righthandside.setToZero()
1342               self.trace("Right hand side is reset to zero.")
1343           return self.__righthandside
1344    
1345     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1346         """         """
1347           makes sure that the operator is instantiated and returns it initialized by zeros
1348         """         """
1349         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1350             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1351         else:         else:
1352             self.__operator.setValue(0.)             self.__operator.resetValues()
1353             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1354         return self.__operator         return self.__operator
1355    
1356     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1357     def getDomain(self):         """
1358           applies the constraints defined by q and r to the system
1359           """
1360           if not self.isUsingLumping():
1361              q=self.getCoefficientOfGeneralPDE("q")
1362              r=self.getCoefficientOfGeneralPDE("r")
1363              if not q.isEmpty() and not self.__operator.isEmpty():
1364                 # q is the row and column mask to indicate where constraints are set:
1365                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1366                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1367                 u=self.__getNewSolution()
1368                 if r.isEmpty():
1369                    r_s=self.__getNewSolution()
1370                 else:
1371                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1372                 u.copyWithMask(r_s,col_q)
1373                 if not self.__righthandside.isEmpty():
1374                    self.__righthandside-=self.__operator*u
1375                    self.__righthandside=self.copyConstraint(self.__righthandside)
1376                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1377       # =============================================================================
1378       # function giving access to coefficients of the general PDE:
1379       # =============================================================================
1380       def getCoefficientOfGeneralPDE(self,name):
1381         """
1382         return the value of the coefficient name of the general PDE.
1383    
1384         @note: This method is called by the assembling routine it can be overwritten
1385               to map coefficients of a particular PDE to the general PDE.
1386         @param name: name of the coefficient requested.
1387         @type name: C{string}
1388         @return: the value of the coefficient  name
1389         @rtype: L{Data<escript.Data>}
1390         @raise IllegalCoefficient: if name is not one of coefficients
1391                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1392                      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}.
1393       """       """
1394       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1395            return self.getCoefficient(name)
1396         else:
1397            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1398    
1399       def hasCoefficientOfGeneralPDE(self,name):
1400       """       """
1401       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1402    
1403         @param name: name of the coefficient enquired.
1404         @type name: C{string}
1405         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1406         @rtype: C{bool}
1407    
    def getDim(self):  
1408       """       """
1409       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1410    
1411       def createCoefficientOfGeneralPDE(self,name):
1412       """       """
1413       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1414    
1415     def getNumEquations(self):       @param name: name of the coefficient requested.
1416         @type name: C{string}
1417         @return: a coefficient name initialized to 0.
1418         @rtype: L{Data<escript.Data>}
1419         @raise IllegalCoefficient: if name is not one of coefficients
1420                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1421                      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}.
1422       """       """
1423       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1424            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1425         else:
1426            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1427    
1428       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1429       """       """
1430       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1431           return self.__numEquations  
1432         @param name: name of the coefficient enquired.
1433         @type name: C{string}
1434         @return: the function space to be used for coefficient name
1435         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1436         @raise IllegalCoefficient: if name is not one of coefficients
1437                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1438                      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}.
1439         """
1440         if self.hasCoefficientOfGeneralPDE(name):
1441            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1442       else:       else:
1443           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1444    
1445     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1446       """       """
1447       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1448    
1449         @param name: name of the coefficient enquired.
1450         @type name: C{string}
1451         @return: the shape of the coefficient name
1452         @rtype: C{tuple} of C{int}
1453         @raise IllegalCoefficient: if name is not one of coefficients
1454                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1455                      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}.
1456       """       """
1457       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1458          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1459       else:       else:
1460          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1461    
1462       # =============================================================================
1463       # functions giving access to coefficients of a particular PDE implementation:
1464       # =============================================================================
1465       def getCoefficient(self,name):
1466         """
1467         returns the value of the coefficient name
1468    
1469     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1470        """       @type name: C{string}
1471        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
1472        """       @rtype: L{Data<escript.Data>}
1473        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1474        out=True       """
1475        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1476           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1477           out=False       else:
1478        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  
1479    
1480     def getFlux(self,u):     def hasCoefficient(self,name):
1481         """       """
1482         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1483    
1484         \f[       @param name: name of the coefficient enquired.
1485         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1486         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1487         @rtype: C{bool}
1488         """
1489         return self.COEFFICIENTS.has_key(name)
1490    
1491         @param u: argument of the operator     def createCoefficient(self, name):
1492         """       """
1493         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1494    
1495     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1496         """       @rtype: L{Data<escript.Data>}
1497         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.
1498         """
1499         if self.hasCoefficient(name):
1500            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1501         else:
1502            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1503    
1504         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1505         """       """
1506         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  
1507    
1508         @param u:       @param name: name of the coefficient enquired.
1509         """       @type name: C{string}
1510         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1511         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1512         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1513         """
1514         if self.hasCoefficient(name):
1515            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1516         else:
1517            raise ValueError,"unknown coefficient %s requested"%name
1518       def getShapeOfCoefficient(self,name):
1519         """
1520         return the shape of the coefficient name
1521    
1522         @param name: name of the coefficient enquired.
1523         @type name: C{string}
1524         @return: the shape of the coefficient name
1525         @rtype: C{tuple} of C{int}
1526         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1527         """
1528         if self.hasCoefficient(name):
1529            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1530         else:
1531            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1532    
1533       def resetCoefficients(self):
1534         """
1535         resets all coefficients to there default values.
1536         """
1537         for i in self.COEFFICIENTS.iterkeys():
1538             self.COEFFICIENTS[i].resetValue()
1539    
1540       def alteredCoefficient(self,name):
1541         """
1542         announce that coefficient name has been changed
1543    
1544         @param name: name of the coefficient enquired.
1545         @type name: C{string}
1546         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1547         @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.
1548         """
1549         if self.hasCoefficient(name):
1550            self.trace("Coefficient %s has been altered."%name)
1551            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1552               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1553               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1554         else:
1555            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1556    
1557       def copyConstraint(self,u):
1558          """
1559          copies the constraint into u and returns u.
1560    
1561          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1562          @type u: L{Data<escript.Data>}
1563          @return: the input u modified by the constraints.
1564          @rtype: L{Data<escript.Data>}
1565          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1566          """
1567          q=self.getCoefficientOfGeneralPDE("q")
1568          r=self.getCoefficientOfGeneralPDE("r")
1569          if not q.isEmpty():
1570             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1571             if r.isEmpty():
1572                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1573             else:
1574                 r=escript.Data(r,u.getFunctionSpace())
1575             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1576          return u
1577    
1578     def __setValue(self,**coefficients):     def setValue(self,**coefficients):
1579        """        """
1580        sets new values to coefficient        sets new values to coefficients
1581    
1582        @param coefficients:        @param coefficients: new values assigned to coefficients
1583          @keyword A: value for coefficient A.
1584          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1585          @keyword A_reduced: value for coefficient A_reduced.
1586          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1587          @keyword B: value for coefficient B
1588          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1589          @keyword B_reduced: value for coefficient B_reduced
1590          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1591          @keyword C: value for coefficient C
1592          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1593          @keyword C_reduced: value for coefficient C_reduced
1594          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1595          @keyword D: value for coefficient D
1596          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1597          @keyword D_reduced: value for coefficient D_reduced
1598          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1599          @keyword X: value for coefficient X
1600          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1601          @keyword X_reduced: value for coefficient X_reduced
1602          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1603          @keyword Y: value for coefficient Y
1604          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1605          @keyword Y_reduced: value for coefficient Y_reduced
1606          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1607          @keyword d: value for coefficient d
1608          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1609          @keyword d_reduced: value for coefficient d_reduced
1610          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1611          @keyword y: value for coefficient y
1612          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1613          @keyword d_contact: value for coefficient d_contact
1614          @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>}.
1615          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1616          @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>}.
1617          @keyword y_contact: value for coefficient y_contact
1618          @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>}.
1619          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1620          @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>}.
1621          @keyword r: values prescribed to the solution at the locations of constraints
1622          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1623                   depending of reduced order is used for the solution.
1624          @keyword q: mask for location of constraints
1625          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1626                   depending of reduced order is used for the representation of the equation.
1627          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1628        """        """
1629        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1630        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1631           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1632              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1633        # 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:
1634        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1635           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1636              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1637                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1641  class LinearPDE:
1641                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1642              if s!=None:              if s!=None:
1643                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1644                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1645                  if res==None:                  if res==None:
1646                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1647                  else:                  else:
1648                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1649                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1650        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1651        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1652        # 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:
1653        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1654          if d==None:          try:
1655               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),
1656          elif isinstance(d,escript.Data):                                           self.getNumEquations(),self.getNumSolutions(),
1657               if d.isEmpty():                                           self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1658                  d2=d             self.alteredCoefficient(i)
1659               else:          except IllegalCoefficientFunctionSpace,m:
1660                  d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              # if the function space is wrong then we try the reduced version:
1661          else:              i_red=i+"_reduced"
1662                d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1663          if not d2.isEmpty():                  try:
1664             if not self.getShapeOfCoefficient(i)==d2.getShape():                      self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1665                 raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())                                                        self.getNumEquations(),self.getNumSolutions(),
1666          # overwrite new values:                                                        self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1667          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i                      self.alteredCoefficient(i_red)
1668          self.COEFFICIENTS[i].setValue(d2)                  except IllegalCoefficientValue,m:
1669          self.alteredCoefficient(i)                      raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1670                          except IllegalCoefficientFunctionSpace,m:
1671        # reset the HomogeneousConstraintFlag:                      raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1672        self.__setHomogeneousConstraintFlag()              else:
1673        if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()                  raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1674            except IllegalCoefficientValue,m:
1675     def __setHomogeneousConstraintFlag(self):             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1676        """        self.__altered_coefficients=True
1677        checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.        # check if the systrem is inhomogeneous:
1678        """        if len(coefficients)>0 and not self.isUsingLumping():
1679        self.__homogeneous_constraint=True           q=self.getCoefficientOfGeneralPDE("q")
1680        q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1681        r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1682        if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1683           if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False               if util.Lsup(q*r)>0.:
1684        if self.debug():                 self.trace("Inhomogeneous constraint detected.")
1685             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.)  
1686    
1687     def getSystem(self):     def getSystem(self):
1688         """         """
1689         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1690    
1691           @return: the discrete version of the PDE
1692           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1693         """         """
1694         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1695            if self.isUsingLumping():            if self.isUsingLumping():
1696                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1697                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1698                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1699                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1700                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1701                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1702                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient B in lumped matrix may not be present."
1703                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1704                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient C in lumped matrix may not be present."
1705                   if self.debug() : print "PDE Debug: New lumped operator is built."                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1706                   mat=self.__getNewOperator()                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1707                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1708                             self.getCoefficientOfPDE("A"), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1709                             self.getCoefficientOfPDE("B"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1710                             self.getCoefficientOfPDE("C"), \                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1711                             self.getCoefficientOfPDE("D"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1712                             escript.Data(), \                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1713                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1714                             self.getCoefficientOfPDE("d"), \                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1715                             escript.Data(),\                   D=self.getCoefficientOfGeneralPDE("D")
1716                             self.getCoefficientOfPDE("d_contact"), \                   d=self.getCoefficientOfGeneralPDE("d")
1717                             escript.Data())                   D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1718                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1719                   self.__applyConstraint()                   if not D.isEmpty():
1720                   self.__operator_isValid=True                       if self.getNumSolutions()>1:
1721                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1722                         else:
1723                            D_times_e=D
1724                     else:
1725                        D_times_e=escript.Data()
1726                     if not d.isEmpty():
1727                         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          
1734                     if not D_reduced.isEmpty():
1735                         if self.getNumSolutions()>1:
1736                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1737                         else:
1738                            D_reduced_times_e=D_reduced
1739                     else:
1740                        D_reduced_times_e=escript.Data()
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    
1749                     self.__operator=self.__getNewRightHandSide()
1750                     if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1751                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1752                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1753                     else:
1754                        self.getDomain().addPDEToRHS(self.__operator, \
1755                                                     escript.Data(), \
1756                                                     D_times_e, \
1757                                                     d_times_e,\
1758                                                     escript.Data())
1759                        self.getDomain().addPDEToRHS(self.__operator, \
1760                                                     escript.Data(), \
1761                                                     D_reduced_times_e, \
1762                                                     d_reduced_times_e,\
1763                                                     escript.Data())
1764                     self.__operator=1./self.__operator
1765                     self.trace("New lumped operator has been built.")
1766                     self.__operator_is_Valid=True
1767                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1768                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1769                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1770                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1771                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1772                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1773                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1774                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1775                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1776                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1777                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1778                     self.trace("New right hand side as been built.")
1779                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1780            else:            else:
1781               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."  
1782                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1783                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1784                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1785                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1786                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1787                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1788                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1789                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1790                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1791                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1792                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1793                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1794                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1804                   self.__applyConstraint()                   self.__applyConstraint()
1805                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1806                   self.__operator_isValid=True                   self.trace("New system has been built.")
1807                     self.__operator_is_Valid=True
1808                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1809               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1810                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1811                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1812                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1813                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1814                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1815                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1816                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1817                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1818                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1819                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1820                     self.__righthandside=self.copyConstraint(self.__righthandside)
1821                     self.trace("New right hand side has been built.")
1822                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1823               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1824                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1825                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1826                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1827                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1828                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1829                                escript.Data(), \
1830                                escript.Data(), \
1831                                self.getCoefficientOfGeneralPDE("d"), \
1832                                escript.Data(),\
1833                                self.getCoefficientOfGeneralPDE("d_contact"), \
1834                                escript.Data())
1835                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1836                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1837                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1839                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1840                              escript.Data(), \                              escript.Data(), \
1841                              escript.Data(), \                              escript.Data(), \
1842                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d_reduced"), \
1843                              escript.Data(),\                              escript.Data(),\
1844                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1845                              escript.Data())                              escript.Data())
1846                   self.__applyConstraint()                   self.__applyConstraint()
1847                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1848                     self.__operator_is_Valid=True
1849         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1850    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
   
    def solve(self,**options):  
       """  
       solve the PDE  
1851    
1852        @param options:  class Poisson(LinearPDE):
1853        """     """
1854        mat,f=self.getSystem()     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
       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  
1855    
1856     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        returns the solution of the PDE  
1857    
1858         @param options:     with natural boundary conditons
        """  
        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  
1859    
1860       M{n[j]*grad(u)[j] = 0 }
1861    
1862       and constraints:
1863    
1864  def ELMAN_RAMAGE(P):     M{u=0} where M{q>0}
      """   """  
      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())  
1865    
 class AdvectivePDE(LinearPDE):  
1866     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1867    
1868     \f[     def __init__(self,domain,debug=False):
1869     -(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       """
1870     \f]       initializes a new Poisson equation
1871    
1872         @param domain: domain of the PDE
1873         @type domain: L{Domain<escript.Domain>}
1874         @param debug: if True debug informations are printed.
1875    
1876         """
1877         super(Poisson, self).__init__(domain,1,1,debug)
1878         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1879                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1880                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1881         self.setSymmetryOn()
1882    
1883       def setValue(self,**coefficients):
1884         """
1885         sets new values to coefficients
1886    
1887         @param coefficients: new values assigned to coefficients
1888         @keyword f: value for right hand side M{f}
1889         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1890         @keyword q: mask for location of constraints
1891         @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>}
1892                   depending of reduced order is used for the representation of the equation.
1893         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1894         """
1895         super(Poisson, self).setValue(**coefficients)
1896    
1897       def getCoefficientOfGeneralPDE(self,name):
1898         """
1899         return the value of the coefficient name of the general PDE
1900         @param name: name of the coefficient requested.
1901         @type name: C{string}
1902         @return: the value of the coefficient  name
1903         @rtype: L{Data<escript.Data>}
1904         @raise IllegalCoefficient: if name is not one of coefficients
1905                      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}.
1906         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1907         """
1908         if name == "A" :
1909             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1910         elif name == "B" :
1911             return escript.Data()
1912         elif name == "C" :
1913             return escript.Data()
1914         elif name == "D" :
1915             return escript.Data()
1916         elif name == "X" :
1917             return escript.Data()
1918         elif name == "Y" :
1919             return self.getCoefficient("f")
1920         elif name == "d" :
1921             return escript.Data()
1922         elif name == "y" :
1923             return escript.Data()
1924         elif name == "d_contact" :
1925             return escript.Data()
1926         elif name == "y_contact" :
1927             return escript.Data()
1928         elif name == "A_reduced" :
1929             return escript.Data()
1930         elif name == "B_reduced" :
1931             return escript.Data()
1932         elif name == "C_reduced" :
1933             return escript.Data()
1934         elif name == "D_reduced" :
1935             return escript.Data()
1936         elif name == "X_reduced" :
1937             return escript.Data()
1938         elif name == "Y_reduced" :
1939             return self.getCoefficient("f_reduced")
1940         elif name == "d_reduced" :
1941             return escript.Data()
1942         elif name == "y_reduced" :
1943             return escript.Data()
1944         elif name == "d_contact_reduced" :
1945             return escript.Data()
1946         elif name == "y_contact_reduced" :
1947             return escript.Data()
1948         elif name == "r" :
1949             return escript.Data()
1950         elif name == "q" :
1951             return self.getCoefficient("q")
1952         else:
1953            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1954    
1955     with boundary conditons:  class Helmholtz(LinearPDE):
1956       """
1957       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1958    
1959     \f[     M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
    n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
    \f]  
1960    
1961     and contact conditions     with natural boundary conditons
1962    
1963     \f[     M{k*n[j]*grad(u)[j] = g- S{alpha}u }
    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]  
1964    
1965     and constraints:     and constraints:
1966    
1967     \f[     M{u=r} where M{q>0}
1968     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1969     """     """
    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.  
1970    
1971     def setValue(self,**args):     def __init__(self,domain,debug=False):
1972         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       """
1973         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)  
1974    
1975              Z_max=util.Lsup(length_of_Z)       @param domain: domain of the PDE
1976              if Z_max>0.:       @type domain: L{Domain<escript.Domain>}
1977                 length_of_A=util.length(A)       @param debug: if True debug informations are printed.
1978                 A_max=util.Lsup(length_of_A)  
1979                 if A_max>0:       """
1980                      inv_A=1./(length_of_A+A_max*self.TOL)       super(Helmholtz, self).__init__(domain,1,1,debug)
1981                 else:       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1982                      inv_A=1./self.TOL                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1983                 peclet_number=length_of_Z*h/2*inv_A                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1984                 xi=self.__xi(peclet_number)                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1985                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1986                 print "@ preclet number = %e"%util.Lsup(peclet_number),util.Lsup(xi),util.Lsup(length_of_Z)                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987        return self.__Xi                          "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                                  "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1989                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1990         self.setSymmetryOn()
1991    
1992     def getCoefficientOfPDE(self,name):     def setValue(self,**coefficients):
1993       """       """
1994       return the value of the coefficient name of the general PDE       sets new values to coefficients
1995    
1996       @param name:       @param coefficients: new values assigned to coefficients
1997         @keyword omega: value for coefficient M{S{omega}}
1998         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1999         @keyword k: value for coefficeint M{k}
2000         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2001         @keyword f: value for right hand side M{f}
2002         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2003         @keyword alpha: value for right hand side M{S{alpha}}
2004         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2005         @keyword g: value for right hand side M{g}
2006         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2007         @keyword r: prescribed values M{r} for the solution in constraints.
2008         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2009                   depending of reduced order is used for the representation of the equation.
2010         @keyword q: mask for location of constraints
2011         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2012                   depending of reduced order is used for the representation of the equation.
2013         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2014       """       """
2015       if not self.getNumEquations() == self.getNumSolutions():       super(Helmholtz, self).setValue(**coefficients)
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
2016    
2017       if name == "A" :     def getCoefficientOfGeneralPDE(self,name):
2018           A=self.getCoefficient("A")       """
2019           B=self.getCoefficient("B")       return the value of the coefficient name of the general PDE
2020           C=self.getCoefficient("C")  
2021           if B.isEmpty() and C.isEmpty():       @param name: name of the coefficient requested.
2022              Aout=A       @type name: C{string}
2023           else:       @return: the value of the coefficient  name
2024              if A.isEmpty():       @rtype: L{Data<escript.Data>}
2025                 Aout=self.createNewCoefficient("A")       @raise IllegalCoefficient: if name is not one of coefficients
2026              else:                    "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}.
2027                 Aout=A[:]       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2028              Xi=self.getXi()       """
2029              if self.getNumEquations()>1:       if name == "A" :
2030                  for i in range(self.getNumEquations()):           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2031                     for j in range(self.getDim()):       elif name == "B" :
2032                        for k in range(self.getNumSolutions()):           return escript.Data()
2033                           for l in range(self.getDim()):       elif name == "C" :
2034                              if not C.isEmpty() and not B.isEmpty():           return escript.Data()
2035                                 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])       elif name == "D" :
2036                              elif C.isEmpty():           return self.getCoefficient("omega")
2037                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]       elif name == "X" :
2038                              else:           return escript.Data()
2039                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]       elif name == "Y" :
2040              else:           return self.getCoefficient("f")
2041                  for j in range(self.getDim()):       elif name == "d" :
2042                     for l in range(self.getDim()):           return self.getCoefficient("alpha")
2043                        if not C.isEmpty() and not B.isEmpty():       elif name == "y" :
2044                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])           return self.getCoefficient("g")
2045                        elif C.isEmpty():       elif name == "d_contact" :
2046                            Aout[j,l]+=Xi*B[j]*B[l]           return escript.Data()
                       else:  
                           Aout[j,l]+=Xi*C[j]*C[l]  
          return Aout  
      elif name == "B" :  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if C.isEmpty() or D.isEmpty():  
             Bout=B  
          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")  
2047       elif name == "y_contact" :       elif name == "y_contact" :
2048           return self.getCoefficient("y_contact")           return escript.Data()
2049       elif name == "r" :       elif name == "A_reduced" :
2050             return escript.Data()
2051         elif name == "B_reduced" :
2052             return escript.Data()
2053         elif name == "C_reduced" :
2054             return escript.Data()
2055         elif name == "D_reduced" :
2056             return escript.Data()
2057         elif name == "X_reduced" :
2058             return escript.Data()
2059         elif name == "Y_reduced" :
2060             return self.getCoefficient("f_reduced")
2061         elif name == "d_reduced" :
2062             return escript.Data()
2063         elif name == "y_reduced" :
2064            return self.getCoefficient("g_reduced")
2065         elif name == "d_contact_reduced" :
2066             return escript.Data()
2067         elif name == "y_contact_reduced" :
2068             return escript.Data()
2069         elif name == "r" :
2070           return self.getCoefficient("r")           return self.getCoefficient("r")
2071       elif name == "q" :       elif name == "q" :
2072           return self.getCoefficient("q")           return self.getCoefficient("q")
2073       else:       else:
2074           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2075    
2076    class LameEquation(LinearPDE):
 class Poisson(LinearPDE):  
2077     """     """
2078     Class to define a Poisson equstion problem:     Class to define a Lame equation problem:
2079    
2080     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] }
2081     \f[  
2082     -u_{,jj} = f     with natural boundary conditons:
2083     \f]  
2084       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*u_{,j} = 0  
    \f]  
2085    
2086     and constraints:     and constraints:
2087    
2088     \f[     M{u[i]=r[i]} where M{q[i]>0}
    u=0 \quad \mathrm{where} \quad q>0  
    \f]  
    """  
2089    
2090     def __init__(self,domain,f=escript.Data(),q=escript.Data()):     """
        LinearPDE.__init__(self,domain,1,1)  
        self.COEFFICIENTS={  
        "f"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
        "q"         : PDECoefficient(PDECoefficient.CONTINUOUS,(PDECoefficient.EQUATION,),PDECoefficient.BOTH)}  
        self.setSymmetryOn()  
        self.setValue(f,q)  
2091    
2092     def setValue(self,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2093         self._LinearPDE__setValue(f=f,q=q)        super(LameEquation, self).__init__(domain,\
2094                                             domain.getDim(),domain.getDim(),debug)
2095          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2096                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2097                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2098                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2099                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2100                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2101                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2102          self.setSymmetryOn()
2103    
2104       def setValues(self,**coefficients):
2105         """
2106         sets new values to coefficients
2107    
2108         @param coefficients: new values assigned to coefficients
2109         @keyword lame_mu: value for coefficient M{S{mu}}
2110         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2111         @keyword lame_lambda: value for coefficient M{S{lambda}}
2112         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2113         @keyword F: value for internal force M{F}
2114         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2115         @keyword sigma: value for initial stress M{S{sigma}}
2116         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2117         @keyword f: value for extrenal force M{f}
2118         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2119         @keyword r: prescribed values M{r} for the solution in constraints.
2120         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2121                   depending of reduced order is used for the representation of the equation.
2122         @keyword q: mask for location of constraints
2123         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2124                   depending of reduced order is used for the representation of the equation.
2125         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2126         """
2127         super(LameEquation, self).setValues(**coefficients)
2128    
2129     def getCoefficientOfPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2130       """       """
2131       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2132    
2133       @param name:       @param name: name of the coefficient requested.
2134       """       @type name: C{string}
2135       if name == "A" :       @return: the value of the coefficient  name
2136           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))       @rtype: L{Data<escript.Data>}
2137       elif name == "B" :       @raise IllegalCoefficient: if name is not one of coefficients
2138                      "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}.
2139         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2140         """
2141         if name == "A" :
2142             out =self.createCoefficientOfGeneralPDE("A")
2143             for i in range(self.getDim()):
2144               for j in range(self.getDim()):
2145                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2146                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2147                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2148             return out
2149         elif name == "B" :
2150           return escript.Data()           return escript.Data()
2151       elif name == "C" :       elif name == "C" :
2152           return escript.Data()           return escript.Data()
2153       elif name == "D" :       elif name == "D" :
2154           return escript.Data()           return escript.Data()
2155       elif name == "X" :       elif name == "X" :
2156             return self.getCoefficient("sigma")
2157         elif name == "Y" :
2158             return self.getCoefficient("F")
2159         elif name == "d" :
2160           return escript.Data()           return escript.Data()
2161       elif name == "Y" :       elif name == "y" :
2162           return self.getCoefficient("f")           return self.getCoefficient("f")
2163       elif name == "d" :       elif name == "d_contact" :
2164           return escript.Data()           return escript.Data()
2165       elif name == "y" :       elif name == "y_contact" :
2166           return escript.Data()           return escript.Data()
2167       elif name == "d_contact" :       elif name == "A_reduced" :
2168           return escript.Data()           return escript.Data()
2169       elif name == "y_contact" :       elif name == "B_reduced" :
2170             return escript.Data()
2171         elif name == "C_reduced" :
2172             return escript.Data()
2173         elif name == "D_reduced" :
2174             return escript.Data()
2175         elif name == "X_reduced" :
2176           return escript.Data()           return escript.Data()
2177       elif name == "r" :       elif name == "Y_reduced" :
2178           return escript.Data()           return escript.Data()
2179       elif name == "q" :       elif name == "d_reduced" :
2180             return escript.Data()
2181         elif name == "y_reduced" :
2182             return escript.Data()
2183         elif name == "d_contact_reduced" :
2184             return escript.Data()
2185         elif name == "y_contact_reduced" :
2186             return escript.Data()
2187         elif name == "r" :
2188             return self.getCoefficient("r")
2189         elif name == "q" :
2190           return self.getCoefficient("q")           return self.getCoefficient("q")
2191       else:       else:
2192           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2193    
2194  # $Log$  def LinearSinglePDE(domain,debug=False):
2195  # Revision 1.8  2005/06/09 05:37:59  jgs     """
2196  # Merge of development branch back to main trunk on 2005-06-09     defines a single linear PDEs
2197  #  
2198  # Revision 1.7  2005/05/06 04:26:10  jgs     @param domain: domain of the PDE
2199  # Merge of development branch back to main trunk on 2005-05-06     @type domain: L{Domain<escript.Domain>}
2200  #     @param debug: if True debug informations are printed.
2201  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane     @rtype: L{LinearPDE}
2202  # Fixed up some docstrings.  Moved module-level functions to top of file so     """
2203  # that epydoc and doxygen can pick them up properly.     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2204  #  
2205  # Revision 1.1.2.22  2005/05/12 11:41:30  gross  def LinearPDESystem(domain,debug=False):
2206  # some basic Models have been added     """
2207  #     defines a system of linear PDEs
2208  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane  
2209  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of     @param domain: domain of the PDE
2210  # file so that the AdvectivePDE class is picked up by doxygen.  Some     @type domain: L{Domain<escript.Domain>}
2211  # reformatting of docstrings.  Addition of code to make equations come out     @param debug: if True debug informations are printed.
2212  # as proper LaTeX.     @rtype: L{LinearPDE}
2213  #     """
2214  # Revision 1.1.2.20  2005/04/15 07:09:08  gross     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2215  # some problems with functionspace and linearPDEs fixed.  
2216  #  class TransportPDE(object):
2217  # Revision 1.1.2.19  2005/03/04 05:27:07  gross       """
2218  # bug in SystemPattern fixed.       Warning: This is still a very experimental. The class is still changing!
2219  #  
2220  # Revision 1.1.2.18  2005/02/08 06:16:45  gross       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2221  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed      
2222  #       u=r where q>0
2223  # Revision 1.1.2.17  2005/02/08 05:56:19  gross      
2224  # Reference Number handling added       all coefficients are constant over time.
2225  #  
2226  # Revision 1.1.2.16  2005/02/07 04:41:28  gross       typical usage:
2227  # some function exposed to python to make mesh merging running  
2228  #           p=TransportPDE(dom)
2229  # Revision 1.1.2.15  2005/02/03 00:14:44  gross           p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2230  # timeseries add and ESySParameter.py renames esysXML.py for consistence           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2231  #           t=0
2232  # Revision 1.1.2.14  2005/02/01 06:44:10  gross           dt=0.1
2233  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working           while (t<1.):
2234  #                u=p.solve(dt)
2235  # Revision 1.1.2.13  2005/01/25 00:47:07  gross  
2236  # updates in the documentation       """
2237  #       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2238  # Revision 1.1.2.12  2005/01/12 01:28:04  matt          self.__domain=domain
2239  # Added createCoefficient method for linearPDEs.          self.__num_equations=num_equations
2240  #          self.__useSUPG=useSUPG
2241  # Revision 1.1.2.11  2005/01/11 01:55:34  gross          self.__trace=trace
2242  # a problem in linearPDE class fixed          self.__theta=theta
2243  #          self.__matrix_type=0
2244  # Revision 1.1.2.10  2005/01/07 01:13:29  gross          self.__reduced=True
2245  # some bugs in linearPDE fixed          self.__reassemble=True
2246  #          if self.__useSUPG:
2247  # Revision 1.1.2.9  2005/01/06 06:24:58  gross             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2248  # some bugs in slicing fixed             self.__pde.setSymmetryOn()
2249  #             self.__pde.setReducedOrderOn()
2250  # Revision 1.1.2.8  2005/01/05 04:21:40  gross          else:
2251  # FunctionSpace checking/matchig in slicing added             self.__transport_problem=self.__getNewTransportProblem()
2252  #          self.setTolerance()
2253  # Revision 1.1.2.7  2004/12/29 10:03:41  gross          self.__M=escript.Data()
2254  # bug in setValue fixed          self.__A=escript.Data()
2255  #          self.__B=escript.Data()
2256  # Revision 1.1.2.6  2004/12/29 05:29:59  gross          self.__C=escript.Data()
2257  # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()          self.__D=escript.Data()
2258  #          self.__X=escript.Data()
2259  # Revision 1.1.2.5  2004/12/29 00:18:41  gross          self.__Y=escript.Data()
2260  # AdvectivePDE added          self.__d=escript.Data()
2261  #          self.__y=escript.Data()
2262  # Revision 1.1.2.4  2004/12/24 06:05:41  gross          self.__d_contact=escript.Data()
2263  # some changes in linearPDEs to add AdevectivePDE          self.__y_contact=escript.Data()
2264  #          self.__r=escript.Data()
2265  # Revision 1.1.2.3  2004/12/16 00:12:34  gross          self.__q=escript.Data()
2266  # __init__ of LinearPDE does not accept any coefficient anymore  
2267  #       def trace(self,text):
2268  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs               if self.__trace: print text
2269  # *** empty log message ***       def getSafeTimeStepSize(self):
2270  #          if self.__useSUPG:
2271  # Revision 1.1.2.1  2004/12/12 22:53:47  gross              if self.__reassemble:
2272  # linearPDE has been renamed LinearPDE                 h=self.__domain.getSize()
2273  #                 dt=None
2274  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross                 if not self.__A.isEmpty():
2275  # GMRES added                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2276  #                    if dt == None:
2277  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross                       dt = dt2
2278  # options for GMRES and PRES20 added                    else:
2279  #                       dt=1./(1./dt+1./dt2)
2280  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross                 if not self.__B.isEmpty():
2281  # some small changes                    dt2=util.inf(h*self.__M/util.length(self.__B))
2282  #                    if dt == None:
2283  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross                       dt = dt2
2284  # Finley solves 4M unknowns now                    else:
2285  #                       dt=1./(1./dt+1./dt2)
2286  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross                 if not  self.__C.isEmpty():
2287  # poisson solver added                    dt2=util.inf(h*self.__M/util.length(self.__C))
2288  #                    if dt == None:
2289  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross                       dt = dt2
2290  # 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:
2291  #                       dt=1./(1./dt+1./dt2)
2292  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross                 if not self.__D.isEmpty():
2293  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed                    dt2=util.inf(self.__M/util.length(self.__D))
2294  #                    if dt == None:
2295  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs                       dt = dt2
2296  # initial import of project esys2                    else:
2297  #                       dt=1./(1./dt+1./dt2)
2298  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs                 self.__dt = dt/2
2299  # committing Lutz's and Paul's changes to brach jgs              return self.__dt
2300  #          else:
2301  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane              return self.__getTransportProblem().getSafeTimeStepSize()
2302  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.       def getDomain(self):
2303  #          return self.__domain
2304  # Revision 1.3  2004/09/23 00:53:23  jgs       def getTheta(self):
2305  # minor fixes          return self.__theta
2306  #       def getNumEquations(self):
2307  # Revision 1.1  2004/08/28 12:58:06  gross          return self.__num_equations
2308  # SimpleSolve is not running yet: problem with == of functionsspace       def setReducedOn(self):
2309  #            if not self.reduced():
2310  #                if self.__useSUPG:
2311                     self.__pde.setReducedOrderOn()
2312                  else:
2313                     self.__transport_problem=self.__getNewTransportProblem()
2314              self.__reduced=True
2315         def setReducedOff(self):
2316              if self.reduced():
2317                  if self.__useSUPG:
2318                     self.__pde.setReducedOrderOff()
2319                  else:
2320                     self.__transport_problem=self.__getNewTransportProblem()
2321              self.__reduced=False
2322         def reduced(self):
2323             return self.__reduced
2324         def getFunctionSpace(self):
2325            if self.reduced():
2326               return escript.ReducedSolution(self.getDomain())
2327            else:
2328               return escript.Solution(self.getDomain())
2329    
2330         def setTolerance(self,tol=1.e-8):
2331            self.__tolerance=tol
2332            if self.__useSUPG:
2333                  self.__pde.setTolerance(self.__tolerance)
2334    
2335         def __getNewTransportProblem(self):
2336           """
2337           returns an instance of a new operator
2338           """
2339           self.trace("New Transport problem is allocated.")
2340           return self.getDomain().newTransportProblem( \
2341                                   self.getTheta(),
2342                                   self.getNumEquations(), \
2343                                   self.getFunctionSpace(), \
2344                                   self.__matrix_type)
2345              
2346         def __getNewSolutionVector(self):
2347             if self.getNumEquations() ==1 :
2348                    out=escript.Data(0.0,(),self.getFunctionSpace())
2349             else:
2350                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2351             return out
2352    
2353         def __getTransportProblem(self):
2354           if self.__reassemble:
2355                 self.__source=self.__getNewSolutionVector()
2356                 self.__transport_problem.reset()
2357                 self.getDomain().addPDEToTransportProblem(
2358                             self.__transport_problem,
2359                             self.__source,
2360                             self.__M,
2361                             self.__A,
2362                             self.__B,
2363                             self.__C,
2364                             self.__D,
2365                             self.__X,
2366                             self.__Y,
2367                             self.__d,
2368                             self.__y,
2369                             self.__d_contact,
2370                             self.__y_contact)
2371                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2372                 self.__reassemble=False
2373           return self.__transport_problem
2374         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2375                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2376                 if not M==None:
2377                      self.__reassemble=True
2378                      self.__M=M
2379                 if not A==None:
2380                      self.__reassemble=True
2381                      self.__A=A
2382                 if not B==None:
2383                      self.__reassemble=True
2384                      self.__B=B
2385                 if not C==None:
2386                      self.__reassemble=True
2387                      self.__C=C
2388                 if not D==None:
2389                      self.__reassemble=True
2390                      self.__D=D
2391                 if not X==None:
2392                      self.__reassemble=True
2393                      self.__X=X
2394                 if not Y==None:
2395                      self.__reassemble=True
2396                      self.__Y=Y
2397                 if not d==None:
2398                      self.__reassemble=True
2399                      self.__d=d
2400                 if not y==None:
2401                      self.__reassemble=True
2402                      self.__y=y
2403                 if not d_contact==None:
2404                      self.__reassemble=True
2405                      self.__d_contact=d_contact
2406                 if not y_contact==None:
2407                      self.__reassemble=True
2408                      self.__y_contact=y_contact
2409                 if not q==None:
2410                      self.__reassemble=True
2411                      self.__q=q
2412                 if not r==None:
2413                      self.__reassemble=True
2414                      self.__r=r
2415    
2416         def setInitialSolution(self,u):
2417                 if self.__useSUPG:
2418                     self.__u=util.interpolate(u,self.getFunctionSpace())
2419                 else:
2420                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2421    
2422         def solve(self,dt,**kwarg):
2423               if self.__useSUPG:
2424                    if self.__reassemble:
2425                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q)
2426                        self.__reassemble=False
2427                    dt2=self.getSafeTimeStepSize()
2428                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2429                    dt2=dt/nn
2430                    nnn=0
2431                    u=self.__u
2432                    self.trace("number of substeps is %d."%nn)
2433                    while nnn<nn :
2434                        self.__setSUPG(u,u,dt2/2)
2435                        u_half=self.__pde.getSolution(verbose=True)
2436                        self.__setSUPG(u,u_half,dt2)
2437                        u=self.__pde.getSolution(verbose=True)
2438                        nnn+=1
2439                    self.__u=u
2440                    return self.__u
2441               else:
2442                   kwarg["tolerance"]=self.__tolerance
2443                   tp=self.__getTransportProblem()
2444                   return tp.solve(self.__source,dt,kwarg)
2445         def __setSUPG(self,u0,u,dt):
2446                g=util.grad(u)
2447                X=0
2448                Y=self.__M*u0
2449                X=0
2450                if not self.__A.isEmpty():
2451                   X=X+dt*util.matrixmult(self.__A,g)
2452                if not self.__B.isEmpty():
2453                   X=X+dt*self.__B*u
2454                if not  self.__C.isEmpty():
2455                   Y=Y+dt*util.inner(self.__C,g)
2456                if not self.__D.isEmpty():
2457                   Y=Y+dt*self.__D*u
2458                if not self.__X.isEmpty():
2459                   X=X+dt*self.__X
2460                if not self.__Y.isEmpty():
2461                   Y=Y+dt*self.__Y
2462                self.__pde.setValue(X=X,Y=Y)
2463                if not self.__y.isEmpty():
2464                   self.__pde.setValue(y=dt*self.__y)
2465                if not self.__y_contact.isEmpty():
2466                   self.__pde.setValue(y=dt*self.__y_contact)
2467                self.__pde.setValue(r=u0)

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