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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 1659 by gross, Fri Jul 18 02:28:13 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       NONLINEAR_GMRES = 25
494    
495       SMALL_TOLERANCE=1.e-13
496       __PACKAGE_KEY="package"
497       __METHOD_KEY="method"
498       __SYMMETRY_KEY="symmetric"
499       __TOLERANCE_KEY="tolerance"
500       __PRECONDITIONER_KEY="preconditioner"
501    
502    
503       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
504         """
505         initializes a new linear PDE
506    
507         @param domain: domain of the PDE
508         @type domain: L{Domain<escript.Domain>}
509         @param numEquations: number of equations. If numEquations==None the number of equations
510                              is exracted from the PDE coefficients.
511         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
512                              is exracted from the PDE coefficients.
513         @param debug: if True debug informations are printed.
514    
515         """
516         super(LinearPDE, self).__init__()
517         #
518         #   the coefficients of the general PDE:
519         #
520         self.__COEFFICIENTS_OF_GENEARL_PDE={
521           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
522           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
523           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
524           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
525           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
526           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
527           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
528           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
529           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
530           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
531           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
532           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
534           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
535           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
536           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
537           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
540           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
541           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
542           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
543    
544         # COEFFICIENTS can be overwritten by subclasses:
545         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
546         self.__altered_coefficients=False
547       # initialize attributes       # initialize attributes
548       self.__debug=None       self.__debug=debug
549       self.__domain=domain       self.__domain=domain
550       self.__numEquations=numEquations       self.__numEquations=numEquations
551       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
552       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  
553    
554       # set some default values:       # set some default values:
555       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
556       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
557       self.__tolerance=1.e-8       self.__tolerance=1.e-8
558       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
559       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
560         self.__preconditioner=self.DEFAULT
561         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
562       self.__sym=False       self.__sym=False
      self.__lumping=False  
563    
564     def createCoefficient(self, name):       self.resetCoefficients()
565         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
566       # =============================================================================
567       #    general stuff:
568       # =============================================================================
569       def __str__(self):
570         """
571         returns string representation of the PDE
572    
573         @return: a simple representation of the PDE
574         @rtype: C{str}
575         """
576         return "<LinearPDE %d>"%id(self)
577       # =============================================================================
578       #    debug :
579       # =============================================================================
580       def setDebugOn(self):
581       """       """
582       create a data object corresponding to coefficient name       switches on debugging
      @param name:  
583       """       """
584       return escript.Data(shape = getShapeOfCoefficient(name), \       self.__debug=not None
                          what = getFunctionSpaceForCoefficient(name))  
585    
586     def __del__(self):     def setDebugOff(self):
      pass  
   
    def getCoefficient(self,name):  
587       """       """
588       return the value of the parameter name       switches off debugging
589         """
590         self.__debug=None
591    
592       @param name:     def trace(self,text):
593         """
594         print the text message if debugging is swiched on.
595         @param text: message
596         @type text: C{string}
597       """       """
598       return self.COEFFICIENTS[name].getValue()       if self.__debug: print "%s: %s"%(str(self),text)
599    
600     def getCoefficientOfPDE(self,name):     # =============================================================================
601       # some service functions:
602       # =============================================================================
603       def getDomain(self):
604       """       """
605       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.  
606    
607       @param name:       @return: the domain of the PDE
608         @rtype: L{Domain<escript.Domain>}
609       """       """
610       return self.getCoefficient(name)       return self.__domain
611    
612     def hasCoefficient(self,name):     def getDim(self):
613        """       """
614        return true if name is the name of a coefficient       returns the spatial dimension of the PDE
615    
616        @param name:       @return: the spatial dimension of the PDE domain
617        """       @rtype: C{int}
618        return self.COEFFICIENTS.has_key(name)       """
619         return self.getDomain().getDim()
620    
621     def getFunctionSpaceForEquation(self):     def getNumEquations(self):
622       """       """
623       return true if the test functions should use reduced order       returns the number of equations
624    
625         @return: the number of equations
626         @rtype: C{int}
627         @raise UndefinedPDEError: if the number of equations is not be specified yet.
628       """       """
629       return self.__row_function_space       if self.__numEquations==None:
630             raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
631         else:
632             return self.__numEquations
633    
634     def getFunctionSpaceForSolution(self):     def getNumSolutions(self):
635       """       """
636       return true if the interpolation of the solution should use reduced order       returns the number of unknowns
637    
638         @return: the number of unknowns
639         @rtype: C{int}
640         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
641       """       """
642       return self.__column_function_space       if self.__numSolutions==None:
643            raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
644         else:
645            return self.__numSolutions
646    
647     def setValue(self,**coefficients):     def reduceEquationOrder(self):
648        """       """
649        sets new values to coefficients       return status for order reduction for equation
650    
651        @param coefficients:       @return: return True is reduced interpolation order is used for the represenation of the equation
652        """       @rtype: L{bool}
653        self.__setValue(**coefficients)       """
654               return self.__reduce_equation_order
655    
656     def cleanCoefficients(self):     def reduceSolutionOrder(self):
657       """       """
658       resets all coefficients to default values.       return status for order reduction for the solution
659    
660         @return: return True is reduced interpolation order is used for the represenation of the solution
661         @rtype: L{bool}
662       """       """
663       for i in self.COEFFICIENTS.iterkeys():       return self.__reduce_solution_order
          self.COEFFICIENTS[i].resetValue()  
664    
665     def createNewCoefficient(self,name):     def getFunctionSpaceForEquation(self):
666       """       """
667       returns a new coefficient appropriate for coefficient name:       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
668    
669         @return: representation space of equation
670         @rtype: L{FunctionSpace<escript.FunctionSpace>}
671       """       """
672       return escript.Data(0,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))       if self.reduceEquationOrder():
673                   return escript.ReducedSolution(self.getDomain())
674         else:
675             return escript.Solution(self.getDomain())
676    
677     def getShapeOfCoefficient(self,name):     def getFunctionSpaceForSolution(self):
678       """       """
679       return the shape of the coefficient name       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
680    
681       @param name:       @return: representation space of solution
682         @rtype: L{FunctionSpace<escript.FunctionSpace>}
683       """       """
684       if self.hasCoefficient(name):       if self.reduceSolutionOrder():
685          return self.COEFFICIENTS[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           return escript.ReducedSolution(self.getDomain())
686       else:       else:
687          raise ValueError,"Solution coefficient %s requested"%name           return escript.Solution(self.getDomain())
688    
689     def getFunctionSpaceForCoefficient(self,name):  
690       def getOperator(self):
691       """       """
692       return the atoms of the coefficient name       provides access to the operator of the PDE
693    
694       @param name:       @return: the operator of the PDE
695         @rtype: L{Operator<escript.Operator>}
696       """       """
697       if self.hasCoefficient(name):       m=self.getSystem()[0]
698          return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())       if self.isUsingLumping():
699             return self.copyConstraint(1./m)
700       else:       else:
701          raise ValueError,"Solution coefficient %s requested"%name           return m
702    
703     def alteredCoefficient(self,name):     def getRightHandSide(self):
704       """       """
705       announce that coefficient name has been changed       provides access to the right hand side of the PDE
706         @return: the right hand side of the PDE
707         @rtype: L{Data<escript.Data>}
708         """
709         r=self.getSystem()[1]
710         if self.isUsingLumping():
711             return self.copyConstraint(r)
712         else:
713             return r
714    
715       @param name:     def applyOperator(self,u=None):
716       """       """
717       if self.hasCoefficient(name):       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
718          if self.COEFFICIENTS[name].isAlteringOperator(): self.__rebuildOperator()  
719          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}
720                   the current solution is used.
721         @type u: L{Data<escript.Data>} or None
722         @return: image of u
723         @rtype: L{Data<escript.Data>}
724         """
725         if u==None:
726            return self.getOperator()*self.getSolution()
727       else:       else:
728          raise ValueError,"unknown coefficient %s requested"%name          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
729    
730     # ===== debug ==============================================================     def getResidual(self,u=None):
731     def setDebugOn(self):       """
732         """       return the residual of u or the current solution if u is not present.
733    
734         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
735                   the current solution is used.
736         @type u: L{Data<escript.Data>} or None
737         @return: residual of u
738         @rtype: L{Data<escript.Data>}
739         """
740         return self.applyOperator(u)-self.getRightHandSide()
741    
742       def checkSymmetry(self,verbose=True):
743          """
744          test the PDE for symmetry.
745    
746          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
747          @type verbose: C{bool}
748          @return:  True if the PDE is symmetric.
749          @rtype: L{Data<escript.Data>}
750          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
751          """
752          verbose=verbose or self.__debug
753          out=True
754          if self.getNumSolutions()!=self.getNumEquations():
755             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
756             out=False
757          else:
758             A=self.getCoefficientOfGeneralPDE("A")
759             if not A.isEmpty():
760                tol=util.Lsup(A)*self.SMALL_TOLERANCE
761                if self.getNumSolutions()>1:
762                   for i in range(self.getNumEquations()):
763                      for j in range(self.getDim()):
764                         for k in range(self.getNumSolutions()):
765                            for l in range(self.getDim()):
766                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
767                                   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)
768                                   out=False
769                else:
770                   for j in range(self.getDim()):
771                      for l in range(self.getDim()):
772                         if util.Lsup(A[j,l]-A[l,j])>tol:
773                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
774                            out=False
775             B=self.getCoefficientOfGeneralPDE("B")
776             C=self.getCoefficientOfGeneralPDE("C")
777             if B.isEmpty() and not C.isEmpty():
778                if verbose: print "non-symmetric PDE because B is not present but C is"
779                out=False
780             elif not B.isEmpty() and C.isEmpty():
781                if verbose: print "non-symmetric PDE because C is not present but B is"
782                out=False
783             elif not B.isEmpty() and not C.isEmpty():
784                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
785                if self.getNumSolutions()>1:
786                   for i in range(self.getNumEquations()):
787                       for j in range(self.getDim()):
788                          for k in range(self.getNumSolutions()):
789                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
790                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
791                                  out=False
792                else:
793                   for j in range(self.getDim()):
794                      if util.Lsup(B[j]-C[j])>tol:
795                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
796                         out=False
797             if self.getNumSolutions()>1:
798               D=self.getCoefficientOfGeneralPDE("D")
799               if not D.isEmpty():
800                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
801                 for i in range(self.getNumEquations()):
802                    for k in range(self.getNumSolutions()):
803                      if util.Lsup(D[i,k]-D[k,i])>tol:
804                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
805                          out=False
806               d=self.getCoefficientOfGeneralPDE("d")
807               if not d.isEmpty():
808                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
809                 for i in range(self.getNumEquations()):
810                    for k in range(self.getNumSolutions()):
811                      if util.Lsup(d[i,k]-d[k,i])>tol:
812                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
813                          out=False
814               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
815               if not d_contact.isEmpty():
816                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
817                 for i in range(self.getNumEquations()):
818                    for k in range(self.getNumSolutions()):
819                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
820                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
821                          out=False
822             # and now the reduced coefficients
823             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
824             if not A_reduced.isEmpty():
825                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
826                if self.getNumSolutions()>1:
827                   for i in range(self.getNumEquations()):
828                      for j in range(self.getDim()):
829                         for k in range(self.getNumSolutions()):
830                            for l in range(self.getDim()):
831                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
832                                   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)
833                                   out=False
834                else:
835                   for j in range(self.getDim()):
836                      for l in range(self.getDim()):
837                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
838                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
839                            out=False
840             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
841             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
842             if B_reduced.isEmpty() and not C_reduced.isEmpty():
843                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
844                out=False
845             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
846                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
847                out=False
848             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
849                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
850                if self.getNumSolutions()>1:
851                   for i in range(self.getNumEquations()):
852                       for j in range(self.getDim()):
853                          for k in range(self.getNumSolutions()):
854                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
855                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
856                                  out=False
857                else:
858                   for j in range(self.getDim()):
859                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
860                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
861                         out=False
862             if self.getNumSolutions()>1:
863               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
864               if not D_reduced.isEmpty():
865                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
866                 for i in range(self.getNumEquations()):
867                    for k in range(self.getNumSolutions()):
868                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
869                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
870                          out=False
871               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
872               if not d_reduced.isEmpty():
873                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
874                 for i in range(self.getNumEquations()):
875                    for k in range(self.getNumSolutions()):
876                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
877                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
878                          out=False
879               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
880               if not d_contact_reduced.isEmpty():
881                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
882                 for i in range(self.getNumEquations()):
883                    for k in range(self.getNumSolutions()):
884                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
885                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
886                          out=False
887          return out
888    
889       def getSolution(self,**options):
890         """         """
891         self.__debug=not None         returns the solution of the PDE. If the solution is not valid the PDE is solved.
892    
893     def setDebugOff(self):         @return: the solution
894           @rtype: L{Data<escript.Data>}
895           @param options: solver options
896           @keyword verbose: True to get some information during PDE solution
897           @type verbose: C{bool}
898           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
899                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
900           @keyword iter_max: maximum number of iteration steps allowed.
901           @keyword drop_tolerance: threshold for drupping in L{ILUT}
902           @keyword drop_storage: maximum of allowed memory in L{ILUT}
903           @keyword truncation: maximum number of residuals in L{GMRES}
904           @keyword restart: restart cycle length in L{GMRES}
905         """         """
906           if not self.__solution_isValid:
907              mat,f=self.getSystem()
908              if self.isUsingLumping():
909                 self.__solution=self.copyConstraint(f*mat)
910              else:
911                 options[self.__TOLERANCE_KEY]=self.getTolerance()
912                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
913                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
914                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
915                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
916                 self.trace("PDE is resolved.")
917                 self.trace("solver options: %s"%str(options))
918                 self.__solution=mat.solve(f,options)
919              self.__solution_isValid=True
920           return self.__solution
921    
922       def getFlux(self,u=None):
923         """
924         returns the flux M{J} for a given M{u}
925    
926         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]}
927    
928         or
929    
930         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
931    
932         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
933         @type u: L{Data<escript.Data>} or None
934         @return: flux
935         @rtype: L{Data<escript.Data>}
936         """
937         if u==None: u=self.getSolution()
938         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
939               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
940               -util.self.getCoefficientOfGeneralPDE("X") \
941               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
942               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
943               -util.self.getCoefficientOfGeneralPDE("X_reduced")
944       # =============================================================================
945       #   solver settings:
946       # =============================================================================
947       def setSolverMethod(self,solver=None,preconditioner=None):
948         """         """
949         self.__debug=None         sets a new solver
950    
951           @param solver: sets a new solver method.
952           @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}
953           @param preconditioner: sets a new solver method.
954           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
955           """
956           if solver==None: solver=self.__solver_method
957           if preconditioner==None: preconditioner=self.__preconditioner
958           if solver==None: solver=self.DEFAULT
959           if preconditioner==None: preconditioner=self.DEFAULT
960           if not (solver,preconditioner)==self.getSolverMethod():
961               self.__solver_method=solver
962               self.__preconditioner=preconditioner
963               self.__checkMatrixType()
964               self.trace("New solver is %s"%self.getSolverMethodName())
965    
966     def debug(self):     def getSolverMethodName(self):
967         """         """
968         returns true if the PDE is in the debug mode         returns the name of the solver currently used
969    
970           @return: the name of the solver currently used.
971           @rtype: C{string}
972         """         """
        return self.__debug  
973    
974     #===== Lumping ===========================         m=self.getSolverMethod()
975     def setLumpingOn(self):         p=self.getSolverPackage()
976        """         method=""
977        indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
978        """         elif m[0]==self.DIRECT: method= "DIRECT"
979        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
980           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
981           self.__rebuildOperator()         elif m[0]==self.PCG: method= "PCG"
982           self.__lumping=True         elif m[0]==self.CR: method= "CR"
983           elif m[0]==self.CGS: method= "CGS"
984           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
985           elif m[0]==self.SSOR: method= "SSOR"
986           elif m[0]==self.GMRES: method= "GMRES"
987           elif m[0]==self.PRES20: method= "PRES20"
988           elif m[0]==self.LUMPING: method= "LUMPING"
989           elif m[0]==self.AMG: method= "AMG"
990           if m[1]==self.DEFAULT: method+="+DEFAULT"
991           elif m[1]==self.JACOBI: method+= "+JACOBI"
992           elif m[1]==self.ILU0: method+= "+ILU0"
993           elif m[1]==self.ILUT: method+= "+ILUT"
994           elif m[1]==self.SSOR: method+= "+SSOR"
995           elif m[1]==self.AMG: method+= "+AMG"
996           elif m[1]==self.RILU: method+= "+RILU"
997           if p==self.DEFAULT: package="DEFAULT"
998           elif p==self.PASO: package= "PASO"
999           elif p==self.MKL: package= "MKL"
1000           elif p==self.SCSL: package= "SCSL"
1001           elif p==self.UMFPACK: package= "UMFPACK"
1002           elif p==self.TRILINOS: package= "TRILINOS"
1003           else : method="unknown"
1004           return "%s solver of %s package"%(method,package)
1005    
    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  
1006    
1007     def setLumping(self,flag=False):     def getSolverMethod(self):
1008        """         """
1009        set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
1010    
1011     def isUsingLumping(self):         @return: the solver method currently be used.
1012        """         @rtype: C{int}
1013                 """
1014        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
1015    
1016     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
1017         """         """
1018         sets a new solver         sets a new solver package
1019    
1020           @param package: sets a new solver method.
1021           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1022         """         """
1023         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
1024             self.__solver_method=solver         if not package==self.getSolverPackage():
1025             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__solver_package=package
1026             self.__checkMatrixType()             self.__checkMatrixType()
1027               self.trace("New solver is %s"%self.getSolverMethodName())
1028    
1029     def getSolverMethod(self):     def getSolverPackage(self):
1030         """         """
1031         returns the solver method         returns the package of the solver
1032    
1033           @return: the solver package currently being used.
1034           @rtype: C{int}
1035         """         """
1036         return self.__solver_method         return self.__solver_package
1037    
1038       def isUsingLumping(self):
1039          """
1040          checks if matrix lumping is used a solver method
1041    
1042          @return: True is lumping is currently used a solver method.
1043          @rtype: C{bool}
1044          """
1045          return self.getSolverMethod()[0]==self.LUMPING
1046    
    #============ tolerance business =========================================================  
1047     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1048         """         """
1049         resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1050    
1051           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1052    
1053           defines the stopping criterion.
1054    
1055           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1056                       the system will be resolved.
1057           @type tol: positive C{float}
1058           @raise ValueError: if tolerance is not positive.
1059         """         """
1060         if not tol>0:         if not tol>0:
1061             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1062         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1063         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1064         self.__tolerance=tol         self.__tolerance=tol
1065         return         return
1066    
1067     def getTolerance(self):     def getTolerance(self):
1068         """         """
1069         returns the tolerance set for the solution         returns the tolerance set for the solution
1070    
1071           @return: tolerance currently used.
1072           @rtype: C{float}
1073         """         """
1074         return self.__tolerance         return self.__tolerance
1075    
1076     #===== symmetry  flag ==========================     # =============================================================================
1077       #    symmetry  flag:
1078       # =============================================================================
1079     def isSymmetric(self):     def isSymmetric(self):
1080        """        """
1081        returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1082    
1083          @return: True is a symmetric PDE is indicated, otherwise False is returned
1084          @rtype: C{bool}
1085        """        """
1086        return self.__sym        return self.__sym
1087    
1088     def setSymmetryOn(self):     def setSymmetryOn(self):
1089        """        """
1090        sets the symmetry flag to true        sets the symmetry flag.
1091        """        """
1092        if not self.isSymmetric():        if not self.isSymmetric():
1093           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1094           self.__sym=True           self.__sym=True
1095           self.__checkMatrixType()           self.__checkMatrixType()
1096    
1097     def setSymmetryOff(self):     def setSymmetryOff(self):
1098        """        """
1099        sets the symmetry flag to false        removes the symmetry flag.
1100        """        """
1101        if self.isSymmetric():        if self.isSymmetric():
1102           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1103           self.__sym=False           self.__sym=False
1104           self.__checkMatrixType()           self.__checkMatrixType()
1105    
1106     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1107       """        """
1108       sets the symmetry flag to flag        sets the symmetry flag to flag
1109    
1110       @param flag:        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1111       """        @type flag: C{bool}
1112       if flag:        """
1113          self.setSymmetryOn()        if flag:
1114       else:           self.setSymmetryOn()
1115          self.setSymmetryOff()        else:
1116             self.setSymmetryOff()
1117    
1118     #===== order reduction ==========================     # =============================================================================
1119       # function space handling for the equation as well as the solution
1120       # =============================================================================
1121     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1122       """       """
1123       switches to on reduced order       switches on reduced order for solution and equation representation
1124    
1125         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1126       """       """
1127       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1128       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1129    
1130     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1131       """       """
1132       switches to full order       switches off reduced order for solution and equation representation
1133    
1134         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1135       """       """
1136       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1137       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1138    
1139     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1140       """       """
1141       sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1142         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1143       @param flag:                    if flag is not present order reduction is switched off
1144         @type flag: C{bool}
1145         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1146       """       """
1147       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1148       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1149    
1150     #===== order reduction solution ==========================  
1151     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1152       """       """
1153       switches to reduced order to interpolate solution       switches on reduced order for solution representation
1154    
1155         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1156       """       """
1157       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1158       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1159           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1160           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1161           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1162             self.__resetSystem()
1163    
1164     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1165       """       """
1166       switches to full order to interpolate solution       switches off reduced order for solution representation
1167    
1168         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1169       """       """
1170       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1171       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1172           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1173           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1174           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1175             self.__resetSystem()
1176    
1177     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1178       """       """
1179       sets order for test functions according to flag       sets order for test functions according to flag
1180    
1181       @param flag:       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1182                      if flag is not present order reduction is switched off
1183         @type flag: C{bool}
1184         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1185       """       """
1186       if flag:       if flag:
1187          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1188       else:       else:
1189          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1190                                                                                                                                                              
    #===== order reduction equation ==========================  
1191     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1192       """       """
1193       switches to reduced order for test functions       switches on reduced order for equation representation
1194    
1195         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1196       """       """
1197       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1198       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1199           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1200           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1201           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1202             self.__resetSystem()
1203    
1204     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1205       """       """
1206       switches to full order for test functions       switches off reduced order for equation representation
1207    
1208         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1209       """       """
1210       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1211       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1212           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1213           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1214           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1215             self.__resetSystem()
1216    
1217     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1218       """       """
1219       sets order for test functions according to flag       sets order for test functions according to flag
1220    
1221       @param flag:       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1222                      if flag is not present order reduction is switched off
1223         @type flag: C{bool}
1224         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1225       """       """
1226       if flag:       if flag:
1227          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1228       else:       else:
1229          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
1230                                                                                                                                                              
1231     # ==== initialization =====================================================================     # =============================================================================
1232       # private method:
1233       # =============================================================================
1234       def __checkMatrixType(self):
1235         """
1236         reassess the matrix type and, if a new matrix is needed, resets the system.
1237         """
1238         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1239         if not new_matrix_type==self.__matrix_type:
1240             self.trace("Matrix type is now %d."%new_matrix_type)
1241             self.__matrix_type=new_matrix_type
1242             self.__resetSystem()
1243       #
1244       #   rebuild switches :
1245       #
1246       def __invalidateSolution(self):
1247           """
1248           indicates the PDE has to be resolved if the solution is requested
1249           """
1250           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1251           self.__solution_isValid=False
1252    
1253       def __invalidateOperator(self):
1254           """
1255           indicates the operator has to be rebuilt next time it is used
1256           """
1257           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1258           self.__invalidateSolution()
1259           self.__operator_is_Valid=False
1260    
1261       def __invalidateRightHandSide(self):
1262           """
1263           indicates the right hand side has to be rebuild next time it is used
1264           """
1265           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1266           self.__invalidateSolution()
1267           self.__righthandside_isValid=False
1268    
1269       def __invalidateSystem(self):
1270           """
1271           annonced that everthing has to be rebuild:
1272           """
1273           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1274           self.__invalidateSolution()
1275           self.__invalidateOperator()
1276           self.__invalidateRightHandSide()
1277    
1278       def __resetSystem(self):
1279           """
1280           annonced that everthing has to be rebuild:
1281           """
1282           self.trace("New System is built from scratch.")
1283           self.__operator=escript.Operator()
1284           self.__operator_is_Valid=False
1285           self.__righthandside=escript.Data()
1286           self.__righthandside_isValid=False
1287           self.__solution=escript.Data()
1288           self.__solution_isValid=False
1289       #
1290       #    system initialization:
1291       #
1292     def __getNewOperator(self):     def __getNewOperator(self):
1293         """         """
1294           returns an instance of a new operator
1295         """         """
1296           self.trace("New operator is allocated.")
1297         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1298                             self.getNumEquations(), \                             self.getNumEquations(), \
1299                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 565  class LinearPDE: Line 1301  class LinearPDE:
1301                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1302                             self.__matrix_type)                             self.__matrix_type)
1303    
1304     def __makeFreshRightHandSide(self):     def __getNewRightHandSide(self):
1305         """         """
1306           returns an instance of a new right hand side
1307         """         """
1308         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New right hand side is allocated.")
1309         if self.getNumEquations()>1:         if self.getNumEquations()>1:
1310             self.__righthandside=escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1311         else:         else:
1312             self.__righthandside=escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)             return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
        return self.__righthandside  
1313    
1314     def __getNewSolution(self):     def __getNewSolution(self):
1315         """         """
1316           returns an instance of a new solution
1317         """         """
1318         if self.debug() : print "PDE Debug: New right hand side allocated"         self.trace("New solution is allocated.")
1319         if self.getNumSolutions()>1:         if self.getNumSolutions()>1:
1320             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1321         else:         else:
1322             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)             return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1323    
1324       def __makeFreshSolution(self):
1325           """
1326           makes sure that the solution is instantiated and returns it initialized by zeros
1327           """
1328           if self.__solution.isEmpty():
1329               self.__solution=self.__getNewSolution()
1330           else:
1331               self.__solution*=0
1332               self.trace("Solution is reset to zero.")
1333           return self.__solution
1334    
1335       def __makeFreshRightHandSide(self):
1336           """
1337           makes sure that the right hand side is instantiated and returns it initialized by zeros
1338           """
1339           if self.__righthandside.isEmpty():
1340               self.__righthandside=self.__getNewRightHandSide()
1341           else:
1342               self.__righthandside.setToZero()
1343               self.trace("Right hand side is reset to zero.")
1344           return self.__righthandside
1345    
1346     def __makeFreshOperator(self):     def __makeFreshOperator(self):
1347         """         """
1348           makes sure that the operator is instantiated and returns it initialized by zeros
1349         """         """
1350         if self.__operator.isEmpty():         if self.__operator.isEmpty():
1351             self.__operator=self.__getNewOperator()             self.__operator=self.__getNewOperator()
            if self.debug() : print "PDE Debug: New operator allocated"  
1352         else:         else:
1353             self.__operator.setValue(0.)             self.__operator.resetValues()
1354             self.__operator.resetSolver()             self.trace("Operator reset to zero")
            if self.debug() : print "PDE Debug: Operator reset to zero"  
1355         return self.__operator         return self.__operator
1356    
1357     #============ some serivice functions  =====================================================     def __applyConstraint(self):
1358     def getDomain(self):         """
1359           applies the constraints defined by q and r to the system
1360           """
1361           if not self.isUsingLumping():
1362              q=self.getCoefficientOfGeneralPDE("q")
1363              r=self.getCoefficientOfGeneralPDE("r")
1364              if not q.isEmpty() and not self.__operator.isEmpty():
1365                 # q is the row and column mask to indicate where constraints are set:
1366                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1367                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1368                 u=self.__getNewSolution()
1369                 if r.isEmpty():
1370                    r_s=self.__getNewSolution()
1371                 else:
1372                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1373                 u.copyWithMask(r_s,col_q)
1374                 if not self.__righthandside.isEmpty():
1375                    self.__righthandside-=self.__operator*u
1376                    self.__righthandside=self.copyConstraint(self.__righthandside)
1377                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1378       # =============================================================================
1379       # function giving access to coefficients of the general PDE:
1380       # =============================================================================
1381       def getCoefficientOfGeneralPDE(self,name):
1382         """
1383         return the value of the coefficient name of the general PDE.
1384    
1385         @note: This method is called by the assembling routine it can be overwritten
1386               to map coefficients of a particular PDE to the general PDE.
1387         @param name: name of the coefficient requested.
1388         @type name: C{string}
1389         @return: the value of the coefficient  name
1390         @rtype: L{Data<escript.Data>}
1391         @raise IllegalCoefficient: if name is not one of coefficients
1392                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1393                      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}.
1394       """       """
1395       returns the domain of the PDE       if self.hasCoefficientOfGeneralPDE(name):
1396            return self.getCoefficient(name)
1397         else:
1398            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1399    
1400       def hasCoefficientOfGeneralPDE(self,name):
1401       """       """
1402       return self.__domain       checks if name is a the name of a coefficient of the general PDE.
1403    
1404         @param name: name of the coefficient enquired.
1405         @type name: C{string}
1406         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1407         @rtype: C{bool}
1408    
    def getDim(self):  
1409       """       """
1410       returns the spatial dimension of the PDE       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1411    
1412       def createCoefficientOfGeneralPDE(self,name):
1413       """       """
1414       return self.getDomain().getDim()       returns a new instance of a coefficient for coefficient name of the general PDE
1415    
1416     def getNumEquations(self):       @param name: name of the coefficient requested.
1417         @type name: C{string}
1418         @return: a coefficient name initialized to 0.
1419         @rtype: L{Data<escript.Data>}
1420         @raise IllegalCoefficient: if name is not one of coefficients
1421                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1422                      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}.
1423       """       """
1424       returns the number of equations       if self.hasCoefficientOfGeneralPDE(name):
1425            return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1426         else:
1427            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1428    
1429       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1430       """       """
1431       if self.__numEquations>0:       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1432           return self.__numEquations  
1433         @param name: name of the coefficient enquired.
1434         @type name: C{string}
1435         @return: the function space to be used for coefficient name
1436         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1437         @raise IllegalCoefficient: if name is not one of coefficients
1438                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1439                      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}.
1440         """
1441         if self.hasCoefficientOfGeneralPDE(name):
1442            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1443       else:       else:
1444           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1445    
1446     def getNumSolutions(self):     def getShapeOfCoefficientOfGeneralPDE(self,name):
1447       """       """
1448       returns the number of unknowns       return the shape of the coefficient name of the general PDE
1449    
1450         @param name: name of the coefficient enquired.
1451         @type name: C{string}
1452         @return: the shape of the coefficient name
1453         @rtype: C{tuple} of C{int}
1454         @raise IllegalCoefficient: if name is not one of coefficients
1455                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1456                      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}.
1457       """       """
1458       if self.__numSolutions>0:       if self.hasCoefficientOfGeneralPDE(name):
1459          return self.__numSolutions          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1460       else:       else:
1461          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1462    
1463       # =============================================================================
1464       # functions giving access to coefficients of a particular PDE implementation:
1465       # =============================================================================
1466       def getCoefficient(self,name):
1467         """
1468         returns the value of the coefficient name
1469    
1470     def checkSymmetry(self,verbose=True):       @param name: name of the coefficient requested.
1471        """       @type name: C{string}
1472        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
1473        """       @rtype: L{Data<escript.Data>}
1474        verbose=verbose or self.debug()       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1475        out=True       """
1476        if self.getNumSolutions()!=self.getNumEquations():       if self.hasCoefficient(name):
1477           if verbose: print "non-symmetric PDE because of different number of equations and solutions"           return self.COEFFICIENTS[name].getValue()
1478           out=False       else:
1479        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  
1480    
1481     def getFlux(self,u):     def hasCoefficient(self,name):
1482         """       """
1483         returns the flux J_ij for a given u       return True if name is the name of a coefficient
1484    
1485         \f[       @param name: name of the coefficient enquired.
1486         J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}       @type name: C{string}
1487         \f]       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1488         @rtype: C{bool}
1489         """
1490         return self.COEFFICIENTS.has_key(name)
1491    
1492         @param u: argument of the operator     def createCoefficient(self, name):
1493         """       """
1494         raise SystemError,"getFlux is not implemented yet"       create a L{Data<escript.Data>} object corresponding to coefficient name
        return None  
1495    
1496     def applyOperator(self,u):       @return: a coefficient name initialized to 0.
1497         """       @rtype: L{Data<escript.Data>}
1498         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.
1499         """
1500         if self.hasCoefficient(name):
1501            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1502         else:
1503            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1504    
1505         @param u: argument of the operator     def getFunctionSpaceForCoefficient(self,name):
1506         """       """
1507         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  
1508    
1509         @param u:       @param name: name of the coefficient enquired.
1510         """       @type name: C{string}
1511         return self.applyOperator(u)-self.getRightHandSide()       @return: the function space to be used for coefficient name
1512         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1513         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1514         """
1515         if self.hasCoefficient(name):
1516            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1517         else:
1518            raise ValueError,"unknown coefficient %s requested"%name
1519       def getShapeOfCoefficient(self,name):
1520         """
1521         return the shape of the coefficient name
1522    
1523         @param name: name of the coefficient enquired.
1524         @type name: C{string}
1525         @return: the shape of the coefficient name
1526         @rtype: C{tuple} of C{int}
1527         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1528         """
1529         if self.hasCoefficient(name):
1530            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1531         else:
1532            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1533    
1534       def resetCoefficients(self):
1535         """
1536         resets all coefficients to there default values.
1537         """
1538         for i in self.COEFFICIENTS.iterkeys():
1539             self.COEFFICIENTS[i].resetValue()
1540    
1541       def alteredCoefficient(self,name):
1542         """
1543         announce that coefficient name has been changed
1544    
1545         @param name: name of the coefficient enquired.
1546         @type name: C{string}
1547         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1548         @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.
1549         """
1550         if self.hasCoefficient(name):
1551            self.trace("Coefficient %s has been altered."%name)
1552            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1553               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1554               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1555         else:
1556            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1557    
1558       def copyConstraint(self,u):
1559          """
1560          copies the constraint into u and returns u.
1561    
1562          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1563          @type u: L{Data<escript.Data>}
1564          @return: the input u modified by the constraints.
1565          @rtype: L{Data<escript.Data>}
1566          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1567          """
1568          q=self.getCoefficientOfGeneralPDE("q")
1569          r=self.getCoefficientOfGeneralPDE("r")
1570          if not q.isEmpty():
1571             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1572             if r.isEmpty():
1573                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1574             else:
1575                 r=escript.Data(r,u.getFunctionSpace())
1576             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1577          return u
1578    
1579     def __setValue(self,**coefficients):     def setValue(self,**coefficients):
1580        """        """
1581        sets new values to coefficient        sets new values to coefficients
1582    
1583        @param coefficients:        @param coefficients: new values assigned to coefficients
1584          @keyword A: value for coefficient A.
1585          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1586          @keyword A_reduced: value for coefficient A_reduced.
1587          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1588          @keyword B: value for coefficient B
1589          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1590          @keyword B_reduced: value for coefficient B_reduced
1591          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1592          @keyword C: value for coefficient C
1593          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1594          @keyword C_reduced: value for coefficient C_reduced
1595          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1596          @keyword D: value for coefficient D
1597          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1598          @keyword D_reduced: value for coefficient D_reduced
1599          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1600          @keyword X: value for coefficient X
1601          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1602          @keyword X_reduced: value for coefficient X_reduced
1603          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1604          @keyword Y: value for coefficient Y
1605          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1606          @keyword Y_reduced: value for coefficient Y_reduced
1607          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1608          @keyword d: value for coefficient d
1609          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1610          @keyword d_reduced: value for coefficient d_reduced
1611          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1612          @keyword y: value for coefficient y
1613          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1614          @keyword d_contact: value for coefficient d_contact
1615          @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>}.
1616          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1617          @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>}.
1618          @keyword y_contact: value for coefficient y_contact
1619          @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>}.
1620          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1621          @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>}.
1622          @keyword r: values prescribed to the solution at the locations of constraints
1623          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1624                   depending of reduced order is used for the solution.
1625          @keyword q: mask for location of constraints
1626          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1627                   depending of reduced order is used for the representation of the equation.
1628          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1629        """        """
1630        # check if the coefficients are  legal:        # check if the coefficients are  legal:
1631        for i in coefficients.iterkeys():        for i in coefficients.iterkeys():
1632           if not self.hasCoefficient(i):           if not self.hasCoefficient(i):
1633              raise ValueError,"Attempt to set unknown coefficient %s"%i              raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1634        # 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:
1635        if self.__numEquations<1 or self.__numSolutions<1:        if self.__numEquations==None or self.__numSolutions==None:
1636           for i,d in coefficients.iteritems():           for i,d in coefficients.iteritems():
1637              if hasattr(d,"shape"):              if hasattr(d,"shape"):
1638                  s=d.shape                  s=d.shape
# Line 739  class LinearPDE: Line 1642  class LinearPDE:
1642                  s=numarray.array(d).shape                  s=numarray.array(d).shape
1643              if s!=None:              if s!=None:
1644                  # get number of equations and number of unknowns:                  # get number of equations and number of unknowns:
1645                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(s,self.getDim())                  res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1646                  if res==None:                  if res==None:
1647                      raise ValueError,"Illegal shape %s of coefficient %s"%(s,i)                      raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1648                  else:                  else:
1649                      if self.__numEquations<1: self.__numEquations=res[0]                      if self.__numEquations==None: self.__numEquations=res[0]
1650                      if self.__numSolutions<1: self.__numSolutions=res[1]                      if self.__numSolutions==None: self.__numSolutions=res[1]
1651        if self.__numEquations<1: raise ValueError,"unidententified number of equations"        if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1652        if self.__numSolutions<1: raise ValueError,"unidententified number of solutions"        if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1653        # 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:
1654        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1655          if d==None:          try:
1656               d2=escript.Data()             self.COEFFICIENTS[i].setValue(self.getDomain(),
1657          elif isinstance(d,escript.Data):                                           self.getNumEquations(),self.getNumSolutions(),
1658               if d.isEmpty():                                           self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1659                  d2=d             self.alteredCoefficient(i)
1660               else:          except IllegalCoefficientFunctionSpace,m:
1661                  d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              # if the function space is wrong then we try the reduced version:
1662          else:              i_red=i+"_reduced"
1663                d2=escript.Data(d,self.getFunctionSpaceForCoefficient(i))              if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1664          if not d2.isEmpty():                  try:
1665             if not self.getShapeOfCoefficient(i)==d2.getShape():                      self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1666                 raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),d2.getShape())                                                        self.getNumEquations(),self.getNumSolutions(),
1667          # overwrite new values:                                                        self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1668          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i                      self.alteredCoefficient(i_red)
1669          self.COEFFICIENTS[i].setValue(d2)                  except IllegalCoefficientValue,m:
1670          self.alteredCoefficient(i)                      raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1671                          except IllegalCoefficientFunctionSpace,m:
1672        # reset the HomogeneousConstraintFlag:                      raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673        self.__setHomogeneousConstraintFlag()              else:
1674        if len(coefficients)>0 and not self.isUsingLumping() and not self.__homogeneous_constraint: self.__rebuildSystem()                  raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1675            except IllegalCoefficientValue,m:
1676     def __setHomogeneousConstraintFlag(self):             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1677        """        self.__altered_coefficients=True
1678        checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.        # check if the systrem is inhomogeneous:
1679        """        if len(coefficients)>0 and not self.isUsingLumping():
1680        self.__homogeneous_constraint=True           q=self.getCoefficientOfGeneralPDE("q")
1681        q=self.getCoefficientOfPDE("q")           r=self.getCoefficientOfGeneralPDE("r")
1682        r=self.getCoefficientOfPDE("r")           homogeneous_constraint=True
1683        if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1684           if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False               if util.Lsup(q*r)>0.:
1685        if self.debug():                 self.trace("Inhomogeneous constraint detected.")
1686             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.)  
1687    
1688     def getSystem(self):     def getSystem(self):
1689         """         """
1690         return the operator and right hand side of the PDE         return the operator and right hand side of the PDE
1691    
1692           @return: the discrete version of the PDE
1693           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1694         """         """
1695         if not self.__operator_isValid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1696            if self.isUsingLumping():            if self.isUsingLumping():
1697                if not self.__operator_isValid:                if not self.__operator_is_Valid:
1698                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1699                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1700                   if not self.getCoefficientOfPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1701                            raise Warning,"Lumped matrix does not allow coefficient A"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1702                   if not self.getCoefficientOfPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1703                            raise Warning,"Lumped matrix does not allow coefficient B"                        raise ValueError,"coefficient B in lumped matrix may not be present."
1704                   if not self.getCoefficientOfPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1705                            raise Warning,"Lumped matrix does not allow coefficient C"                        raise ValueError,"coefficient C in lumped matrix may not be present."
1706                   if self.debug() : print "PDE Debug: New lumped operator is built."                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1707                   mat=self.__getNewOperator()                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1708                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1709                             self.getCoefficientOfPDE("A"), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1710                             self.getCoefficientOfPDE("B"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1711                             self.getCoefficientOfPDE("C"), \                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1712                             self.getCoefficientOfPDE("D"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1713                             escript.Data(), \                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1714                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1715                             self.getCoefficientOfPDE("d"), \                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1716                             escript.Data(),\                   D=self.getCoefficientOfGeneralPDE("D")
1717                             self.getCoefficientOfPDE("d_contact"), \                   d=self.getCoefficientOfGeneralPDE("d")
1718                             escript.Data())                   D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1719                   self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)                   d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1720                   self.__applyConstraint()                   if not D.isEmpty():
1721                   self.__operator_isValid=True                       if self.getNumSolutions()>1:
1722                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1723                         else:
1724                            D_times_e=D
1725                     else:
1726                        D_times_e=escript.Data()
1727                     if not d.isEmpty():
1728                         if self.getNumSolutions()>1:
1729                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1730                         else:
1731                            d_times_e=d
1732                     else:
1733                        d_times_e=escript.Data()
1734          
1735                     if not D_reduced.isEmpty():
1736                         if self.getNumSolutions()>1:
1737                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1738                         else:
1739                            D_reduced_times_e=D_reduced
1740                     else:
1741                        D_reduced_times_e=escript.Data()
1742                     if not d_reduced.isEmpty():
1743                         if self.getNumSolutions()>1:
1744                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1745                         else:
1746                            d_reduced_times_e=d_reduced
1747                     else:
1748                        d_reduced_times_e=escript.Data()
1749    
1750                     self.__operator=self.__getNewRightHandSide()
1751                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1752                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1753                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1754                     else:
1755                        self.getDomain().addPDEToRHS(self.__operator, \
1756                                                     escript.Data(), \
1757                                                     D_times_e, \
1758                                                     d_times_e,\
1759                                                     escript.Data())
1760                        self.getDomain().addPDEToRHS(self.__operator, \
1761                                                     escript.Data(), \
1762                                                     D_reduced_times_e, \
1763                                                     d_reduced_times_e,\
1764                                                     escript.Data())
1765                        print "RHS:",util.inf(self.__operator),util.sup(self.__operator)
1766                     self.__operator=1./self.__operator
1767                     self.trace("New lumped operator has been built.")
1768                     self.__operator_is_Valid=True
1769                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1770                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1771                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1772                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1773                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1774                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1775                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1776                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1777                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1778                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1779                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1780                     self.trace("New right hand side as been built.")
1781                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1782            else:            else:
1783               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."  
1784                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1785                                 self.getCoefficientOfPDE("A"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1786                                 self.getCoefficientOfPDE("B"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1787                                 self.getCoefficientOfPDE("C"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1788                                 self.getCoefficientOfPDE("D"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1789                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1790                                 self.getCoefficientOfPDE("Y"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1791                                 self.getCoefficientOfPDE("d"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1792                                 self.getCoefficientOfPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1793                                 self.getCoefficientOfPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1794                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1795                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1796                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1806                   self.__applyConstraint()                   self.__applyConstraint()
1807                   self.__copyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1808                   self.__operator_isValid=True                   self.trace("New system has been built.")
1809                     self.__operator_is_Valid=True
1810                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1811               elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
                  if self.debug() : print "PDE Debug: New right hand side is built."  
1812                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1813                                 self.getCoefficientOfPDE("X"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1814                                 self.getCoefficientOfPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1815                                 self.getCoefficientOfPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1816                                 self.getCoefficientOfPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1817                   self.__copyConstraint()                   self.getDomain().addPDEToRHS(self.__righthandside, \
1818                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1819                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1820                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1821                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1822                     self.__righthandside=self.copyConstraint(self.__righthandside)
1823                     self.trace("New right hand side has been built.")
1824                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1825               elif not self.__operator_isValid:               elif not self.__operator_is_Valid:
                  if self.debug() : print "PDE Debug: New operator is built."  
1826                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1827                              self.getCoefficientOfPDE("A"), \                              self.getCoefficientOfGeneralPDE("A"), \
1828                              self.getCoefficientOfPDE("B"), \                              self.getCoefficientOfGeneralPDE("B"), \
1829                              self.getCoefficientOfPDE("C"), \                              self.getCoefficientOfGeneralPDE("C"), \
1830                              self.getCoefficientOfPDE("D"), \                              self.getCoefficientOfGeneralPDE("D"), \
1831                                escript.Data(), \
1832                                escript.Data(), \
1833                                self.getCoefficientOfGeneralPDE("d"), \
1834                                escript.Data(),\
1835                                self.getCoefficientOfGeneralPDE("d_contact"), \
1836                                escript.Data())
1837                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1838                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1839                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1840                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1841                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1842                              escript.Data(), \                              escript.Data(), \
1843                              escript.Data(), \                              escript.Data(), \
1844                              self.getCoefficientOfPDE("d"), \                              self.getCoefficientOfGeneralPDE("d_reduced"), \
1845                              escript.Data(),\                              escript.Data(),\
1846                              self.getCoefficientOfPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1847                              escript.Data())                              escript.Data())
1848                   self.__applyConstraint()                   self.__applyConstraint()
1849                   self.__operator_isValid=True                   self.trace("New operator has been built.")
1850                     self.__operator_is_Valid=True
1851         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
    def getOperator(self):  
        """  
        returns the operator of the PDE  
        """  
        return self.getSystem()[0]  
1852    
    def getRightHandSide(self):  
        """  
        returns the right hand side of the PDE  
        """  
        return self.getSystem()[1]  
   
    def solve(self,**options):  
       """  
       solve the PDE  
1853    
1854        @param options:  class Poisson(LinearPDE):
1855        """     """
1856        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  
1857    
1858     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        returns the solution of the PDE  
1859    
1860         @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  
1861    
1862       M{n[j]*grad(u)[j] = 0 }
1863    
1864       and constraints:
1865    
1866  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())  
1867    
 class AdvectivePDE(LinearPDE):  
1868     """     """
    Class to handle a linear PDE dominated by advective terms:  
     
    class to define a linear PDE of the form  
1869    
1870     \f[     def __init__(self,domain,debug=False):
1871     -(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       """
1872     \f]       initializes a new Poisson equation
1873    
1874         @param domain: domain of the PDE
1875         @type domain: L{Domain<escript.Domain>}
1876         @param debug: if True debug informations are printed.
1877    
1878         """
1879         super(Poisson, self).__init__(domain,1,1,debug)
1880         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1881                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1882                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1883         self.setSymmetryOn()
1884    
1885       def setValue(self,**coefficients):
1886         """
1887         sets new values to coefficients
1888    
1889         @param coefficients: new values assigned to coefficients
1890         @keyword f: value for right hand side M{f}
1891         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1892         @keyword q: mask for location of constraints
1893         @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>}
1894                   depending of reduced order is used for the representation of the equation.
1895         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1896         """
1897         super(Poisson, self).setValue(**coefficients)
1898    
1899       def getCoefficientOfGeneralPDE(self,name):
1900         """
1901         return the value of the coefficient name of the general PDE
1902         @param name: name of the coefficient requested.
1903         @type name: C{string}
1904         @return: the value of the coefficient  name
1905         @rtype: L{Data<escript.Data>}
1906         @raise IllegalCoefficient: if name is not one of coefficients
1907                      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}.
1908         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1909         """
1910         if name == "A" :
1911             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1912         elif name == "B" :
1913             return escript.Data()
1914         elif name == "C" :
1915             return escript.Data()
1916         elif name == "D" :
1917             return escript.Data()
1918         elif name == "X" :
1919             return escript.Data()
1920         elif name == "Y" :
1921             return self.getCoefficient("f")
1922         elif name == "d" :
1923             return escript.Data()
1924         elif name == "y" :
1925             return escript.Data()
1926         elif name == "d_contact" :
1927             return escript.Data()
1928         elif name == "y_contact" :
1929             return escript.Data()
1930         elif name == "A_reduced" :
1931             return escript.Data()
1932         elif name == "B_reduced" :
1933             return escript.Data()
1934         elif name == "C_reduced" :
1935             return escript.Data()
1936         elif name == "D_reduced" :
1937             return escript.Data()
1938         elif name == "X_reduced" :
1939             return escript.Data()
1940         elif name == "Y_reduced" :
1941             return self.getCoefficient("f_reduced")
1942         elif name == "d_reduced" :
1943             return escript.Data()
1944         elif name == "y_reduced" :
1945             return escript.Data()
1946         elif name == "d_contact_reduced" :
1947             return escript.Data()
1948         elif name == "y_contact_reduced" :
1949             return escript.Data()
1950         elif name == "r" :
1951             return escript.Data()
1952         elif name == "q" :
1953             return self.getCoefficient("q")
1954         else:
1955            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1956    
1957     with boundary conditons:  class Helmholtz(LinearPDE):
1958       """
1959       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1960    
1961     \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]  
1962    
1963     and contact conditions     with natural boundary conditons
1964    
1965     \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]  
1966    
1967     and constraints:     and constraints:
1968    
1969     \f[     M{u=r} where M{q>0}
1970     u_i=r_i \quad \mathrm{where} \quad q_i>0  
    \f]  
1971     """     """
    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.  
1972    
1973     def setValue(self,**args):     def __init__(self,domain,debug=False):
1974         if "A" in args.keys()   or "B" in args.keys() or "C" in args.keys(): self.__Xi=escript.Data()       """
1975         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)  
1976    
1977              Z_max=util.Lsup(length_of_Z)       @param domain: domain of the PDE
1978              if Z_max>0.:       @type domain: L{Domain<escript.Domain>}
1979                 length_of_A=util.length(A)       @param debug: if True debug informations are printed.
1980                 A_max=util.Lsup(length_of_A)  
1981                 if A_max>0:       """
1982                      inv_A=1./(length_of_A+A_max*self.TOL)       super(Helmholtz, self).__init__(domain,1,1,debug)
1983                 else:       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1984                      inv_A=1./self.TOL                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1985                 peclet_number=length_of_Z*h/2*inv_A                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986                 xi=self.__xi(peclet_number)                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987                 self.__Xi=h*xi/(length_of_Z+Z_max*self.TOL)                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1988                 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),
1989        return self.__Xi                          "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1990                                  "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1991                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1992         self.setSymmetryOn()
1993    
1994     def getCoefficientOfPDE(self,name):     def setValue(self,**coefficients):
1995       """       """
1996       return the value of the coefficient name of the general PDE       sets new values to coefficients
1997    
1998       @param name:       @param coefficients: new values assigned to coefficients
1999         @keyword omega: value for coefficient M{S{omega}}
2000         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2001         @keyword k: value for coefficeint M{k}
2002         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2003         @keyword f: value for right hand side M{f}
2004         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2005         @keyword alpha: value for right hand side M{S{alpha}}
2006         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2007         @keyword g: value for right hand side M{g}
2008         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2009         @keyword r: prescribed values M{r} for the solution in constraints.
2010         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2011                   depending of reduced order is used for the representation of the equation.
2012         @keyword q: mask for location of constraints
2013         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2014                   depending of reduced order is used for the representation of the equation.
2015         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2016       """       """
2017       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."  
2018    
2019       if name == "A" :     def getCoefficientOfGeneralPDE(self,name):
2020           A=self.getCoefficient("A")       """
2021           B=self.getCoefficient("B")       return the value of the coefficient name of the general PDE
2022           C=self.getCoefficient("C")  
2023           if B.isEmpty() and C.isEmpty():       @param name: name of the coefficient requested.
2024              Aout=A       @type name: C{string}
2025           else:       @return: the value of the coefficient  name
2026              if A.isEmpty():       @rtype: L{Data<escript.Data>}
2027                 Aout=self.createNewCoefficient("A")       @raise IllegalCoefficient: if name is not one of coefficients
2028              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}.
2029                 Aout=A[:]       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2030              Xi=self.getXi()       """
2031              if self.getNumEquations()>1:       if name == "A" :
2032                  for i in range(self.getNumEquations()):           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2033                     for j in range(self.getDim()):       elif name == "B" :
2034                        for k in range(self.getNumSolutions()):           return escript.Data()
2035                           for l in range(self.getDim()):       elif name == "C" :
2036                              if not C.isEmpty() and not B.isEmpty():           return escript.Data()
2037                                 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" :
2038                              elif C.isEmpty():           return self.getCoefficient("omega")
2039                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]       elif name == "X" :
2040                              else:           return escript.Data()
2041                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]       elif name == "Y" :
2042              else:           return self.getCoefficient("f")
2043                  for j in range(self.getDim()):       elif name == "d" :
2044                     for l in range(self.getDim()):           return self.getCoefficient("alpha")
2045                        if not C.isEmpty() and not B.isEmpty():       elif name == "y" :
2046                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])           return self.getCoefficient("g")
2047                        elif C.isEmpty():       elif name == "d_contact" :
2048                            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")  
2049       elif name == "y_contact" :       elif name == "y_contact" :
2050           return self.getCoefficient("y_contact")           return escript.Data()
2051       elif name == "r" :       elif name == "A_reduced" :
2052             return escript.Data()
2053         elif name == "B_reduced" :
2054             return escript.Data()
2055         elif name == "C_reduced" :
2056             return escript.Data()
2057         elif name == "D_reduced" :
2058             return escript.Data()
2059         elif name == "X_reduced" :
2060             return escript.Data()
2061         elif name == "Y_reduced" :
2062             return self.getCoefficient("f_reduced")
2063         elif name == "d_reduced" :
2064             return escript.Data()
2065         elif name == "y_reduced" :
2066            return self.getCoefficient("g_reduced")
2067         elif name == "d_contact_reduced" :
2068             return escript.Data()
2069         elif name == "y_contact_reduced" :
2070             return escript.Data()
2071         elif name == "r" :
2072           return self.getCoefficient("r")           return self.getCoefficient("r")
2073       elif name == "q" :       elif name == "q" :
2074           return self.getCoefficient("q")           return self.getCoefficient("q")
2075       else:       else:
2076           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2077    
2078    class LameEquation(LinearPDE):
 class Poisson(LinearPDE):  
2079     """     """
2080     Class to define a Poisson equstion problem:     Class to define a Lame equation problem:
2081    
2082     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] }
2083     \f[  
2084     -u_{,jj} = f     with natural boundary conditons:
2085     \f]  
2086       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]  
2087    
2088     and constraints:     and constraints:
2089    
2090     \f[     M{u[i]=r[i]} where M{q[i]>0}
    u=0 \quad \mathrm{where} \quad q>0  
    \f]  
    """  
2091    
2092     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)  
2093    
2094     def setValue(self,f=escript.Data(),q=escript.Data()):     def __init__(self,domain,debug=False):
2095         self._LinearPDE__setValue(f=f,q=q)        super(LameEquation, self).__init__(domain,\
2096                                             domain.getDim(),domain.getDim(),debug)
2097          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2098                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2099                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2100                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2101                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2102                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2103                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2104          self.setSymmetryOn()
2105    
2106       def setValues(self,**coefficients):
2107         """
2108         sets new values to coefficients
2109    
2110         @param coefficients: new values assigned to coefficients
2111         @keyword lame_mu: value for coefficient M{S{mu}}
2112         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2113         @keyword lame_lambda: value for coefficient M{S{lambda}}
2114         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2115         @keyword F: value for internal force M{F}
2116         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2117         @keyword sigma: value for initial stress M{S{sigma}}
2118         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2119         @keyword f: value for extrenal force M{f}
2120         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2121         @keyword r: prescribed values M{r} for the solution in constraints.
2122         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2123                   depending of reduced order is used for the representation of the equation.
2124         @keyword q: mask for location of constraints
2125         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2126                   depending of reduced order is used for the representation of the equation.
2127         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2128         """
2129         super(LameEquation, self).setValues(**coefficients)
2130    
2131     def getCoefficientOfPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2132       """       """
2133       return the value of the coefficient name of the general PDE       return the value of the coefficient name of the general PDE
2134    
2135       @param name:       @param name: name of the coefficient requested.
2136       """       @type name: C{string}
2137       if name == "A" :       @return: the value of the coefficient  name
2138           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))       @rtype: L{Data<escript.Data>}
2139       elif name == "B" :       @raise IllegalCoefficient: if name is not one of coefficients
2140                      "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}.
2141         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2142         """
2143         if name == "A" :
2144             out =self.createCoefficientOfGeneralPDE("A")
2145             for i in range(self.getDim()):
2146               for j in range(self.getDim()):
2147                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2148                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2149                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2150             return out
2151         elif name == "B" :
2152           return escript.Data()           return escript.Data()
2153       elif name == "C" :       elif name == "C" :
2154           return escript.Data()           return escript.Data()
2155       elif name == "D" :       elif name == "D" :
2156           return escript.Data()           return escript.Data()
2157       elif name == "X" :       elif name == "X" :
2158             return self.getCoefficient("sigma")
2159         elif name == "Y" :
2160             return self.getCoefficient("F")
2161         elif name == "d" :
2162           return escript.Data()           return escript.Data()
2163       elif name == "Y" :       elif name == "y" :
2164           return self.getCoefficient("f")           return self.getCoefficient("f")
2165       elif name == "d" :       elif name == "d_contact" :
2166           return escript.Data()           return escript.Data()
2167       elif name == "y" :       elif name == "y_contact" :
2168           return escript.Data()           return escript.Data()
2169       elif name == "d_contact" :       elif name == "A_reduced" :
2170           return escript.Data()           return escript.Data()
2171       elif name == "y_contact" :       elif name == "B_reduced" :
2172             return escript.Data()
2173         elif name == "C_reduced" :
2174             return escript.Data()
2175         elif name == "D_reduced" :
2176             return escript.Data()
2177         elif name == "X_reduced" :
2178           return escript.Data()           return escript.Data()
2179       elif name == "r" :       elif name == "Y_reduced" :
2180           return escript.Data()           return escript.Data()
2181       elif name == "q" :       elif name == "d_reduced" :
2182             return escript.Data()
2183         elif name == "y_reduced" :
2184             return escript.Data()
2185         elif name == "d_contact_reduced" :
2186             return escript.Data()
2187         elif name == "y_contact_reduced" :
2188             return escript.Data()
2189         elif name == "r" :
2190             return self.getCoefficient("r")
2191         elif name == "q" :
2192           return self.getCoefficient("q")           return self.getCoefficient("q")
2193       else:       else:
2194           raise SystemError,"unknown PDE coefficient %s",name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2195    
2196  # $Log$  def LinearSinglePDE(domain,debug=False):
2197  # Revision 1.8  2005/06/09 05:37:59  jgs     """
2198  # Merge of development branch back to main trunk on 2005-06-09     defines a single linear PDEs
2199  #  
2200  # Revision 1.7  2005/05/06 04:26:10  jgs     @param domain: domain of the PDE
2201  # Merge of development branch back to main trunk on 2005-05-06     @type domain: L{Domain<escript.Domain>}
2202  #     @param debug: if True debug informations are printed.
2203  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane     @rtype: L{LinearPDE}
2204  # Fixed up some docstrings.  Moved module-level functions to top of file so     """
2205  # that epydoc and doxygen can pick them up properly.     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2206  #  
2207  # Revision 1.1.2.22  2005/05/12 11:41:30  gross  def LinearPDESystem(domain,debug=False):
2208  # some basic Models have been added     """
2209  #     defines a system of linear PDEs
2210  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane  
2211  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of     @param domain: domain of the PDE
2212  # file so that the AdvectivePDE class is picked up by doxygen.  Some     @type domain: L{Domain<escript.Domain>}
2213  # reformatting of docstrings.  Addition of code to make equations come out     @param debug: if True debug informations are printed.
2214  # as proper LaTeX.     @rtype: L{LinearPDE}
2215  #     """
2216  # Revision 1.1.2.20  2005/04/15 07:09:08  gross     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2217  # some problems with functionspace and linearPDEs fixed.  
2218  #  class TransportPDE(object):
2219  # Revision 1.1.2.19  2005/03/04 05:27:07  gross       """
2220  # bug in SystemPattern fixed.       Warning: This is still a very experimental. The class is still changing!
2221  #  
2222  # 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}
2223  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed      
2224  #       u=r where q>0
2225  # Revision 1.1.2.17  2005/02/08 05:56:19  gross      
2226  # Reference Number handling added       all coefficients are constant over time.
2227  #  
2228  # Revision 1.1.2.16  2005/02/07 04:41:28  gross       typical usage:
2229  # some function exposed to python to make mesh merging running  
2230  #           p=TransportPDE(dom)
2231  # 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.])
2232  # timeseries add and ESySParameter.py renames esysXML.py for consistence           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2233  #           t=0
2234  # Revision 1.1.2.14  2005/02/01 06:44:10  gross           dt=0.1
2235  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working           while (t<1.):
2236  #                u=p.solve(dt)
2237  # Revision 1.1.2.13  2005/01/25 00:47:07  gross  
2238  # updates in the documentation       """
2239  #       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2240  # Revision 1.1.2.12  2005/01/12 01:28:04  matt          self.__domain=domain
2241  # Added createCoefficient method for linearPDEs.          self.__num_equations=num_equations
2242  #          self.__useSUPG=useSUPG
2243  # Revision 1.1.2.11  2005/01/11 01:55:34  gross          self.__trace=trace
2244  # a problem in linearPDE class fixed          self.__theta=theta
2245  #          self.__matrix_type=0
2246  # Revision 1.1.2.10  2005/01/07 01:13:29  gross          self.__reduced=True
2247  # some bugs in linearPDE fixed          self.__reassemble=True
2248  #          if self.__useSUPG:
2249  # Revision 1.1.2.9  2005/01/06 06:24:58  gross             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2250  # some bugs in slicing fixed             self.__pde.setSymmetryOn()
2251  #             self.__pde.setReducedOrderOn()
2252  # Revision 1.1.2.8  2005/01/05 04:21:40  gross          else:
2253  # FunctionSpace checking/matchig in slicing added             self.__transport_problem=self.__getNewTransportProblem()
2254  #          self.setTolerance()
2255  # Revision 1.1.2.7  2004/12/29 10:03:41  gross          self.__M=escript.Data()
2256  # bug in setValue fixed          self.__A=escript.Data()
2257  #          self.__B=escript.Data()
2258  # Revision 1.1.2.6  2004/12/29 05:29:59  gross          self.__C=escript.Data()
2259  # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()          self.__D=escript.Data()
2260  #          self.__X=escript.Data()
2261  # Revision 1.1.2.5  2004/12/29 00:18:41  gross          self.__Y=escript.Data()
2262  # AdvectivePDE added          self.__d=escript.Data()
2263  #          self.__y=escript.Data()
2264  # Revision 1.1.2.4  2004/12/24 06:05:41  gross          self.__d_contact=escript.Data()
2265  # some changes in linearPDEs to add AdevectivePDE          self.__y_contact=escript.Data()
2266  #          self.__r=escript.Data()
2267  # Revision 1.1.2.3  2004/12/16 00:12:34  gross          self.__q=escript.Data()
2268  # __init__ of LinearPDE does not accept any coefficient anymore  
2269  #       def trace(self,text):
2270  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs               if self.__trace: print text
2271  # *** empty log message ***       def getSafeTimeStepSize(self):
2272  #          if self.__useSUPG:
2273  # Revision 1.1.2.1  2004/12/12 22:53:47  gross              if self.__reassemble:
2274  # linearPDE has been renamed LinearPDE                 h=self.__domain.getSize()
2275  #                 dt=None
2276  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross                 if not self.__A.isEmpty():
2277  # GMRES added                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2278  #                    if dt == None:
2279  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross                       dt = dt2
2280  # options for GMRES and PRES20 added                    else:
2281  #                       dt=1./(1./dt+1./dt2)
2282  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross                 if not self.__B.isEmpty():
2283  # some small changes                    dt2=util.inf(h*self.__M/util.length(self.__B))
2284  #                    if dt == None:
2285  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross                       dt = dt2
2286  # Finley solves 4M unknowns now                    else:
2287  #                       dt=1./(1./dt+1./dt2)
2288  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross                 if not  self.__C.isEmpty():
2289  # poisson solver added                    dt2=util.inf(h*self.__M/util.length(self.__C))
2290  #                    if dt == None:
2291  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross                       dt = dt2
2292  # 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:
2293  #                       dt=1./(1./dt+1./dt2)
2294  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross                 if not self.__D.isEmpty():
2295  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed                    dt2=util.inf(self.__M/util.length(self.__D))
2296  #                    if dt == None:
2297  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs                       dt = dt2
2298  # initial import of project esys2                    else:
2299  #                       dt=1./(1./dt+1./dt2)
2300  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs                 self.__dt = dt/2
2301  # committing Lutz's and Paul's changes to brach jgs              return self.__dt
2302  #          else:
2303  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane              return self.__getTransportProblem().getSafeTimeStepSize()
2304  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.       def getDomain(self):
2305  #          return self.__domain
2306  # Revision 1.3  2004/09/23 00:53:23  jgs       def getTheta(self):
2307  # minor fixes          return self.__theta
2308  #       def getNumEquations(self):
2309  # Revision 1.1  2004/08/28 12:58:06  gross          return self.__num_equations
2310  # SimpleSolve is not running yet: problem with == of functionsspace       def setReducedOn(self):
2311  #            if not self.reduced():
2312  #                if self.__useSUPG:
2313                     self.__pde.setReducedOrderOn()
2314                  else:
2315                     self.__transport_problem=self.__getNewTransportProblem()
2316              self.__reduced=True
2317         def setReducedOff(self):
2318              if self.reduced():
2319                  if self.__useSUPG:
2320                     self.__pde.setReducedOrderOff()
2321                  else:
2322                     self.__transport_problem=self.__getNewTransportProblem()
2323              self.__reduced=False
2324         def reduced(self):
2325             return self.__reduced
2326         def getFunctionSpace(self):
2327            if self.reduced():
2328               return escript.ReducedSolution(self.getDomain())
2329            else:
2330               return escript.Solution(self.getDomain())
2331    
2332         def setTolerance(self,tol=1.e-8):
2333            self.__tolerance=tol
2334            if self.__useSUPG:
2335                  self.__pde.setTolerance(self.__tolerance)
2336    
2337         def __getNewTransportProblem(self):
2338           """
2339           returns an instance of a new operator
2340           """
2341           self.trace("New Transport problem is allocated.")
2342           return self.getDomain().newTransportProblem( \
2343                                   self.getTheta(),
2344                                   self.getNumEquations(), \
2345                                   self.getFunctionSpace(), \
2346                                   self.__matrix_type)
2347              
2348         def __getNewSolutionVector(self):
2349             if self.getNumEquations() ==1 :
2350                    out=escript.Data(0.0,(),self.getFunctionSpace())
2351             else:
2352                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2353             return out
2354    
2355         def __getTransportProblem(self):
2356           if self.__reassemble:
2357                 self.__source=self.__getNewSolutionVector()
2358                 self.__transport_problem.reset()
2359                 self.getDomain().addPDEToTransportProblem(
2360                             self.__transport_problem,
2361                             self.__source,
2362                             self.__M,
2363                             self.__A,
2364                             self.__B,
2365                             self.__C,
2366                             self.__D,
2367                             self.__X,
2368                             self.__Y,
2369                             self.__d,
2370                             self.__y,
2371                             self.__d_contact,
2372                             self.__y_contact)
2373                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2374                 self.__reassemble=False
2375           return self.__transport_problem
2376         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2377                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2378                 if not M==None:
2379                      self.__reassemble=True
2380                      self.__M=M
2381                 if not A==None:
2382                      self.__reassemble=True
2383                      self.__A=A
2384                 if not B==None:
2385                      self.__reassemble=True
2386                      self.__B=B
2387                 if not C==None:
2388                      self.__reassemble=True
2389                      self.__C=C
2390                 if not D==None:
2391                      self.__reassemble=True
2392                      self.__D=D
2393                 if not X==None:
2394                      self.__reassemble=True
2395                      self.__X=X
2396                 if not Y==None:
2397                      self.__reassemble=True
2398                      self.__Y=Y
2399                 if not d==None:
2400                      self.__reassemble=True
2401                      self.__d=d
2402                 if not y==None:
2403                      self.__reassemble=True
2404                      self.__y=y
2405                 if not d_contact==None:
2406                      self.__reassemble=True
2407                      self.__d_contact=d_contact
2408                 if not y_contact==None:
2409                      self.__reassemble=True
2410                      self.__y_contact=y_contact
2411                 if not q==None:
2412                      self.__reassemble=True
2413                      self.__q=q
2414                 if not r==None:
2415                      self.__reassemble=True
2416                      self.__r=r
2417    
2418         def setInitialSolution(self,u):
2419                 if self.__useSUPG:
2420                     self.__u=util.interpolate(u,self.getFunctionSpace())
2421                 else:
2422                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2423    
2424         def solve(self,dt,**kwarg):
2425               if self.__useSUPG:
2426                    if self.__reassemble:
2427                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2428                        self.__reassemble=False
2429                    dt2=self.getSafeTimeStepSize()
2430                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2431                    dt2=dt/nn
2432                    nnn=0
2433                    u=self.__u
2434                    self.trace("number of substeps is %d."%nn)
2435                    while nnn<nn :
2436                        self.__setSUPG(u,u,dt2/2)
2437                        u_half=self.__pde.getSolution(verbose=True)
2438                        self.__setSUPG(u,u_half,dt2)
2439                        u=self.__pde.getSolution(verbose=True)
2440                        nnn+=1
2441                    self.__u=u
2442                    return self.__u
2443               else:
2444                   kwarg["tolerance"]=self.__tolerance
2445                   tp=self.__getTransportProblem()
2446                   return tp.solve(self.__source,dt,kwarg)
2447         def __setSUPG(self,u0,u,dt):
2448                g=util.grad(u)
2449                X=0
2450                Y=self.__M*u0
2451                X=0
2452                self.__pde.setValue(r=u0)
2453                if not self.__A.isEmpty():
2454                   X=X+dt*util.matrixmult(self.__A,g)
2455                if not self.__B.isEmpty():
2456                   X=X+dt*self.__B*u
2457                if not  self.__C.isEmpty():
2458                   Y=Y+dt*util.inner(self.__C,g)
2459                if not self.__D.isEmpty():
2460                   Y=Y+dt*self.__D*u
2461                if not self.__X.isEmpty():
2462                   X=X+dt*self.__X
2463                if not self.__Y.isEmpty():
2464                   Y=Y+dt*self.__Y
2465                self.__pde.setValue(X=X,Y=Y)
2466                if not self.__y.isEmpty():
2467                   self.__pde.setValue(y=dt*self.__y)
2468                if not self.__y_contact.isEmpty():
2469                   self.__pde.setValue(y=dt*self.__y_contact)
2470                self.__pde.setValue(r=u0)

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