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trunk/esys2/escript/py_src/linearPDEs.py revision 102 by jgs, Wed Dec 15 07:08:39 2004 UTC trunk/escript/py_src/linearPDEs.py revision 1639 by gross, Mon Jul 14 08:55:25 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  @brief 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  def identifyDomain(domain=None,data={}):  __author__="Lutz Gross, l.gross@uq.edu.au"
43       """  __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
44       @brief Return the Domain which is equal to the input domain (if not None)                      http://www.access.edu.au
45       and is the domain of all Data objects in the dictionary data.                  Primary Business: Queensland, Australia"""
46       An exception is raised if this is not possible  __license__="""Licensed under the Open Software License version 3.0
47                 http://www.opensource.org/licenses/osl-3.0.php"""
48       @param domain  __url__="http://www.iservo.edu.au/esys"
49       @param data  __version__="$Revision$"
50       """  __date__="$Date$"
51       # get the domain used by any Data object in the list data:  
52       data_domain=None  
53       for d in data.itervalues():  class IllegalCoefficient(ValueError):
54            if isinstance(d,escript.Data):     """
55               if not d.isEmpty(): data_domain=d.getDomain()     raised if an illegal coefficient of the general ar particular PDE is requested.
56       # check if domain and data_domain are identical?     """
57       if domain == None:     pass
          if data_domain == None:  
               raise ValueError,"Undefined PDE domain. Specify a domain or use a Data class object as coefficient"  
      else:  
          if data_domain == None:  
               data_domain=domain  
          else:  
            if not data_domain == domain:  
                  raise ValueError,"Domain of coefficients doesnot match specified domain"  
      # now we check if all Data class object coefficients are defined on data_domain:  
      for i,d in data.iteritems():  
          if isinstance(d,escript.Data):  
             if not d.isEmpty():  
                if not data_domain==d.getDomain():  
                  raise ValueError,"Illegal domain for coefficient %s."%i  
      # done:  
      return data_domain  
   
 def identifyNumEquationsAndSolutions(dim,coef={}):  
      # get number of equations and number of unknowns:  
      numEquations=0  
      numSolutions=0  
      for i in coef.iterkeys():  
         if not coef[i].isEmpty():  
            res=_PDECoefficientTypes[i].estimateNumEquationsAndNumSolutions(coef[i].getShape(),dim)  
            if res==None:  
                raise ValueError,"Illegal shape %s of coefficient %s"%(coef[i].getShape().__str__(),i)  
            else:  
                numEquations=max(numEquations,res[0])  
                numSolutions=max(numSolutions,res[1])  
      return numEquations,numSolutions  
58    
59    class IllegalCoefficientValue(ValueError):
60       """
61       raised if an incorrect value for a coefficient is used.
62       """
63       pass
64    
65  def _CompTuple2(t1,t2):  class IllegalCoefficientFunctionSpace(ValueError):
66       """
67       raised if an incorrect function space for a coefficient is used.
68     """     """
    @brief  
69    
70     @param t1  class UndefinedPDEError(ValueError):
    @param t2  
71     """     """
72     dif=t1[0]+t1[1]-(t2[0]+t2[1])     raised if a PDE is not fully defined yet.
73     if dif<0: return 1     """
74     elif dif>0: return -1     pass
    else: return 0  
75    
76  class PDECoefficientType:  class PDECoefficient(object):
77      """      """
78      @brief      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         @brief Initialise a PDE Coefficient type         """
113           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
135           self.resetValue()
136    
137      def getFunctionSpace(self,domain):      def resetValue(self):
138         """         """
139         @brief defines the FunctionSpace of the coefficient on the domain         resets coefficient value to default
   
        @param domain  
140         """         """
141         if self.what==self.INTERIOR: return escript.Function(domain)         self.value=escript.Data()
142         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)  
143         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
144         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         """
145           defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
146    
147           @param domain: domain on which the PDE uses the coefficient
148           @type domain: L{Domain<escript.Domain>}
149           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
150           @type reducedEquationOrder: C{bool}
151           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
152           @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):
177           """
178           returns the value of the coefficient
179    
180           @return:  value of the coefficient
181           @rtype:  L{Data<escript.Data>}
182           """
183           return self.value
184    
185        def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
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
219    
220      def isAlteringOperator(self):      def isAlteringOperator(self):
221          """          """
222      @brief 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 119  class PDECoefficientType: Line 231  class PDECoefficientType:
231    
232      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
233          """          """
234      @brief 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         @brief 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      @brief 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
   
 _PDECoefficientTypes={  
 "A"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM,PDECoefficientType.SOLUTION,PDECoefficientType.DIM),PDECoefficientType.OPERATOR),  
 "B"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "C"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION,PDECoefficientType.DIM),PDECoefficientType.OPERATOR),  
 "D"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "X"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,PDECoefficientType.DIM),PDECoefficientType.RIGHTHANDSIDE),  
 "Y"         : PDECoefficientType(PDECoefficientType.INTERIOR,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "d"         : PDECoefficientType(PDECoefficientType.BOUNDARY,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "y"         : PDECoefficientType(PDECoefficientType.BOUNDARY,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "d_contact" : PDECoefficientType(PDECoefficientType.CONTACT,(PDECoefficientType.EQUATION,PDECoefficientType.SOLUTION),PDECoefficientType.OPERATOR),  
 "y_contact" : PDECoefficientType(PDECoefficientType.CONTACT,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "r"         : PDECoefficientType(PDECoefficientType.CONTINUOUS,(PDECoefficientType.EQUATION,),PDECoefficientType.RIGHTHANDSIDE),  
 "q"         : PDECoefficientType(PDECoefficientType.CONTINUOUS,(PDECoefficientType.SOLUTION,),PDECoefficientType.BOTH),  
 }  
348    
349  class LinearPDE:  class LinearPDE(object):
350     """     """
351     @brief Class to define 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       -(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     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
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    
         n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i  
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          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i     The following natural boundary conditions are considered:
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           u_i=r_i where q_i>0     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>}.
372    
    """  
    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  
373    
374     def __init__(self,**args):     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
      """  
      @brief initializes a new linear PDE.  
375    
376       @param args     M{u=r}  where M{q>0}
      """  
377    
378       # initialize attributes     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
379       self.__debug=None     The constraints override any other condition set by the PDE or the boundary condition.
380       self.__domain=None  
381       self.__numEquations=0     The PDE is symmetrical if
382       self.__numSolutions=0  
383       self.cleanCoefficients()     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    
385       self.__operator=escript.Operator()     For a system of PDEs and a solution with several components the PDE has the form
386       self.__operator_isValid=False  
387       self.__righthandside=escript.Data()     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       self.__righthandside_isValid=False  
389       self.__solution=escript.Data()     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       self.__solution_isValid=False     The natural boundary conditions take the form:
391    
392       # check the arguments     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       coef={}  
394       for arg in args.iterkeys():  
395            if arg=="domain":     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                self.__domain=args[arg]  
397            elif arg=="numEquations":     Constraints take the form
398                self.__numEquations=args[arg]  
399            elif arg=="numSolutions":     M{u[i]=r[i]}  where  M{q[i]>0}
400                self.__numSolutions=args[arg]  
401            elif _PDECoefficientTypes.has_key(arg):     M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
402                coef[arg]=args[arg]  
403            else:     The system of PDEs is symmetrical if
               raise ValueError,"Illegal argument %s"%arg  
404    
405       # get the domain of the PDE          - M{A[i,j,k,l]=A[k,l,i,j]}
406       self.__domain=identifyDomain(self.__domain,coef)          - 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
548         self.__debug=debug
549         self.__domain=domain
550         self.__numEquations=numEquations
551         self.__numSolutions=numSolutions
552         self.__resetSystem()
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  
      self.__numEquations=0  
      self.__numSolutions=0  
      # now we can set the ceofficients:  
      self._setCoefficient(**coef)  
563    
564     def getCoefficient(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         switches on debugging
583       """       """
584       @brief return the value of the coefficient name       self.__debug=not None
585    
586       @param name     def setDebugOff(self):
587         """
588         switches off debugging
589       """       """
590       return self.__coefficient[name]       self.__debug=None
591    
592     def setValue(self,**coefficients):     def trace(self,text):
593        """       """
594        @brief sets new values to coefficients       print the text message if debugging is swiched on.
595         @param text: message
596         @type text: C{string}
597         """
598         if self.__debug: print "%s: %s"%(str(self),text)
599    
600        @param coefficients     # =============================================================================
601        """     # some service functions:
602        self._setCoefficient(**coefficients)     # =============================================================================
603             def getDomain(self):
604         """
605         returns the domain of the PDE
606    
607     def _setCoefficient(self,**coefficients):       @return: the domain of the PDE
608        """       @rtype: L{Domain<escript.Domain>}
609        @brief sets new values to coefficients       """
610         return self.__domain
611    
612        @param coefficients     def getDim(self):
613        """       """
614               returns the spatial dimension of the PDE
       # get the dictionary of the coefficinets been altered:  
       alteredCoefficients={}  
       for i,d in coefficients.iteritems():  
          if self.hasCoefficient(i):  
             if d == None:  
                 alteredCoefficients[i]=escript.Data()  
             elif isinstance(d,escript.Data):  
                 if d.isEmpty():  
                   alteredCoefficients[i]=escript.Data()  
                 else:  
                   alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
             else:  
                 if self.__numEquations>0 and  self.__numSolutions>0:  
                    alteredCoefficients[i]=escript.Data(d,self.getShapeOfCoefficient(i),self.getFunctionSpaceOfCoefficient(i))  
                 else:  
                    alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
          else:  
             raise ValueError,"Attempt to set undefined coefficient %s"%i  
       # if numEquations and numSolutions is undefined we try identify their values based on the coefficients:  
       if self.__numEquations<1 or self.__numSolutions<1:  
             numEquations,numSolutions=identifyNumEquationsAndSolutions(self.getDomain().getDim(),alteredCoefficients)  
             if self.__numEquations<1 and numEquations>0: self.__numEquations=numEquations  
             if self.__numSolutions<1 and numSolutions>0: self.__numSolutions=numSolutions  
             if self.debug() and self.__numEquations>0: print "PDE Debug: identified number of equations is ",self.__numEquations  
             if self.debug() and self.__numSolutions>0: print "PDE Debug: identified number of solutions is ",self.__numSolutions  
615    
616        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
617        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
618           for i in self.__coefficient.iterkeys():       """
619               if alteredCoefficients.has_key(i) and not alteredCoefficients[i].isEmpty():       return self.getDomain().getDim()
                  if not self.getShapeOfCoefficient(i)==alteredCoefficients[i].getShape():  
                     raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),alteredCoefficients[i].getShape())  
              else:  
                  if not self.__coefficient[i].isEmpty():  
                     if not self.getShapeOfCoefficient(i)==self.__coefficient[i].getShape():  
                        raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),self.__coefficient[i].getShape())  
       # overwrite new values:  
       for i,d in alteredCoefficients.iteritems():  
          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i  
          self.__coefficient[i]=d  
          self.alteredCoefficient(i)  
   
       # reset the HomogeneousConstraintFlag:  
       self.__setHomogeneousConstraintFlag()  
       if not "q" in alteredCoefficients and not self.__homogeneous_constraint: self.__rebuildSystem()  
   
    def cleanCoefficients(self):  
      """  
      @brief resets all coefficients to default values.  
      """  
      self.__coefficient={}  
      for i in _PDECoefficientTypes.iterkeys():  
          self.__coefficient[i]=escript.Data()  
620    
621     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
622       """       """
623       @brief return the shape of the coefficient name       returns the number of equations
624    
625       @param name       @return: the number of equations
626         @rtype: C{int}
627         @raise UndefinedPDEError: if the number of equations is not be specified yet.
628       """       """
629       if self.hasCoefficient(name):       if self.__numEquations==None:
630          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
631       else:       else:
632          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
633    
634     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
635       """       """
636       @brief return the atoms of the coefficient name       returns the number of unknowns
637    
638       @param name       @return: the number of unknowns
639         @rtype: C{int}
640         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
641       """       """
642       if self.hasCoefficient(name):       if self.__numSolutions==None:
643          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
644       else:       else:
645          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
646    
647     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
648       """       """
649       @brief annonced that coefficient name has been changed       return status for order reduction for equation
650    
651       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
652         @rtype: L{bool}
653       """       """
654       if self.hasCoefficient(name):       return self.__reduce_equation_order
         if _PDECoefficientTypes[name].isAlteringOperator(): self.__rebuildOperator()  
         if _PDECoefficientTypes[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()  
      else:  
         raise ValueError,"Solution coefficient %s requested"%name  
   
    def __setHomogeneousConstraintFlag(self):  
       """  
       @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.  
       """  
       self.__homogeneous_constraint=True  
       q=self.getCoefficient("q")  
       r=self.getCoefficient("r")  
       if not q.isEmpty() and not r.isEmpty():  
          print (q*r).Lsup(), 1.e-13*r.Lsup()  
          if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False  
       if self.debug():  
            if self.__homogeneous_constraint:  
                print "PDE Debug: Constraints are homogeneous."  
            else:  
                print "PDE Debug: Constraints are inhomogeneous."  
   
655    
656     def hasCoefficient(self,name):     def reduceSolutionOrder(self):
657        """       """
658        @brief return true if name is the name of a coefficient       return status for order reduction for the solution
659    
660        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
661        """       @rtype: L{bool}
662        return self.__coefficient.has_key(name)       """
663         return self.__reduce_solution_order
664    
665     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
666       """       """
667       @brief return true if the test functions should use reduced order       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 self.__row_function_space       if self.reduceEquationOrder():
673             return escript.ReducedSolution(self.getDomain())
674         else:
675             return escript.Solution(self.getDomain())
676    
677     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
678       """       """
679       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
680    
681         @return: representation space of solution
682         @rtype: L{FunctionSpace<escript.FunctionSpace>}
683       """       """
684       return self.__column_function_space       if self.reduceSolutionOrder():
685             return escript.ReducedSolution(self.getDomain())
686         else:
687             return escript.Solution(self.getDomain())
688    
    # ===== debug ==============================================================  
    def setDebugOn(self):  
        """  
        @brief  
        """  
        self.__debug=not None  
689    
690     def setDebugOff(self):     def getOperator(self):
691         """       """
692         @brief       provides access to the operator of the PDE
        """  
        self.__debug=None  
693    
694     def debug(self):       @return: the operator of the PDE
695         """       @rtype: L{Operator<escript.Operator>}
696         @brief returns true if the PDE is in the debug mode       """
697         """       m=self.getSystem()[0]
698         return self.__debug       if self.isUsingLumping():
699             return self.copyConstraint(1./m)
700         else:
701             return m
702    
703     #===== Lumping ===========================     def getRightHandSide(self):
704     def setLumpingOn(self):       """
705        """       provides access to the right hand side of the PDE
706        @brief indicates to use matrix lumping       @return: the right hand side of the PDE
707        """       @rtype: L{Data<escript.Data>}
708        if not self.isUsingLumping():       """
709           raise SystemError,"Lumping is not working yet! Talk to the experts"       r=self.getSystem()[1]
710           if self.debug() : print "PDE Debug: lumping is set on"       if self.isUsingLumping():
711           self.__rebuildOperator()           return self.copyConstraint(r)
712           self.__lumping=True       else:
713             return r
714    
715     def setLumpingOff(self):     def applyOperator(self,u=None):
716        """       """
717        @brief switches off matrix lumping       applies the operator of the PDE to a given u or the solution of PDE if u is not present.
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
718    
719     def setLumping(self,flag=False):       @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        @brief set the matrix lumping flag to flag       @type u: L{Data<escript.Data>} or None
722        """       @return: image of u
723        if flag:       @rtype: L{Data<escript.Data>}
724           self.setLumpingOn()       """
725        else:       if u==None:
726           self.setLumpingOff()          return self.getOperator()*self.getSolution()
727         else:
728            return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
729    
730     def isUsingLumping(self):     def getResidual(self,u=None):
731         """
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        @brief        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        return self.__lumping        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     #============ method business =========================================================     def getSolution(self,**options):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
890         """         """
891         @brief sets a new solver         returns the solution of the PDE. If the solution is not valid the PDE is solved.
892    
893           @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 solver==self.getSolverMethod():         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           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             self.__solver_method=solver
962             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__preconditioner=preconditioner
963             self.__checkMatrixType()             self.__checkMatrixType()
964               self.trace("New solver is %s"%self.getSolverMethodName())
965    
966       def getSolverMethodName(self):
967           """
968           returns the name of the solver currently used
969    
970           @return: the name of the solver currently used.
971           @rtype: C{string}
972           """
973    
974           m=self.getSolverMethod()
975           p=self.getSolverPackage()
976           method=""
977           if m[0]==self.DEFAULT: method="DEFAULT"
978           elif m[0]==self.DIRECT: method= "DIRECT"
979           elif m[0]==self.ITERATIVE: method= "ITERATIVE"
980           elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
981           elif m[0]==self.PCG: method= "PCG"
982           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    
1006    
1007     def getSolverMethod(self):     def getSolverMethod(self):
1008         """         """
1009         @brief returns the solver method         returns the solver method
1010    
1011           @return: the solver method currently be used.
1012           @rtype: C{int}
1013           """
1014           return self.__solver_method,self.__preconditioner
1015    
1016       def setSolverPackage(self,package=None):
1017           """
1018           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 package==None: package=self.DEFAULT
1024           if not package==self.getSolverPackage():
1025               self.__solver_package=package
1026               self.__checkMatrixType()
1027               self.trace("New solver is %s"%self.getSolverMethodName())
1028    
1029       def getSolverPackage(self):
1030         """         """
1031         return self.__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_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         @brief 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         @brief 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        @brief 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        @brief 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        @brief 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       @brief 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       @brief 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       @brief 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       @brief 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       @brief 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       @brief 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       @brief 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       @brief 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       @brief 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       @brief 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     def __makeNewOperator(self):     # 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         @brief         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):
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 641  class LinearPDE: Line 1301  class LinearPDE:
1301                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1302                             self.__matrix_type)                             self.__matrix_type)
1303    
1304     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1305         """         """
1306         @brief         returns an instance of a new right hand side
1307         """         """
1308         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1309           if self.getNumEquations()>1:
1310               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1311           else:
1312               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1313    
1314     def __makeNewSolution(self):     def __getNewSolution(self):
1315         """         """
1316         @brief         returns an instance of a new solution
1317         """         """
1318         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1319           if self.getNumSolutions()>1:
1320               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1321           else:
1322               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1323    
1324     def __getFreshOperator(self):     def __makeFreshSolution(self):
1325         """         """
1326         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1327         """         """
1328         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1329             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1330         else:         else:
1331             self.__operator.setValue(0.)             self.__solution*=0
1332             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1333         return self.__operator         return self.__solution
1334    
1335     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1336         """         """
1337         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1338         """         """
1339         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1340             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1341         else:         else:
1342             print "fix self.__righthandside*=0"             self.__righthandside.setToZero()
1343             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1344             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1345    
1346     # ==== rebuild switches =====================================================================     def __makeFreshOperator(self):
    def __rebuildSolution(self,deep=False):  
1347         """         """
1348         @brief indicates the PDE has to be reolved if the solution is requested         makes sure that the operator is instantiated and returns it initialized by zeros
1349         """         """
1350         if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."         if self.__operator.isEmpty():
1351         self.__solution_isValid=False             self.__operator=self.__getNewOperator()
1352         if deep: self.__solution=escript.Data(deep)         else:
1353               self.__operator.resetValues()
1354               self.trace("Operator reset to zero")
1355           return self.__operator
1356    
1357     def __rebuildOperator(self,deep=False):     def __applyConstraint(self):
1358         """         """
1359         @brief indicates the operator has to be rebuilt next time it is used         applies the constraints defined by q and r to the system
1360         """         """
1361         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if not self.isUsingLumping():
1362         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1363         self.__operator_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1364         if deep: self.__operator=escript.Operator()            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         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 __rebuildRightHandSide(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
1401         """       """
1402         @brief indicates the right hand side has to be rebuild next time it is used       checks if name is a the name of a coefficient of the general PDE.
1403         """  
1404         if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."       @param name: name of the coefficient enquired.
1405         self.__rebuildSolution(deep)       @type name: C{string}
1406         self.__righthandside_isValid=False       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1407         if not self.__homogeneous_constraint: self.__rebuildOperator()       @rtype: C{bool}
        if deep: self.__righthandside=escript.Data()  
1408    
    def __rebuildSystem(self,deep=False):  
        """  
        @brief annonced that all coefficient name has been changed  
        """  
        self.__rebuildSolution(deep)  
        self.__rebuildOperator(deep)  
        self.__rebuildRightHandSide(deep)  
     
    def __checkMatrixType(self):  
1409       """       """
1410       @brief reassess the matrix type and, if needed, initiates an operator rebuild       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1411    
1412       def createCoefficientOfGeneralPDE(self,name):
1413       """       """
1414       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       returns a new instance of a coefficient for coefficient name of the general PDE
      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)  
1415    
1416     #============ assembling =======================================================       @param name: name of the coefficient requested.
1417     def __copyConstraint(self,u):       @type name: C{string}
1418        """       @return: a coefficient name initialized to 0.
1419        @brief copies the constrint condition into u       @rtype: L{Data<escript.Data>}
1420        """       @raise IllegalCoefficient: if name is not one of coefficients
1421        q=self.getCoefficient("q")                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1422        r=self.getCoefficient("r")                    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        if not q.isEmpty():       """
1424            if r.isEmpty():       if self.hasCoefficientOfGeneralPDE(name):
1425               r2=escript.Data(0,u.getShape(),u.getFunctionSpace())          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1426            else:       else:
1427               r2=escript.Data(r,u.getFunctionSpace())          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
           u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))  
1428    
1429     def __applyConstraint(self,rhs_update=True):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1430         """       """
1431         @brief applies the constraints  defined by q and r to the system       return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
        """  
        q=self.getCoefficient("q")  
        r=self.getCoefficient("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.__makeNewSolution()  
           if r.isEmpty():  
              r_s=self.__makeNewSolution()  
           else:  
              r_s=escript.Data(r,self.getFunctionSpaceForSolution())  
           u.copyWithMask(r_s,col_q)  
           if not self.__righthandside.isEmpty() and rhs_update: self.__righthandside-=self.__operator*u  
           self.__operator.nullifyRowsAndCols(row_q,col_q,1.)  
1432    
1433     def getOperator(self):       @param name: name of the coefficient enquired.
1434         """       @type name: C{string}
1435         @brief returns the operator of the PDE       @return: the function space to be used for coefficient name
1436         """       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1437         if not self.__operator_isValid:       @raise IllegalCoefficient: if name is not one of coefficients
1438             # some Constraints are applying for a lumpled stifness matrix:                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1439             if self.isUsingLumping():                    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                if self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():       """
1441                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"       if self.hasCoefficientOfGeneralPDE(name):
1442                if not self.getCoefficient("A").isEmpty():          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1443                         raise Warning,"Lumped matrix does not allow coefficient A"       else:
1444                if not self.getCoefficient("B").isEmpty():          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
                        raise Warning,"Lumped matrix does not allow coefficient B"  
               if not self.getCoefficient("C").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient C"  
               if not self.getCoefficient("D").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient D"  
               if self.debug() : print "PDE Debug: New lumped operator is built."  
               mat=self.__makeNewOperator(self)  
            else:  
               if self.debug() : print "PDE Debug: New operator is built."  
               mat=self.__getFreshOperator()  
1445    
1446             self.getDomain().addPDEToSystem(mat,escript.Data(), \     def getShapeOfCoefficientOfGeneralPDE(self,name):
1447                          self.getCoefficient("A"), \       """
1448                          self.getCoefficient("B"), \       return the shape of the coefficient name of the general PDE
                         self.getCoefficient("C"), \  
                         self.getCoefficient("D"), \  
                         escript.Data(), \  
                         escript.Data(), \  
                         self.getCoefficient("d"), \  
                         escript.Data(),\  
                         self.getCoefficient("d_contact"), \  
                         escript.Data())  
            if self.isUsingLumping():  
               self.__operator=mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceOfSolution(),True)  
            else:  
               self.__applyConstraint(rhs_update=False)  
            self.__operator_isValid=True  
        return self.__operator  
1449    
1450     def getRightHandSide(self,ignoreConstraint=False):       @param name: name of the coefficient enquired.
1451         """       @type name: C{string}
1452         @brief returns the right hand side of the PDE       @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.hasCoefficientOfGeneralPDE(name):
1459            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1460         else:
1461            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1462    
1463         @param ignoreConstraint     # =============================================================================
1464         """     # functions giving access to coefficients of a particular PDE implementation:
1465         if not self.__righthandside_isValid:     # =============================================================================
1466             if self.debug() : print "PDE Debug: New right hand side is built."     def getCoefficient(self,name):
1467             self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \       """
1468                           self.getCoefficient("X"), \       returns the value of the coefficient name
1469                           self.getCoefficient("Y"),\  
1470                           self.getCoefficient("y"),\       @param name: name of the coefficient requested.
1471                           self.getCoefficient("y_contact"))       @type name: C{string}
1472             self.__righthandside_isValid=True       @return: the value of the coefficient name
1473             if ignoreConstraint: self.__copyConstraint(self.__righthandside)       @rtype: L{Data<escript.Data>}
1474         return self.__righthandside       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1475         """
1476         if self.hasCoefficient(name):
1477             return self.COEFFICIENTS[name].getValue()
1478         else:
1479            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1480    
1481       def hasCoefficient(self,name):
1482         """
1483         return True if name is the name of a coefficient
1484    
1485         @param name: name of the coefficient enquired.
1486         @type name: C{string}
1487         @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       def createCoefficient(self, name):
1493         """
1494         create a L{Data<escript.Data>} object corresponding to coefficient name
1495    
1496         @return: a coefficient name initialized to 0.
1497         @rtype: L{Data<escript.Data>}
1498         @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       def getFunctionSpaceForCoefficient(self,name):
1506         """
1507         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1508    
1509         @param name: name of the coefficient enquired.
1510         @type name: C{string}
1511         @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):
1580          """
1581          sets new values to coefficients
1582    
1583          @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:
1631          for i in coefficients.iterkeys():
1632             if not self.hasCoefficient(i):
1633                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:
1635          if self.__numEquations==None or self.__numSolutions==None:
1636             for i,d in coefficients.iteritems():
1637                if hasattr(d,"shape"):
1638                    s=d.shape
1639                elif hasattr(d,"getShape"):
1640                    s=d.getShape()
1641                else:
1642                    s=numarray.array(d).shape
1643                if s!=None:
1644                    # get number of equations and number of unknowns:
1645                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1646                    if res==None:
1647                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1648                    else:
1649                        if self.__numEquations==None: self.__numEquations=res[0]
1650                        if self.__numSolutions==None: self.__numSolutions=res[1]
1651          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1652          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:
1654          for i,d in coefficients.iteritems():
1655            try:
1656               self.COEFFICIENTS[i].setValue(self.getDomain(),
1657                                             self.getNumEquations(),self.getNumSolutions(),
1658                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1659               self.alteredCoefficient(i)
1660            except IllegalCoefficientFunctionSpace,m:
1661                # if the function space is wrong then we try the reduced version:
1662                i_red=i+"_reduced"
1663                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1664                    try:
1665                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1666                                                          self.getNumEquations(),self.getNumSolutions(),
1667                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1668                        self.alteredCoefficient(i_red)
1669                    except IllegalCoefficientValue,m:
1670                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1671                    except IllegalCoefficientFunctionSpace,m:
1672                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673                else:
1674                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1675            except IllegalCoefficientValue,m:
1676               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1677          self.__altered_coefficients=True
1678          # check if the systrem is inhomogeneous:
1679          if len(coefficients)>0 and not self.isUsingLumping():
1680             q=self.getCoefficientOfGeneralPDE("q")
1681             r=self.getCoefficientOfGeneralPDE("r")
1682             homogeneous_constraint=True
1683             if not q.isEmpty() and not r.isEmpty():
1684                 if util.Lsup(q*r)>0.:
1685                   self.trace("Inhomogeneous constraint detected.")
1686                   self.__invalidateSystem()
1687    
1688     def getSystem(self):     def getSystem(self):
1689         """         """
1690         @brief         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 and not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
           if self.debug() : print "PDE Debug: New PDE is built."  
1696            if self.isUsingLumping():            if self.isUsingLumping():
1697                self.getRightHandSide(ignoreConstraint=True)                if not self.__operator_is_Valid:
1698                self.getOperator()                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1699                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1700                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1701                          raise ValueError,"coefficient A in lumped matrix may not be present."
1702                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1703                          raise ValueError,"coefficient B in lumped matrix may not be present."
1704                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1705                          raise ValueError,"coefficient C in lumped matrix may not be present."
1706                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1707                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1708                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1709                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1710                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1711                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1712                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1713                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1714                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1715                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1716                     D=self.getCoefficientOfGeneralPDE("D")
1717                     d=self.getCoefficientOfGeneralPDE("d")
1718                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1719                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1720                     if not D.isEmpty():
1721                         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 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                     self.__operator=1./self.__operator
1766                     self.trace("New lumped operator has been built.")
1767                     self.__operator_is_Valid=True
1768                  if not self.__righthandside_isValid:
1769                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1770                                   self.getCoefficientOfGeneralPDE("X"), \
1771                                   self.getCoefficientOfGeneralPDE("Y"),\
1772                                   self.getCoefficientOfGeneralPDE("y"),\
1773                                   self.getCoefficientOfGeneralPDE("y_contact"))
1774                     self.getDomain().addPDEToRHS(self.__righthandside, \
1775                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1776                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1777                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1778                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1779                     self.trace("New right hand side as been built.")
1780                     self.__righthandside_isValid=True
1781            else:            else:
1782                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1783                              self.getCoefficient("A"), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1784                              self.getCoefficient("B"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1785                              self.getCoefficient("C"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1786                              self.getCoefficient("D"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1787                              self.getCoefficient("X"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1788                              self.getCoefficient("Y"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1789                              self.getCoefficient("d"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1790                              self.getCoefficient("y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1791                              self.getCoefficient("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1792                              self.getCoefficient("y_contact"))                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1793            self.__operator_isValid=True                                 self.getCoefficientOfGeneralPDE("y_contact"))
1794            self.__righthandside_isValid=True                   self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1795            self.__applyConstraint()                                 self.getCoefficientOfGeneralPDE("A_reduced"), \
1796            self.__copyConstraint(self.__righthandside)                                 self.getCoefficientOfGeneralPDE("B_reduced"), \
1797         elif not self.__operator_isValid:                                 self.getCoefficientOfGeneralPDE("C_reduced"), \
1798            self.getOperator()                                 self.getCoefficientOfGeneralPDE("D_reduced"), \
1799         elif not self.__righthandside_isValid:                                 self.getCoefficientOfGeneralPDE("X_reduced"), \
1800            self.getRightHandSide()                                 self.getCoefficientOfGeneralPDE("Y_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1805                     self.__applyConstraint()
1806                     self.__righthandside=self.copyConstraint(self.__righthandside)
1807                     self.trace("New system has been built.")
1808                     self.__operator_is_Valid=True
1809                     self.__righthandside_isValid=True
1810                 elif not self.__righthandside_isValid:
1811                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1812                                   self.getCoefficientOfGeneralPDE("X"), \
1813                                   self.getCoefficientOfGeneralPDE("Y"),\
1814                                   self.getCoefficientOfGeneralPDE("y"),\
1815                                   self.getCoefficientOfGeneralPDE("y_contact"))
1816                     self.getDomain().addPDEToRHS(self.__righthandside, \
1817                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1818                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1819                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1820                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1821                     self.__righthandside=self.copyConstraint(self.__righthandside)
1822                     self.trace("New right hand side has been built.")
1823                     self.__righthandside_isValid=True
1824                 elif not self.__operator_is_Valid:
1825                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1826                                self.getCoefficientOfGeneralPDE("A"), \
1827                                self.getCoefficientOfGeneralPDE("B"), \
1828                                self.getCoefficientOfGeneralPDE("C"), \
1829                                self.getCoefficientOfGeneralPDE("D"), \
1830                                escript.Data(), \
1831                                escript.Data(), \
1832                                self.getCoefficientOfGeneralPDE("d"), \
1833                                escript.Data(),\
1834                                self.getCoefficientOfGeneralPDE("d_contact"), \
1835                                escript.Data())
1836                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1837                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1839                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1840                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1841                                escript.Data(), \
1842                                escript.Data(), \
1843                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1844                                escript.Data(),\
1845                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1846                                escript.Data())
1847                     self.__applyConstraint()
1848                     self.trace("New operator has been built.")
1849                     self.__operator_is_Valid=True
1850         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1851    
    def solve(self,**options):  
       """  
       @brief solve the PDE  
1852    
1853        @param options  class Poisson(LinearPDE):
1854        """     """
1855        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  
          self.__copyConstraint(out)  
       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  
1856    
1857     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief returns the solution of the PDE  
1858    
1859         @param options     with natural boundary conditons
1860         """  
1861         if not self.__solution_isValid:     M{n[j]*grad(u)[j] = 0 }
1862             if self.debug() : print "PDE Debug: PDE is resolved."  
1863             self.__solution=self.solve(**options)     and constraints:
1864             self.__solution_isValid=True  
1865         return self.__solution     M{u=0} where M{q>0}
1866     #============ some serivice functions  =====================================================  
1867     def getDomain(self):     """
1868       """  
1869       @brief returns the domain of the PDE     def __init__(self,domain,debug=False):
1870       """       """
1871       return self.__domain       initializes a new Poisson equation
1872    
1873         @param domain: domain of the PDE
1874         @type domain: L{Domain<escript.Domain>}
1875         @param debug: if True debug informations are printed.
1876    
    def getNumEquations(self):  
1877       """       """
1878       @brief returns the number of equations       super(Poisson, self).__init__(domain,1,1,debug)
1879         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1880                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1881                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1882         self.setSymmetryOn()
1883    
1884       def setValue(self,**coefficients):
1885       """       """
1886       if self.__numEquations>0:       sets new values to coefficients
1887           return self.__numEquations  
1888         @param coefficients: new values assigned to coefficients
1889         @keyword f: value for right hand side M{f}
1890         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1891         @keyword q: mask for location of constraints
1892         @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>}
1893                   depending of reduced order is used for the representation of the equation.
1894         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1895         """
1896         super(Poisson, self).setValue(**coefficients)
1897    
1898       def getCoefficientOfGeneralPDE(self,name):
1899         """
1900         return the value of the coefficient name of the general PDE
1901         @param name: name of the coefficient requested.
1902         @type name: C{string}
1903         @return: the value of the coefficient  name
1904         @rtype: L{Data<escript.Data>}
1905         @raise IllegalCoefficient: if name is not one of coefficients
1906                      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}.
1907         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1908         """
1909         if name == "A" :
1910             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1911         elif name == "B" :
1912             return escript.Data()
1913         elif name == "C" :
1914             return escript.Data()
1915         elif name == "D" :
1916             return escript.Data()
1917         elif name == "X" :
1918             return escript.Data()
1919         elif name == "Y" :
1920             return self.getCoefficient("f")
1921         elif name == "d" :
1922             return escript.Data()
1923         elif name == "y" :
1924             return escript.Data()
1925         elif name == "d_contact" :
1926             return escript.Data()
1927         elif name == "y_contact" :
1928             return escript.Data()
1929         elif name == "A_reduced" :
1930             return escript.Data()
1931         elif name == "B_reduced" :
1932             return escript.Data()
1933         elif name == "C_reduced" :
1934             return escript.Data()
1935         elif name == "D_reduced" :
1936             return escript.Data()
1937         elif name == "X_reduced" :
1938             return escript.Data()
1939         elif name == "Y_reduced" :
1940             return self.getCoefficient("f_reduced")
1941         elif name == "d_reduced" :
1942             return escript.Data()
1943         elif name == "y_reduced" :
1944             return escript.Data()
1945         elif name == "d_contact_reduced" :
1946             return escript.Data()
1947         elif name == "y_contact_reduced" :
1948             return escript.Data()
1949         elif name == "r" :
1950             return escript.Data()
1951         elif name == "q" :
1952             return self.getCoefficient("q")
1953       else:       else:
1954           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1955    
1956     def getNumSolutions(self):  class Helmholtz(LinearPDE):
1957       """
1958       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1959    
1960       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1961    
1962       with natural boundary conditons
1963    
1964       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1965    
1966       and constraints:
1967    
1968       M{u=r} where M{q>0}
1969    
1970       """
1971    
1972       def __init__(self,domain,debug=False):
1973       """       """
1974       @brief returns the number of unknowns       initializes a new Poisson equation
1975    
1976         @param domain: domain of the PDE
1977         @type domain: L{Domain<escript.Domain>}
1978         @param debug: if True debug informations are printed.
1979    
1980         """
1981         super(Helmholtz, self).__init__(domain,1,1,debug)
1982         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1983                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1984                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1985                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1987                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1990                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1991         self.setSymmetryOn()
1992    
1993       def setValue(self,**coefficients):
1994       """       """
1995       if self.__numSolutions>0:       sets new values to coefficients
1996          return self.__numSolutions  
1997         @param coefficients: new values assigned to coefficients
1998         @keyword omega: value for coefficient M{S{omega}}
1999         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2000         @keyword k: value for coefficeint M{k}
2001         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2002         @keyword f: value for right hand side M{f}
2003         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2004         @keyword alpha: value for right hand side M{S{alpha}}
2005         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2006         @keyword g: value for right hand side M{g}
2007         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2008         @keyword r: prescribed values M{r} for the solution in constraints.
2009         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2010                   depending of reduced order is used for the representation of the equation.
2011         @keyword q: mask for location of constraints
2012         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2013                   depending of reduced order is used for the representation of the equation.
2014         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2015         """
2016         super(Helmholtz, self).setValue(**coefficients)
2017    
2018       def getCoefficientOfGeneralPDE(self,name):
2019         """
2020         return the value of the coefficient name of the general PDE
2021    
2022         @param name: name of the coefficient requested.
2023         @type name: C{string}
2024         @return: the value of the coefficient  name
2025         @rtype: L{Data<escript.Data>}
2026         @raise IllegalCoefficient: if name is not one of coefficients
2027                      "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}.
2028         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2029         """
2030         if name == "A" :
2031             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2032         elif name == "B" :
2033             return escript.Data()
2034         elif name == "C" :
2035             return escript.Data()
2036         elif name == "D" :
2037             return self.getCoefficient("omega")
2038         elif name == "X" :
2039             return escript.Data()
2040         elif name == "Y" :
2041             return self.getCoefficient("f")
2042         elif name == "d" :
2043             return self.getCoefficient("alpha")
2044         elif name == "y" :
2045             return self.getCoefficient("g")
2046         elif name == "d_contact" :
2047             return escript.Data()
2048         elif name == "y_contact" :
2049             return escript.Data()
2050         elif name == "A_reduced" :
2051             return escript.Data()
2052         elif name == "B_reduced" :
2053             return escript.Data()
2054         elif name == "C_reduced" :
2055             return escript.Data()
2056         elif name == "D_reduced" :
2057             return escript.Data()
2058         elif name == "X_reduced" :
2059             return escript.Data()
2060         elif name == "Y_reduced" :
2061             return self.getCoefficient("f_reduced")
2062         elif name == "d_reduced" :
2063             return escript.Data()
2064         elif name == "y_reduced" :
2065            return self.getCoefficient("g_reduced")
2066         elif name == "d_contact_reduced" :
2067             return escript.Data()
2068         elif name == "y_contact_reduced" :
2069             return escript.Data()
2070         elif name == "r" :
2071             return self.getCoefficient("r")
2072         elif name == "q" :
2073             return self.getCoefficient("q")
2074       else:       else:
2075          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2076    
2077    class LameEquation(LinearPDE):
2078       """
2079       Class to define a Lame equation problem:
2080    
2081     def checkSymmetry(self):     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] }
       """  
       @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.  
       """  
       raise SystemError,"checkSymmetry is not implemented yet"  
2082    
2083        return None     with natural boundary conditons:
2084    
2085     def getFlux(self,u):     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] }
        """  
        @brief returns the flux J_ij for a given u  
2086    
2087              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}     and constraints:
2088    
2089         @param u argument of the operator     M{u[i]=r[i]} where M{q[i]>0}
2090    
2091         """     """
        raise SystemError,"getFlux is not implemented yet"  
        return None  
2092    
2093     def applyOperator(self,u):     def __init__(self,domain,debug=False):
2094         """        super(LameEquation, self).__init__(domain,\
2095         @brief applies the operator of the PDE to a given solution u in weak from                                           domain.getDim(),domain.getDim(),debug)
2096          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2097                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2098                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2099                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2100                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2101                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2102                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2103          self.setSymmetryOn()
2104    
2105       def setValues(self,**coefficients):
2106         """
2107         sets new values to coefficients
2108    
2109         @param coefficients: new values assigned to coefficients
2110         @keyword lame_mu: value for coefficient M{S{mu}}
2111         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2112         @keyword lame_lambda: value for coefficient M{S{lambda}}
2113         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2114         @keyword F: value for internal force M{F}
2115         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2116         @keyword sigma: value for initial stress M{S{sigma}}
2117         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2118         @keyword f: value for extrenal force M{f}
2119         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2120         @keyword r: prescribed values M{r} for the solution in constraints.
2121         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2122                   depending of reduced order is used for the representation of the equation.
2123         @keyword q: mask for location of constraints
2124         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2125                   depending of reduced order is used for the representation of the equation.
2126         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2127         """
2128         super(LameEquation, self).setValues(**coefficients)
2129    
2130       def getCoefficientOfGeneralPDE(self,name):
2131         """
2132         return the value of the coefficient name of the general PDE
2133    
2134         @param name: name of the coefficient requested.
2135         @type name: C{string}
2136         @return: the value of the coefficient  name
2137         @rtype: L{Data<escript.Data>}
2138         @raise IllegalCoefficient: if name is not one of coefficients
2139                      "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}.
2140         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2141         """
2142         if name == "A" :
2143             out =self.createCoefficientOfGeneralPDE("A")
2144             for i in range(self.getDim()):
2145               for j in range(self.getDim()):
2146                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2147                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2148                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2149             return out
2150         elif name == "B" :
2151             return escript.Data()
2152         elif name == "C" :
2153             return escript.Data()
2154         elif name == "D" :
2155             return escript.Data()
2156         elif name == "X" :
2157             return self.getCoefficient("sigma")
2158         elif name == "Y" :
2159             return self.getCoefficient("F")
2160         elif name == "d" :
2161             return escript.Data()
2162         elif name == "y" :
2163             return self.getCoefficient("f")
2164         elif name == "d_contact" :
2165             return escript.Data()
2166         elif name == "y_contact" :
2167             return escript.Data()
2168         elif name == "A_reduced" :
2169             return escript.Data()
2170         elif name == "B_reduced" :
2171             return escript.Data()
2172         elif name == "C_reduced" :
2173             return escript.Data()
2174         elif name == "D_reduced" :
2175             return escript.Data()
2176         elif name == "X_reduced" :
2177             return escript.Data()
2178         elif name == "Y_reduced" :
2179             return escript.Data()
2180         elif name == "d_reduced" :
2181             return escript.Data()
2182         elif name == "y_reduced" :
2183             return escript.Data()
2184         elif name == "d_contact_reduced" :
2185             return escript.Data()
2186         elif name == "y_contact_reduced" :
2187             return escript.Data()
2188         elif name == "r" :
2189             return self.getCoefficient("r")
2190         elif name == "q" :
2191             return self.getCoefficient("q")
2192         else:
2193            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2194    
2195         @param u argument of the operator  def LinearSinglePDE(domain,debug=False):
2196       """
2197       defines a single linear PDEs
2198    
2199         """     @param domain: domain of the PDE
2200         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())     @type domain: L{Domain<escript.Domain>}
2201                                                                                                                                                                 @param debug: if True debug informations are printed.
2202     def getResidual(self,u):     @rtype: L{LinearPDE}
2203         """     """
2204         @brief return the residual of u in the weak from     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2205    
2206         @param u  def LinearPDESystem(domain,debug=False):
2207         """     """
2208         return self.applyOperator(u)-self.getRightHandSide()     defines a system of linear PDEs
2209    
2210  class Poisson(LinearPDE):     @param domain: domain of the PDE
2211       @type domain: L{Domain<escript.Domain>}
2212       @param debug: if True debug informations are printed.
2213       @rtype: L{LinearPDE}
2214     """     """
2215     @brief Class to define a Poisson equstion problem:     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2216                                                                                                                                                                
2217     class to define a linear PDE of the form  class TransportPDE(object):
2218                                                                                                                                                                     """
2219          -u_{,jj} = f       Warning: This is still a very experimental. The class is still changing!
2220                                                                                                                                                                
2221       with boundary conditons:       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2222                                                                                                                                                                    
2223          n_j*u_{,j} = 0       u=r where q>0
2224                                                                                                                                                                    
2225      and constraints:       all coefficients are constant over time.
2226                                                                                                                                                                
2227           u=0 where q>0       typical usage:
2228                                                                                                                                                                
2229     """           p=TransportPDE(dom)
2230             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2231     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2232         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))           t=0
2233         self._setCoefficient(A=numarray.identity(self.getDomain().getDim()))           dt=0.1
2234         self.setSymmetryOn()           while (t<1.):
2235         self.setValue(f,q)                u=p.solve(dt)
2236    
2237     def setValue(self,f=escript.Data(),q=escript.Data()):       """
2238         self._setCoefficient(Y=f,q=q)       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2239            self.__domain=domain
2240                                                                                                                                                                      self.__num_equations=num_equations
2241  # $Log$          self.__useSUPG=useSUPG
2242  # Revision 1.2  2004/12/15 07:08:27  jgs          self.__trace=trace
2243  # *** empty log message ***          self.__theta=theta
2244  #          self.__matrix_type=0
2245  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs          self.__reduced=True
2246  # *** empty log message ***          self.__reassemble=True
2247  #          if self.__useSUPG:
2248  # Revision 1.1.2.1  2004/12/12 22:53:47  gross             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2249  # linearPDE has been renamed LinearPDE             self.__pde.setSymmetryOn()
2250  #             self.__pde.setReducedOrderOn()
2251  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross          else:
2252  # GMRES added             self.__transport_problem=self.__getNewTransportProblem()
2253  #          self.setTolerance()
2254  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross          self.__M=escript.Data()
2255  # options for GMRES and PRES20 added          self.__A=escript.Data()
2256  #          self.__B=escript.Data()
2257  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross          self.__C=escript.Data()
2258  # some small changes          self.__D=escript.Data()
2259  #          self.__X=escript.Data()
2260  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross          self.__Y=escript.Data()
2261  # Finley solves 4M unknowns now          self.__d=escript.Data()
2262  #          self.__y=escript.Data()
2263  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross          self.__d_contact=escript.Data()
2264  # poisson solver added          self.__y_contact=escript.Data()
2265  #          self.__r=escript.Data()
2266  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross          self.__q=escript.Data()
2267  # 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  
2268  #       def trace(self,text):
2269  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross               if self.__trace: print text
2270  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed       def getSafeTimeStepSize(self):
2271  #          if self.__useSUPG:
2272  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs              if self.__reassemble:
2273  # initial import of project esys2                 h=self.__domain.getSize()
2274  #                 dt=None
2275  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs                 if not self.__A.isEmpty():
2276  # committing Lutz's and Paul's changes to brach jgs                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2277  #                    if dt == None:
2278  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane                       dt = dt2
2279  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.                    else:
2280  #                       dt=1./(1./dt+1./dt2)
2281  # Revision 1.3  2004/09/23 00:53:23  jgs                 if not self.__B.isEmpty():
2282  # minor fixes                    dt2=util.inf(h*self.__M/util.length(self.__B))
2283  #                    if dt == None:
2284  # Revision 1.1  2004/08/28 12:58:06  gross                       dt = dt2
2285  # SimpleSolve is not running yet: problem with == of functionsspace                    else:
2286  #                       dt=1./(1./dt+1./dt2)
2287  #                 if not  self.__C.isEmpty():
2288                      dt2=util.inf(h*self.__M/util.length(self.__C))
2289                      if dt == None:
2290                         dt = dt2
2291                      else:
2292                         dt=1./(1./dt+1./dt2)
2293                   if not self.__D.isEmpty():
2294                      dt2=util.inf(self.__M/util.length(self.__D))
2295                      if dt == None:
2296                         dt = dt2
2297                      else:
2298                         dt=1./(1./dt+1./dt2)
2299                   self.__dt = dt/2
2300                return self.__dt
2301            else:
2302                return self.__getTransportProblem().getSafeTimeStepSize()
2303         def getDomain(self):
2304            return self.__domain
2305         def getTheta(self):
2306            return self.__theta
2307         def getNumEquations(self):
2308            return self.__num_equations
2309         def setReducedOn(self):
2310              if not self.reduced():
2311                  if self.__useSUPG:
2312                     self.__pde.setReducedOrderOn()
2313                  else:
2314                     self.__transport_problem=self.__getNewTransportProblem()
2315              self.__reduced=True
2316         def setReducedOff(self):
2317              if self.reduced():
2318                  if self.__useSUPG:
2319                     self.__pde.setReducedOrderOff()
2320                  else:
2321                     self.__transport_problem=self.__getNewTransportProblem()
2322              self.__reduced=False
2323         def reduced(self):
2324             return self.__reduced
2325         def getFunctionSpace(self):
2326            if self.reduced():
2327               return escript.ReducedSolution(self.getDomain())
2328            else:
2329               return escript.Solution(self.getDomain())
2330    
2331         def setTolerance(self,tol=1.e-8):
2332            self.__tolerance=tol
2333            if self.__useSUPG:
2334                  self.__pde.setTolerance(self.__tolerance)
2335    
2336         def __getNewTransportProblem(self):
2337           """
2338           returns an instance of a new operator
2339           """
2340           self.trace("New Transport problem is allocated.")
2341           return self.getDomain().newTransportProblem( \
2342                                   self.getTheta(),
2343                                   self.getNumEquations(), \
2344                                   self.getFunctionSpace(), \
2345                                   self.__matrix_type)
2346              
2347         def __getNewSolutionVector(self):
2348             if self.getNumEquations() ==1 :
2349                    out=escript.Data(0.0,(),self.getFunctionSpace())
2350             else:
2351                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2352             return out
2353    
2354         def __getTransportProblem(self):
2355           if self.__reassemble:
2356                 self.__source=self.__getNewSolutionVector()
2357                 self.__transport_problem.reset()
2358                 self.getDomain().addPDEToTransportProblem(
2359                             self.__transport_problem,
2360                             self.__source,
2361                             self.__M,
2362                             self.__A,
2363                             self.__B,
2364                             self.__C,
2365                             self.__D,
2366                             self.__X,
2367                             self.__Y,
2368                             self.__d,
2369                             self.__y,
2370                             self.__d_contact,
2371                             self.__y_contact)
2372                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2373                 self.__reassemble=False
2374           return self.__transport_problem
2375         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2376                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2377                 if not M==None:
2378                      self.__reassemble=True
2379                      self.__M=M
2380                 if not A==None:
2381                      self.__reassemble=True
2382                      self.__A=A
2383                 if not B==None:
2384                      self.__reassemble=True
2385                      self.__B=B
2386                 if not C==None:
2387                      self.__reassemble=True
2388                      self.__C=C
2389                 if not D==None:
2390                      self.__reassemble=True
2391                      self.__D=D
2392                 if not X==None:
2393                      self.__reassemble=True
2394                      self.__X=X
2395                 if not Y==None:
2396                      self.__reassemble=True
2397                      self.__Y=Y
2398                 if not d==None:
2399                      self.__reassemble=True
2400                      self.__d=d
2401                 if not y==None:
2402                      self.__reassemble=True
2403                      self.__y=y
2404                 if not d_contact==None:
2405                      self.__reassemble=True
2406                      self.__d_contact=d_contact
2407                 if not y_contact==None:
2408                      self.__reassemble=True
2409                      self.__y_contact=y_contact
2410                 if not q==None:
2411                      self.__reassemble=True
2412                      self.__q=q
2413                 if not r==None:
2414                      self.__reassemble=True
2415                      self.__r=r
2416    
2417         def setInitialSolution(self,u):
2418                 if self.__useSUPG:
2419                     self.__u=util.interpolate(u,self.getFunctionSpace())
2420                 else:
2421                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2422    
2423         def solve(self,dt,**kwarg):
2424               if self.__useSUPG:
2425                    if self.__reassemble:
2426                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2427                        self.__reassemble=False
2428                    dt2=self.getSafeTimeStepSize()
2429                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2430                    dt2=dt/nn
2431                    nnn=0
2432                    u=self.__u
2433                    self.trace("number of substeps is %d."%nn)
2434                    while nnn<nn :
2435                        self.__setSUPG(u,u,dt2/2)
2436                        u_half=self.__pde.getSolution(verbose=True)
2437                        self.__setSUPG(u,u_half,dt2)
2438                        u=self.__pde.getSolution(verbose=True)
2439                        nnn+=1
2440                    self.__u=u
2441                    return self.__u
2442               else:
2443                   kwarg["tolerance"]=self.__tolerance
2444                   tp=self.__getTransportProblem()
2445                   return tp.solve(self.__source,dt,kwarg)
2446         def __setSUPG(self,u0,u,dt):
2447                g=util.grad(u)
2448                X=0
2449                Y=self.__M*u0
2450                X=0
2451                self.__pde.setValue(r=u0)
2452                if not self.__A.isEmpty():
2453                   X=X+dt*util.matrixmult(self.__A,g)
2454                if not self.__B.isEmpty():
2455                   X=X+dt*self.__B*u
2456                if not  self.__C.isEmpty():
2457                   Y=Y+dt*util.inner(self.__C,g)
2458                if not self.__D.isEmpty():
2459                   Y=Y+dt*self.__D*u
2460                if not self.__X.isEmpty():
2461                   X=X+dt*self.__X
2462                if not self.__Y.isEmpty():
2463                   Y=Y+dt*self.__Y
2464                self.__pde.setValue(X=X,Y=Y)
2465                if not self.__y.isEmpty():
2466                   self.__pde.setValue(y=dt*self.__y)
2467                if not self.__y_contact.isEmpty():
2468                   self.__pde.setValue(y=dt*self.__y_contact)
2469                self.__pde.setValue(r=u0)

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