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trunk/esys2/escript/py_src/linearPDEs.py revision 104 by jgs, Fri Dec 17 07:43:12 2004 UTC trunk/escript/py_src/linearPDEs.py revision 1552 by gross, Thu May 8 08:52:41 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,domain,numEquations=0,numSolutions=0):     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
      """  
      @brief initializes a new linear PDE.  
375    
376       @param args     M{u=r}  where M{q>0}
377       """  
378       M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
379       The constraints override any other condition set by the PDE or the boundary condition.
380    
381       The PDE is symmetrical if
382    
383       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       For a system of PDEs and a solution with several components the PDE has the form
386    
387       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    
389       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       The natural boundary conditions take the form:
391    
392       M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
393    
394    
395       The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
396    
397       Constraints take the form
398    
399       M{u[i]=r[i]}  where  M{q[i]>0}
400    
401       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
402    
403       The system of PDEs is symmetrical if
404    
405            - M{A[i,j,k,l]=A[k,l,i,j]}
406            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
407            - M{B[i,j,k]=C[k,i,j]}
408            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
409            - M{D[i,k]=D[i,k]}
410            - M{D_reduced[i,k]=D_reduced[i,k]}
411            - M{d[i,k]=d[k,i]}
412            - M{d_reduced[i,k]=d_reduced[k,i]}
413    
414       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
415       discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
416       defined as
417    
418       M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
419    
420       For the case of single solution component and single PDE M{J} is defined
421    
422       M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
423    
424       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
425       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
426       the contact condition takes the form
427    
428       M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
429    
430       where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
431       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
432       L{jump<util.jump>}.
433       The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
434       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
435       In case of a single PDE and a single component solution the contact condition takes the form
436    
437       M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
438    
439       In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
440    
441       @cvar DEFAULT: The default method used to solve the system of linear equations
442       @cvar DIRECT: The direct solver based on LDU factorization
443       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
444       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
445       @cvar CR: The conjugate residual method
446       @cvar CGS: The conjugate gardient square method
447       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
448       @cvar SSOR: The symmetric overrealaxtion method
449       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
450       @cvar ILUT: The incomplete LU factorization preconditioner with will in
451       @cvar JACOBI: The Jacobi preconditioner
452       @cvar GMRES: The Gram-Schmidt minimum residual method
453       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
454       @cvar LUMPING: Matrix lumping.
455       @cvar NO_REORDERING: No matrix reordering allowed
456       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
457       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
458       @cvar PASO: PASO solver package
459       @cvar SCSL: SGI SCSL solver library
460       @cvar MKL: Intel's MKL solver library
461       @cvar UMFPACK: the UMFPACK library
462       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
463       @cvar ITERATIVE: The default iterative solver
464       @cvar AMG: algebraic multi grid
465       @cvar RILU: recursive ILU
466    
467       """
468       DEFAULT= 0
469       DIRECT= 1
470       CHOLEVSKY= 2
471       PCG= 3
472       CR= 4
473       CGS= 5
474       BICGSTAB= 6
475       SSOR= 7
476       ILU0= 8
477       ILUT= 9
478       JACOBI= 10
479       GMRES= 11
480       PRES20= 12
481       LUMPING= 13
482       NO_REORDERING= 17
483       MINIMUM_FILL_IN= 18
484       NESTED_DISSECTION= 19
485       SCSL= 14
486       MKL= 15
487       UMFPACK= 16
488       ITERATIVE= 20
489       PASO= 21
490       AMG= 22
491       RILU = 23
492       TRILINOS = 24
493    
494       SMALL_TOLERANCE=1.e-13
495       __PACKAGE_KEY="package"
496       __METHOD_KEY="method"
497       __SYMMETRY_KEY="symmetric"
498       __TOLERANCE_KEY="tolerance"
499       __PRECONDITIONER_KEY="preconditioner"
500    
501    
502       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
503         """
504         initializes a new linear PDE
505    
506         @param domain: domain of the PDE
507         @type domain: L{Domain<escript.Domain>}
508         @param numEquations: number of equations. If numEquations==None the number of equations
509                              is exracted from the PDE coefficients.
510         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
511                              is exracted from the PDE coefficients.
512         @param debug: if True debug informations are printed.
513    
514         """
515         super(LinearPDE, self).__init__()
516         #
517         #   the coefficients of the general PDE:
518         #
519         self.__COEFFICIENTS_OF_GENEARL_PDE={
520           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
521           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
522           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
523           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
524           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
525           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
526           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
527           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
528           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
529           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
530           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
531           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
532           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
533           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
535           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
536           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
537           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
538           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
541           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
542    
543         # COEFFICIENTS can be overwritten by subclasses:
544         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
545         self.__altered_coefficients=False
546       # initialize attributes       # initialize attributes
547       self.__debug=None       self.__debug=debug
548       self.__domain=domain       self.__domain=domain
549       self.__numEquations=numEquations       self.__numEquations=numEquations
550       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
551       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
552    
553       # set some default values:       # set some default values:
554       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
555       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
556       self.__tolerance=1.e-8       self.__tolerance=1.e-8
557       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
558       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
559         self.__preconditioner=self.DEFAULT
560         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
561       self.__sym=False       self.__sym=False
      self.__lumping=False  
562    
563     def getCoefficient(self,name):       self.resetCoefficients()
564         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
565       # =============================================================================
566       #    general stuff:
567       # =============================================================================
568       def __str__(self):
569         """
570         returns string representation of the PDE
571    
572         @return: a simple representation of the PDE
573         @rtype: C{str}
574         """
575         return "<LinearPDE %d>"%id(self)
576       # =============================================================================
577       #    debug :
578       # =============================================================================
579       def setDebugOn(self):
580         """
581         switches on debugging
582       """       """
583       @brief return the value of the coefficient name       self.__debug=not None
584    
585       @param name     def setDebugOff(self):
586         """
587         switches off debugging
588       """       """
589       return self.__coefficient[name]       self.__debug=None
590    
591     def setValue(self,**coefficients):     def trace(self,text):
592        """       """
593        @brief sets new values to coefficients       print the text message if debugging is swiched on.
594         @param text: message
595         @type text: C{string}
596         """
597         if self.__debug: print "%s: %s"%(str(self),text)
598    
599        @param coefficients     # =============================================================================
600        """     # some service functions:
601        self._setValue(**coefficients)     # =============================================================================
602             def getDomain(self):
603         """
604         returns the domain of the PDE
605    
606     def _setValue(self,**coefficients):       @return: the domain of the PDE
607        """       @rtype: L{Domain<escript.Domain>}
608        @brief sets new values to coefficients       """
609         return self.__domain
610    
611        @param coefficients     def getDim(self):
612        """       """
613               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:  
                 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  
614    
615        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
616        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
617           for i in self.__coefficient.iterkeys():       """
618               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()  
619    
620     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
621       """       """
622       @brief return the shape of the coefficient name       returns the number of equations
623    
624       @param name       @return: the number of equations
625         @rtype: C{int}
626         @raise UndefinedPDEError: if the number of equations is not be specified yet.
627       """       """
628       if self.hasCoefficient(name):       if self.__numEquations==None:
629          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
630       else:       else:
631          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
632    
633     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
634       """       """
635       @brief return the atoms of the coefficient name       returns the number of unknowns
636    
637       @param name       @return: the number of unknowns
638         @rtype: C{int}
639         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
640       """       """
641       if self.hasCoefficient(name):       if self.__numSolutions==None:
642          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
643       else:       else:
644          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
645    
646     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
647       """       """
648       @brief annonced that coefficient name has been changed       return status for order reduction for equation
649    
650       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
651         @rtype: L{bool}
652       """       """
653       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  
654    
655     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
656        """       """
657        @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.       return status for order reduction for the solution
       """  
       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."  
   
   
    def hasCoefficient(self,name):  
       """  
       @brief return true if name is the name of a coefficient  
658    
659        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
660        """       @rtype: L{bool}
661        return self.__coefficient.has_key(name)       """
662         return self.__reduce_solution_order
663    
664     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
665       """       """
666       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
667    
668         @return: representation space of equation
669         @rtype: L{FunctionSpace<escript.FunctionSpace>}
670       """       """
671       return self.__row_function_space       if self.reduceEquationOrder():
672             return escript.ReducedSolution(self.getDomain())
673         else:
674             return escript.Solution(self.getDomain())
675    
676     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
677       """       """
678       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
679    
680         @return: representation space of solution
681         @rtype: L{FunctionSpace<escript.FunctionSpace>}
682       """       """
683       return self.__column_function_space       if self.reduceSolutionOrder():
684             return escript.ReducedSolution(self.getDomain())
685         else:
686             return escript.Solution(self.getDomain())
687    
    # ===== debug ==============================================================  
    def setDebugOn(self):  
        """  
        @brief  
        """  
        self.__debug=not None  
688    
689     def setDebugOff(self):     def getOperator(self):
690         """       """
691         @brief       provides access to the operator of the PDE
        """  
        self.__debug=None  
692    
693     def debug(self):       @return: the operator of the PDE
694         """       @rtype: L{Operator<escript.Operator>}
695         @brief returns true if the PDE is in the debug mode       """
696         """       m=self.getSystem()[0]
697         return self.__debug       if self.isUsingLumping():
698             return self.copyConstraint(1./m)
699         else:
700             return m
701    
702     #===== Lumping ===========================     def getRightHandSide(self):
703     def setLumpingOn(self):       """
704        """       provides access to the right hand side of the PDE
705        @brief indicates to use matrix lumping       @return: the right hand side of the PDE
706        """       @rtype: L{Data<escript.Data>}
707        if not self.isUsingLumping():       """
708           raise SystemError,"Lumping is not working yet! Talk to the experts"       r=self.getSystem()[1]
709           if self.debug() : print "PDE Debug: lumping is set on"       if self.isUsingLumping():
710           self.__rebuildOperator()           return self.copyConstraint(r)
711           self.__lumping=True       else:
712             return r
713    
714     def setLumpingOff(self):     def applyOperator(self,u=None):
715        """       """
716        @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  
717    
718     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}
719        """                 the current solution is used.
720        @brief set the matrix lumping flag to flag       @type u: L{Data<escript.Data>} or None
721        """       @return: image of u
722        if flag:       @rtype: L{Data<escript.Data>}
723           self.setLumpingOn()       """
724        else:       if u==None:
725           self.setLumpingOff()          return self.getOperator()*self.getSolution()
726         else:
727            return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
728    
729     def isUsingLumping(self):     def getResidual(self,u=None):
730         """
731         return the residual of u or the current solution if u is not present.
732    
733         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
734                   the current solution is used.
735         @type u: L{Data<escript.Data>} or None
736         @return: residual of u
737         @rtype: L{Data<escript.Data>}
738         """
739         return self.applyOperator(u)-self.getRightHandSide()
740    
741       def checkSymmetry(self,verbose=True):
742        """        """
743        @brief        test the PDE for symmetry.
744    
745          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
746          @type verbose: C{bool}
747          @return:  True if the PDE is symmetric.
748          @rtype: L{Data<escript.Data>}
749          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
750        """        """
751        return self.__lumping        verbose=verbose or self.__debug
752          out=True
753          if self.getNumSolutions()!=self.getNumEquations():
754             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
755             out=False
756          else:
757             A=self.getCoefficientOfGeneralPDE("A")
758             if not A.isEmpty():
759                tol=util.Lsup(A)*self.SMALL_TOLERANCE
760                if self.getNumSolutions()>1:
761                   for i in range(self.getNumEquations()):
762                      for j in range(self.getDim()):
763                         for k in range(self.getNumSolutions()):
764                            for l in range(self.getDim()):
765                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
766                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
767                                   out=False
768                else:
769                   for j in range(self.getDim()):
770                      for l in range(self.getDim()):
771                         if util.Lsup(A[j,l]-A[l,j])>tol:
772                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
773                            out=False
774             B=self.getCoefficientOfGeneralPDE("B")
775             C=self.getCoefficientOfGeneralPDE("C")
776             if B.isEmpty() and not C.isEmpty():
777                if verbose: print "non-symmetric PDE because B is not present but C is"
778                out=False
779             elif not B.isEmpty() and C.isEmpty():
780                if verbose: print "non-symmetric PDE because C is not present but B is"
781                out=False
782             elif not B.isEmpty() and not C.isEmpty():
783                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
784                if self.getNumSolutions()>1:
785                   for i in range(self.getNumEquations()):
786                       for j in range(self.getDim()):
787                          for k in range(self.getNumSolutions()):
788                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
789                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
790                                  out=False
791                else:
792                   for j in range(self.getDim()):
793                      if util.Lsup(B[j]-C[j])>tol:
794                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
795                         out=False
796             if self.getNumSolutions()>1:
797               D=self.getCoefficientOfGeneralPDE("D")
798               if not D.isEmpty():
799                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
800                 for i in range(self.getNumEquations()):
801                    for k in range(self.getNumSolutions()):
802                      if util.Lsup(D[i,k]-D[k,i])>tol:
803                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
804                          out=False
805               d=self.getCoefficientOfGeneralPDE("d")
806               if not d.isEmpty():
807                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
808                 for i in range(self.getNumEquations()):
809                    for k in range(self.getNumSolutions()):
810                      if util.Lsup(d[i,k]-d[k,i])>tol:
811                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
812                          out=False
813               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
814               if not d_contact.isEmpty():
815                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
816                 for i in range(self.getNumEquations()):
817                    for k in range(self.getNumSolutions()):
818                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
819                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
820                          out=False
821             # and now the reduced coefficients
822             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
823             if not A_reduced.isEmpty():
824                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
825                if self.getNumSolutions()>1:
826                   for i in range(self.getNumEquations()):
827                      for j in range(self.getDim()):
828                         for k in range(self.getNumSolutions()):
829                            for l in range(self.getDim()):
830                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
831                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
832                                   out=False
833                else:
834                   for j in range(self.getDim()):
835                      for l in range(self.getDim()):
836                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
837                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
838                            out=False
839             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
840             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
841             if B_reduced.isEmpty() and not C_reduced.isEmpty():
842                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
843                out=False
844             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
845                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
846                out=False
847             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
848                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
849                if self.getNumSolutions()>1:
850                   for i in range(self.getNumEquations()):
851                       for j in range(self.getDim()):
852                          for k in range(self.getNumSolutions()):
853                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
854                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
855                                  out=False
856                else:
857                   for j in range(self.getDim()):
858                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
859                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
860                         out=False
861             if self.getNumSolutions()>1:
862               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
863               if not D_reduced.isEmpty():
864                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
865                 for i in range(self.getNumEquations()):
866                    for k in range(self.getNumSolutions()):
867                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
868                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
869                          out=False
870               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
871               if not d_reduced.isEmpty():
872                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
873                 for i in range(self.getNumEquations()):
874                    for k in range(self.getNumSolutions()):
875                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
876                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
877                          out=False
878               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
879               if not d_contact_reduced.isEmpty():
880                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
881                 for i in range(self.getNumEquations()):
882                    for k in range(self.getNumSolutions()):
883                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
884                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
885                          out=False
886          return out
887    
888     #============ method business =========================================================     def getSolution(self,**options):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
889         """         """
890         @brief sets a new solver         returns the solution of the PDE. If the solution is not valid the PDE is solved.
891    
892           @return: the solution
893           @rtype: L{Data<escript.Data>}
894           @param options: solver options
895           @keyword verbose: True to get some information during PDE solution
896           @type verbose: C{bool}
897           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
898                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
899           @keyword iter_max: maximum number of iteration steps allowed.
900           @keyword drop_tolerance: threshold for drupping in L{ILUT}
901           @keyword drop_storage: maximum of allowed memory in L{ILUT}
902           @keyword truncation: maximum number of residuals in L{GMRES}
903           @keyword restart: restart cycle length in L{GMRES}
904         """         """
905         if not solver==self.getSolverMethod():         if not self.__solution_isValid:
906              mat,f=self.getSystem()
907              if self.isUsingLumping():
908                 self.__solution=self.copyConstraint(f*mat)
909              else:
910                 options[self.__TOLERANCE_KEY]=self.getTolerance()
911                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
912                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
913                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
914                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
915                 self.trace("PDE is resolved.")
916                 self.trace("solver options: %s"%str(options))
917                 self.__solution=mat.solve(f,options)
918              self.__solution_isValid=True
919           return self.__solution
920    
921       def getFlux(self,u=None):
922         """
923         returns the flux M{J} for a given M{u}
924    
925         M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
926    
927         or
928    
929         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
930    
931         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
932         @type u: L{Data<escript.Data>} or None
933         @return: flux
934         @rtype: L{Data<escript.Data>}
935         """
936         if u==None: u=self.getSolution()
937         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
938               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
939               -util.self.getCoefficientOfGeneralPDE("X") \
940               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
941               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
942               -util.self.getCoefficientOfGeneralPDE("X_reduced")
943       # =============================================================================
944       #   solver settings:
945       # =============================================================================
946       def setSolverMethod(self,solver=None,preconditioner=None):
947           """
948           sets a new solver
949    
950           @param solver: sets a new solver method.
951           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, L{AMG}
952           @param preconditioner: sets a new solver method.
953           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
954           """
955           if solver==None: solver=self.__solver_method
956           if preconditioner==None: preconditioner=self.__preconditioner
957           if solver==None: solver=self.DEFAULT
958           if preconditioner==None: preconditioner=self.DEFAULT
959           if not (solver,preconditioner)==self.getSolverMethod():
960             self.__solver_method=solver             self.__solver_method=solver
961             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__preconditioner=preconditioner
962             self.__checkMatrixType()             self.__checkMatrixType()
963               self.trace("New solver is %s"%self.getSolverMethodName())
964    
965       def getSolverMethodName(self):
966           """
967           returns the name of the solver currently used
968    
969           @return: the name of the solver currently used.
970           @rtype: C{string}
971           """
972    
973           m=self.getSolverMethod()
974           p=self.getSolverPackage()
975           method=""
976           if m[0]==self.DEFAULT: method="DEFAULT"
977           elif m[0]==self.DIRECT: method= "DIRECT"
978           elif m[0]==self.ITERATIVE: method= "ITERATIVE"
979           elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
980           elif m[0]==self.PCG: method= "PCG"
981           elif m[0]==self.CR: method= "CR"
982           elif m[0]==self.CGS: method= "CGS"
983           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
984           elif m[0]==self.SSOR: method= "SSOR"
985           elif m[0]==self.GMRES: method= "GMRES"
986           elif m[0]==self.PRES20: method= "PRES20"
987           elif m[0]==self.LUMPING: method= "LUMPING"
988           elif m[0]==self.AMG: method= "AMG"
989           if m[1]==self.DEFAULT: method+="+DEFAULT"
990           elif m[1]==self.JACOBI: method+= "+JACOBI"
991           elif m[1]==self.ILU0: method+= "+ILU0"
992           elif m[1]==self.ILUT: method+= "+ILUT"
993           elif m[1]==self.SSOR: method+= "+SSOR"
994           elif m[1]==self.AMG: method+= "+AMG"
995           elif m[1]==self.RILU: method+= "+RILU"
996           if p==self.DEFAULT: package="DEFAULT"
997           elif p==self.PASO: package= "PASO"
998           elif p==self.MKL: package= "MKL"
999           elif p==self.SCSL: package= "SCSL"
1000           elif p==self.UMFPACK: package= "UMFPACK"
1001           elif p==self.TRILINOS: package= "TRILINOS"
1002           else : method="unknown"
1003           return "%s solver of %s package"%(method,package)
1004    
1005    
1006     def getSolverMethod(self):     def getSolverMethod(self):
1007         """         """
1008         @brief returns the solver method         returns the solver method
1009    
1010           @return: the solver method currently be used.
1011           @rtype: C{int}
1012           """
1013           return self.__solver_method,self.__preconditioner
1014    
1015       def setSolverPackage(self,package=None):
1016         """         """
1017         return self.__solver_method         sets a new solver package
1018    
1019           @param package: sets a new solver method.
1020           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1021           """
1022           if package==None: package=self.DEFAULT
1023           if not package==self.getSolverPackage():
1024               self.__solver_package=package
1025               self.__checkMatrixType()
1026               self.trace("New solver is %s"%self.getSolverMethodName())
1027    
1028       def getSolverPackage(self):
1029           """
1030           returns the package of the solver
1031    
1032           @return: the solver package currently being used.
1033           @rtype: C{int}
1034           """
1035           return self.__solver_package
1036    
1037       def isUsingLumping(self):
1038          """
1039          checks if matrix lumping is used a solver method
1040    
1041          @return: True is lumping is currently used a solver method.
1042          @rtype: C{bool}
1043          """
1044          return self.getSolverMethod()[0]==self.LUMPING
1045    
    #============ tolerance business =========================================================  
1046     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1047         """         """
1048         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1049    
1050           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1051    
1052           defines the stopping criterion.
1053    
1054           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1055                       the system will be resolved.
1056           @type tol: positive C{float}
1057           @raise ValueError: if tolerance is not positive.
1058         """         """
1059         if not tol>0:         if not tol>0:
1060             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1061         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1062         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1063         self.__tolerance=tol         self.__tolerance=tol
1064         return         return
1065    
1066     def getTolerance(self):     def getTolerance(self):
1067         """         """
1068         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
1069    
1070           @return: tolerance currently used.
1071           @rtype: C{float}
1072         """         """
1073         return self.__tolerance         return self.__tolerance
1074    
1075     #===== symmetry  flag ==========================     # =============================================================================
1076       #    symmetry  flag:
1077       # =============================================================================
1078     def isSymmetric(self):     def isSymmetric(self):
1079        """        """
1080        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1081    
1082          @return: True is a symmetric PDE is indicated, otherwise False is returned
1083          @rtype: C{bool}
1084        """        """
1085        return self.__sym        return self.__sym
1086    
1087     def setSymmetryOn(self):     def setSymmetryOn(self):
1088        """        """
1089        @brief sets the symmetry flag to true        sets the symmetry flag.
1090        """        """
1091        if not self.isSymmetric():        if not self.isSymmetric():
1092           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1093           self.__sym=True           self.__sym=True
1094           self.__checkMatrixType()           self.__checkMatrixType()
1095    
1096     def setSymmetryOff(self):     def setSymmetryOff(self):
1097        """        """
1098        @brief sets the symmetry flag to false        removes the symmetry flag.
1099        """        """
1100        if self.isSymmetric():        if self.isSymmetric():
1101           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1102           self.__sym=False           self.__sym=False
1103           self.__checkMatrixType()           self.__checkMatrixType()
1104    
1105     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1106       """        """
1107       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
1108    
1109       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1110       """        @type flag: C{bool}
1111       if flag:        """
1112          self.setSymmetryOn()        if flag:
1113       else:           self.setSymmetryOn()
1114          self.setSymmetryOff()        else:
1115             self.setSymmetryOff()
1116    
1117     #===== order reduction ==========================     # =============================================================================
1118       # function space handling for the equation as well as the solution
1119       # =============================================================================
1120     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1121       """       """
1122       @brief switches to on reduced order       switches on reduced order for solution and equation representation
1123    
1124         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1125       """       """
1126       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1127       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1128    
1129     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1130       """       """
1131       @brief switches to full order       switches off reduced order for solution and equation representation
1132    
1133         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1134       """       """
1135       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1136       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1137    
1138     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1139       """       """
1140       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1141         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1142       @param flag                    if flag is not present order reduction is switched off
1143         @type flag: C{bool}
1144         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1145       """       """
1146       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1147       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1148    
1149     #===== order reduction solution ==========================  
1150     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1151       """       """
1152       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1153    
1154         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1155       """       """
1156       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1157       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1158           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1159           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1160           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1161             self.__resetSystem()
1162    
1163     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1164       """       """
1165       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1166    
1167         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1168       """       """
1169       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1170       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1171           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1172           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1173           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1174             self.__resetSystem()
1175    
1176     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1177       """       """
1178       @brief sets order for test functions according to flag       sets order for test functions according to flag
1179    
1180       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1181                      if flag is not present order reduction is switched off
1182         @type flag: C{bool}
1183         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1184       """       """
1185       if flag:       if flag:
1186          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1187       else:       else:
1188          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1189                                                                                                                                                              
    #===== order reduction equation ==========================  
1190     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1191       """       """
1192       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1193    
1194         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1195       """       """
1196       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1197       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1198           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1199           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1200           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1201             self.__resetSystem()
1202    
1203     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1204       """       """
1205       @brief switches to full order for test functions       switches off reduced order for equation representation
1206    
1207         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1208       """       """
1209       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1210       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1211           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1212           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1213           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1214             self.__resetSystem()
1215    
1216     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1217       """       """
1218       @brief sets order for test functions according to flag       sets order for test functions according to flag
1219    
1220       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1221                      if flag is not present order reduction is switched off
1222         @type flag: C{bool}
1223         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1224       """       """
1225       if flag:       if flag:
1226          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1227       else:       else:
1228          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1229    
1230     # ==== initialization =====================================================================     # =============================================================================
1231     def __makeNewOperator(self):     # private method:
1232       # =============================================================================
1233       def __checkMatrixType(self):
1234         """
1235         reassess the matrix type and, if a new matrix is needed, resets the system.
1236         """
1237         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1238         if not new_matrix_type==self.__matrix_type:
1239             self.trace("Matrix type is now %d."%new_matrix_type)
1240             self.__matrix_type=new_matrix_type
1241             self.__resetSystem()
1242       #
1243       #   rebuild switches :
1244       #
1245       def __invalidateSolution(self):
1246           """
1247           indicates the PDE has to be resolved if the solution is requested
1248           """
1249           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1250           self.__solution_isValid=False
1251    
1252       def __invalidateOperator(self):
1253           """
1254           indicates the operator has to be rebuilt next time it is used
1255           """
1256           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1257           self.__invalidateSolution()
1258           self.__operator_is_Valid=False
1259    
1260       def __invalidateRightHandSide(self):
1261           """
1262           indicates the right hand side has to be rebuild next time it is used
1263           """
1264           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1265           self.__invalidateSolution()
1266           self.__righthandside_isValid=False
1267    
1268       def __invalidateSystem(self):
1269           """
1270           annonced that everthing has to be rebuild:
1271           """
1272           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1273           self.__invalidateSolution()
1274           self.__invalidateOperator()
1275           self.__invalidateRightHandSide()
1276    
1277       def __resetSystem(self):
1278           """
1279           annonced that everthing has to be rebuild:
1280           """
1281           self.trace("New System is built from scratch.")
1282           self.__operator=escript.Operator()
1283           self.__operator_is_Valid=False
1284           self.__righthandside=escript.Data()
1285           self.__righthandside_isValid=False
1286           self.__solution=escript.Data()
1287           self.__solution_isValid=False
1288       #
1289       #    system initialization:
1290       #
1291       def __getNewOperator(self):
1292         """         """
1293         @brief         returns an instance of a new operator
1294         """         """
1295           self.trace("New operator is allocated.")
1296         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1297                             self.getNumEquations(), \                             self.getNumEquations(), \
1298                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 617  class LinearPDE: Line 1300  class LinearPDE:
1300                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1301                             self.__matrix_type)                             self.__matrix_type)
1302    
1303     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1304         """         """
1305         @brief         returns an instance of a new right hand side
1306         """         """
1307         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1308           if self.getNumEquations()>1:
1309               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1310           else:
1311               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1312    
1313     def __makeNewSolution(self):     def __getNewSolution(self):
1314         """         """
1315         @brief         returns an instance of a new solution
1316         """         """
1317         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1318           if self.getNumSolutions()>1:
1319               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1320           else:
1321               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1322    
1323     def __getFreshOperator(self):     def __makeFreshSolution(self):
1324         """         """
1325         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1326         """         """
1327         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1328             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1329         else:         else:
1330             self.__operator.setValue(0.)             self.__solution*=0
1331             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1332         return self.__operator         return self.__solution
1333    
1334     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1335         """         """
1336         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1337         """         """
1338         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1339             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1340         else:         else:
1341             print "fix self.__righthandside*=0"             self.__righthandside.setToZero()
1342             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1343             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1344    
1345     # ==== rebuild switches =====================================================================     def __makeFreshOperator(self):
    def __rebuildSolution(self,deep=False):  
1346         """         """
1347         @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
1348         """         """
1349         if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."         if self.__operator.isEmpty():
1350         self.__solution_isValid=False             self.__operator=self.__getNewOperator()
1351         if deep: self.__solution=escript.Data(deep)         else:
1352               self.__operator.resetValues()
1353               self.trace("Operator reset to zero")
1354           return self.__operator
1355    
1356     def __rebuildOperator(self,deep=False):     def __applyConstraint(self):
1357         """         """
1358         @brief indicates the operator has to be rebuilt next time it is used         applies the constraints defined by q and r to the system
1359         """         """
1360         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if not self.isUsingLumping():
1361         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1362         self.__operator_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1363         if deep: self.__operator=escript.Operator()            if not q.isEmpty() and not self.__operator.isEmpty():
1364                 # q is the row and column mask to indicate where constraints are set:
1365                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1366                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1367                 u=self.__getNewSolution()
1368                 if r.isEmpty():
1369                    r_s=self.__getNewSolution()
1370                 else:
1371                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1372                 u.copyWithMask(r_s,col_q)
1373                 if not self.__righthandside.isEmpty():
1374                    self.__righthandside-=self.__operator*u
1375                    self.__righthandside=self.copyConstraint(self.__righthandside)
1376                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1377       # =============================================================================
1378       # function giving access to coefficients of the general PDE:
1379       # =============================================================================
1380       def getCoefficientOfGeneralPDE(self,name):
1381         """
1382         return the value of the coefficient name of the general PDE.
1383    
1384         @note: This method is called by the assembling routine it can be overwritten
1385               to map coefficients of a particular PDE to the general PDE.
1386         @param name: name of the coefficient requested.
1387         @type name: C{string}
1388         @return: the value of the coefficient  name
1389         @rtype: L{Data<escript.Data>}
1390         @raise IllegalCoefficient: if name is not one of coefficients
1391                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1392                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1393         """
1394         if self.hasCoefficientOfGeneralPDE(name):
1395            return self.getCoefficient(name)
1396         else:
1397            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1398    
1399     def __rebuildRightHandSide(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
1400         """       """
1401         @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.
1402         """  
1403         if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."       @param name: name of the coefficient enquired.
1404         self.__rebuildSolution(deep)       @type name: C{string}
1405         self.__righthandside_isValid=False       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1406         if not self.__homogeneous_constraint: self.__rebuildOperator()       @rtype: C{bool}
        if deep: self.__righthandside=escript.Data()  
1407    
    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):  
1408       """       """
1409       @brief reassess the matrix type and, if needed, initiates an operator rebuild       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1410    
1411       def createCoefficientOfGeneralPDE(self,name):
1412       """       """
1413       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)  
1414    
1415     #============ assembling =======================================================       @param name: name of the coefficient requested.
1416     def __copyConstraint(self,u):       @type name: C{string}
1417        """       @return: a coefficient name initialized to 0.
1418        @brief copies the constrint condition into u       @rtype: L{Data<escript.Data>}
1419        """       @raise IllegalCoefficient: if name is not one of coefficients
1420        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},
1421        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}.
1422        if not q.isEmpty():       """
1423            if r.isEmpty():       if self.hasCoefficientOfGeneralPDE(name):
1424               r2=escript.Data(0,u.getShape(),u.getFunctionSpace())          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1425            else:       else:
1426               r2=escript.Data(r,u.getFunctionSpace())          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
           u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))  
1427    
1428     def __applyConstraint(self,rhs_update=True):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1429         """       """
1430         @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.)  
1431    
1432     def getOperator(self):       @param name: name of the coefficient enquired.
1433         """       @type name: C{string}
1434         @brief returns the operator of the PDE       @return: the function space to be used for coefficient name
1435         """       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1436         if not self.__operator_isValid:       @raise IllegalCoefficient: if name is not one of coefficients
1437             # 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},
1438             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}.
1439                if self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():       """
1440                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"       if self.hasCoefficientOfGeneralPDE(name):
1441                if not self.getCoefficient("A").isEmpty():          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1442                         raise Warning,"Lumped matrix does not allow coefficient A"       else:
1443                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()  
1444    
1445             self.getDomain().addPDEToSystem(mat,escript.Data(), \     def getShapeOfCoefficientOfGeneralPDE(self,name):
1446                          self.getCoefficient("A"), \       """
1447                          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  
1448    
1449     def getRightHandSide(self,ignoreConstraint=False):       @param name: name of the coefficient enquired.
1450         """       @type name: C{string}
1451         @brief returns the right hand side of the PDE       @return: the shape of the coefficient name
1452         @rtype: C{tuple} of C{int}
1453         @raise IllegalCoefficient: if name is not one of coefficients
1454                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1455                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1456         """
1457         if self.hasCoefficientOfGeneralPDE(name):
1458            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1459         else:
1460            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1461    
1462         @param ignoreConstraint     # =============================================================================
1463         """     # functions giving access to coefficients of a particular PDE implementation:
1464         if not self.__righthandside_isValid:     # =============================================================================
1465             if self.debug() : print "PDE Debug: New right hand side is built."     def getCoefficient(self,name):
1466             self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \       """
1467                           self.getCoefficient("X"), \       returns the value of the coefficient name
1468                           self.getCoefficient("Y"),\  
1469                           self.getCoefficient("y"),\       @param name: name of the coefficient requested.
1470                           self.getCoefficient("y_contact"))       @type name: C{string}
1471             self.__righthandside_isValid=True       @return: the value of the coefficient name
1472             if ignoreConstraint: self.__copyConstraint(self.__righthandside)       @rtype: L{Data<escript.Data>}
1473         return self.__righthandside       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1474         """
1475         if self.hasCoefficient(name):
1476             return self.COEFFICIENTS[name].getValue()
1477         else:
1478            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1479    
1480       def hasCoefficient(self,name):
1481         """
1482         return True if name is the name of a coefficient
1483    
1484         @param name: name of the coefficient enquired.
1485         @type name: C{string}
1486         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1487         @rtype: C{bool}
1488         """
1489         return self.COEFFICIENTS.has_key(name)
1490    
1491       def createCoefficient(self, name):
1492         """
1493         create a L{Data<escript.Data>} object corresponding to coefficient name
1494    
1495         @return: a coefficient name initialized to 0.
1496         @rtype: L{Data<escript.Data>}
1497         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1498         """
1499         if self.hasCoefficient(name):
1500            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1501         else:
1502            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1503    
1504       def getFunctionSpaceForCoefficient(self,name):
1505         """
1506         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1507    
1508         @param name: name of the coefficient enquired.
1509         @type name: C{string}
1510         @return: the function space to be used for coefficient name
1511         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1512         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1513         """
1514         if self.hasCoefficient(name):
1515            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1516         else:
1517            raise ValueError,"unknown coefficient %s requested"%name
1518       def getShapeOfCoefficient(self,name):
1519         """
1520         return the shape of the coefficient name
1521    
1522         @param name: name of the coefficient enquired.
1523         @type name: C{string}
1524         @return: the shape of the coefficient name
1525         @rtype: C{tuple} of C{int}
1526         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1527         """
1528         if self.hasCoefficient(name):
1529            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1530         else:
1531            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1532    
1533       def resetCoefficients(self):
1534         """
1535         resets all coefficients to there default values.
1536         """
1537         for i in self.COEFFICIENTS.iterkeys():
1538             self.COEFFICIENTS[i].resetValue()
1539    
1540       def alteredCoefficient(self,name):
1541         """
1542         announce that coefficient name has been changed
1543    
1544         @param name: name of the coefficient enquired.
1545         @type name: C{string}
1546         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1547         @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1548         """
1549         if self.hasCoefficient(name):
1550            self.trace("Coefficient %s has been altered."%name)
1551            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1552               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1553               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1554         else:
1555            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1556    
1557       def copyConstraint(self,u):
1558          """
1559          copies the constraint into u and returns u.
1560    
1561          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1562          @type u: L{Data<escript.Data>}
1563          @return: the input u modified by the constraints.
1564          @rtype: L{Data<escript.Data>}
1565          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1566          """
1567          q=self.getCoefficientOfGeneralPDE("q")
1568          r=self.getCoefficientOfGeneralPDE("r")
1569          if not q.isEmpty():
1570             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1571             if r.isEmpty():
1572                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1573             else:
1574                 r=escript.Data(r,u.getFunctionSpace())
1575             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1576          return u
1577    
1578       def setValue(self,**coefficients):
1579          """
1580          sets new values to coefficients
1581    
1582          @param coefficients: new values assigned to coefficients
1583          @keyword A: value for coefficient A.
1584          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1585          @keyword A_reduced: value for coefficient A_reduced.
1586          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1587          @keyword B: value for coefficient B
1588          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1589          @keyword B_reduced: value for coefficient B_reduced
1590          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1591          @keyword C: value for coefficient C
1592          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1593          @keyword C_reduced: value for coefficient C_reduced
1594          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1595          @keyword D: value for coefficient D
1596          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1597          @keyword D_reduced: value for coefficient D_reduced
1598          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1599          @keyword X: value for coefficient X
1600          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1601          @keyword X_reduced: value for coefficient X_reduced
1602          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1603          @keyword Y: value for coefficient Y
1604          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1605          @keyword Y_reduced: value for coefficient Y_reduced
1606          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1607          @keyword d: value for coefficient d
1608          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1609          @keyword d_reduced: value for coefficient d_reduced
1610          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1611          @keyword y: value for coefficient y
1612          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1613          @keyword d_contact: value for coefficient d_contact
1614          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1615          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1616          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1617          @keyword y_contact: value for coefficient y_contact
1618          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1619          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1620          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1621          @keyword r: values prescribed to the solution at the locations of constraints
1622          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1623                   depending of reduced order is used for the solution.
1624          @keyword q: mask for location of constraints
1625          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1626                   depending of reduced order is used for the representation of the equation.
1627          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1628          """
1629          # check if the coefficients are  legal:
1630          for i in coefficients.iterkeys():
1631             if not self.hasCoefficient(i):
1632                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1633          # if the number of unknowns or equations is still unknown we try to estimate them:
1634          if self.__numEquations==None or self.__numSolutions==None:
1635             for i,d in coefficients.iteritems():
1636                if hasattr(d,"shape"):
1637                    s=d.shape
1638                elif hasattr(d,"getShape"):
1639                    s=d.getShape()
1640                else:
1641                    s=numarray.array(d).shape
1642                if s!=None:
1643                    # get number of equations and number of unknowns:
1644                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1645                    if res==None:
1646                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1647                    else:
1648                        if self.__numEquations==None: self.__numEquations=res[0]
1649                        if self.__numSolutions==None: self.__numSolutions=res[1]
1650          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1651          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1652          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1653          for i,d in coefficients.iteritems():
1654            try:
1655               self.COEFFICIENTS[i].setValue(self.getDomain(),
1656                                             self.getNumEquations(),self.getNumSolutions(),
1657                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1658               self.alteredCoefficient(i)
1659            except IllegalCoefficientFunctionSpace,m:
1660                # if the function space is wrong then we try the reduced version:
1661                i_red=i+"_reduced"
1662                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1663                    try:
1664                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1665                                                          self.getNumEquations(),self.getNumSolutions(),
1666                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1667                        self.alteredCoefficient(i_red)
1668                    except IllegalCoefficientValue,m:
1669                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1670                    except IllegalCoefficientFunctionSpace,m:
1671                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1672                else:
1673                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1674            except IllegalCoefficientValue,m:
1675               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1676          self.__altered_coefficients=True
1677          # check if the systrem is inhomogeneous:
1678          if len(coefficients)>0 and not self.isUsingLumping():
1679             q=self.getCoefficientOfGeneralPDE("q")
1680             r=self.getCoefficientOfGeneralPDE("r")
1681             homogeneous_constraint=True
1682             if not q.isEmpty() and not r.isEmpty():
1683                 if util.Lsup(q*r)>0.:
1684                   self.trace("Inhomogeneous constraint detected.")
1685                   self.__invalidateSystem()
1686    
1687     def getSystem(self):     def getSystem(self):
1688         """         """
1689         @brief         return the operator and right hand side of the PDE
1690    
1691           @return: the discrete version of the PDE
1692           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1693         """         """
1694         if not self.__operator_isValid 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."  
1695            if self.isUsingLumping():            if self.isUsingLumping():
1696                self.getRightHandSide(ignoreConstraint=True)                if not self.__operator_is_Valid:
1697                self.getOperator()                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1698                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1699                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1700                          raise ValueError,"coefficient A in lumped matrix may not be present."
1701                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1702                          raise ValueError,"coefficient B in lumped matrix may not be present."
1703                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1704                          raise ValueError,"coefficient C in lumped matrix may not be present."
1705                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1706                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1707                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1708                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1709                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1710                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1711                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1712                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1713                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1714                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1715                     D=self.getCoefficientOfGeneralPDE("D")
1716                     d=self.getCoefficientOfGeneralPDE("d")
1717                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1718                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1719                     if not D.isEmpty():
1720                         if self.getNumSolutions()>1:
1721                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1722                         else:
1723                            D_times_e=D
1724                     else:
1725                        D_times_e=escript.Data()
1726                     if not d.isEmpty():
1727                         if self.getNumSolutions()>1:
1728                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1729                         else:
1730                            d_times_e=d
1731                     else:
1732                        d_times_e=escript.Data()
1733          
1734                     if not D_reduced.isEmpty():
1735                         if self.getNumSolutions()>1:
1736                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1737                         else:
1738                            D_reduced_times_e=D_reduced
1739                     else:
1740                        D_reduced_times_e=escript.Data()
1741                     if not d_reduced.isEmpty():
1742                         if self.getNumSolutions()>1:
1743                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1744                         else:
1745                            d_reduced_times_e=d_reduced
1746                     else:
1747                        d_reduced_times_e=escript.Data()
1748    
1749                     self.__operator=self.__getNewRightHandSide()
1750                     if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1751                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1752                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1753                     else:
1754                        self.getDomain().addPDEToRHS(self.__operator, \
1755                                                     escript.Data(), \
1756                                                     D_times_e, \
1757                                                     d_times_e,\
1758                                                     escript.Data())
1759                        self.getDomain().addPDEToRHS(self.__operator, \
1760                                                     escript.Data(), \
1761                                                     D_reduced_times_e, \
1762                                                     d_reduced_times_e,\
1763                                                     escript.Data())
1764                     self.__operator=1./self.__operator
1765                     self.trace("New lumped operator has been built.")
1766                     self.__operator_is_Valid=True
1767                  if not self.__righthandside_isValid:
1768                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1769                                   self.getCoefficientOfGeneralPDE("X"), \
1770                                   self.getCoefficientOfGeneralPDE("Y"),\
1771                                   self.getCoefficientOfGeneralPDE("y"),\
1772                                   self.getCoefficientOfGeneralPDE("y_contact"))
1773                     self.getDomain().addPDEToRHS(self.__righthandside, \
1774                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1775                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1776                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1777                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1778                     self.trace("New right hand side as been built.")
1779                     self.__righthandside_isValid=True
1780            else:            else:
1781                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1782                              self.getCoefficient("A"), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1783                              self.getCoefficient("B"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1784                              self.getCoefficient("C"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1785                              self.getCoefficient("D"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1786                              self.getCoefficient("X"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1787                              self.getCoefficient("Y"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1788                              self.getCoefficient("d"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1789                              self.getCoefficient("y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1790                              self.getCoefficient("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1791                              self.getCoefficient("y_contact"))                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1792            self.__operator_isValid=True                                 self.getCoefficientOfGeneralPDE("y_contact"))
1793            self.__righthandside_isValid=True                   self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1794            self.__applyConstraint()                                 self.getCoefficientOfGeneralPDE("A_reduced"), \
1795            self.__copyConstraint(self.__righthandside)                                 self.getCoefficientOfGeneralPDE("B_reduced"), \
1796         elif not self.__operator_isValid:                                 self.getCoefficientOfGeneralPDE("C_reduced"), \
1797            self.getOperator()                                 self.getCoefficientOfGeneralPDE("D_reduced"), \
1798         elif not self.__righthandside_isValid:                                 self.getCoefficientOfGeneralPDE("X_reduced"), \
1799            self.getRightHandSide()                                 self.getCoefficientOfGeneralPDE("Y_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1804                     self.__applyConstraint()
1805                     self.__righthandside=self.copyConstraint(self.__righthandside)
1806                     self.trace("New system has been built.")
1807                     self.__operator_is_Valid=True
1808                     self.__righthandside_isValid=True
1809                 elif not self.__righthandside_isValid:
1810                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1811                                   self.getCoefficientOfGeneralPDE("X"), \
1812                                   self.getCoefficientOfGeneralPDE("Y"),\
1813                                   self.getCoefficientOfGeneralPDE("y"),\
1814                                   self.getCoefficientOfGeneralPDE("y_contact"))
1815                     self.getDomain().addPDEToRHS(self.__righthandside, \
1816                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1817                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1818                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1819                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1820                     self.__righthandside=self.copyConstraint(self.__righthandside)
1821                     self.trace("New right hand side has been built.")
1822                     self.__righthandside_isValid=True
1823                 elif not self.__operator_is_Valid:
1824                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1825                                self.getCoefficientOfGeneralPDE("A"), \
1826                                self.getCoefficientOfGeneralPDE("B"), \
1827                                self.getCoefficientOfGeneralPDE("C"), \
1828                                self.getCoefficientOfGeneralPDE("D"), \
1829                                escript.Data(), \
1830                                escript.Data(), \
1831                                self.getCoefficientOfGeneralPDE("d"), \
1832                                escript.Data(),\
1833                                self.getCoefficientOfGeneralPDE("d_contact"), \
1834                                escript.Data())
1835                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1836                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1837                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1839                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1840                                escript.Data(), \
1841                                escript.Data(), \
1842                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1843                                escript.Data(),\
1844                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1845                                escript.Data())
1846                     self.__applyConstraint()
1847                     self.trace("New operator has been built.")
1848                     self.__operator_is_Valid=True
1849         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1850    
    def solve(self,**options):  
       """  
       @brief solve the PDE  
1851    
1852        @param options  class Poisson(LinearPDE):
1853        """     """
1854        mat,f=self.getSystem()     Class to define a Poisson equation problem, which is genear L{LinearPDE} of the form
       if self.isUsingLumping():  
          out=f/mat  
          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  
1855    
1856     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief returns the solution of the PDE  
1857    
1858         @param options     with natural boundary conditons
        """  
        if not self.__solution_isValid:  
            if self.debug() : print "PDE Debug: PDE is resolved."  
            self.__solution=self.solve(**options)  
            self.__solution_isValid=True  
        return self.__solution  
    #============ some serivice functions  =====================================================  
    def getDomain(self):  
      """  
      @brief returns the domain of the PDE  
      """  
      return self.__domain  
1859    
1860     def getDim(self):     M{n[j]*grad(u)[j] = 0 }
1861       """  
1862       @brief returns the spatial dimension of the PDE     and constraints:
1863    
1864       M{u=0} where M{q>0}
1865    
1866       """
1867    
1868       def __init__(self,domain,debug=False):
1869       """       """
1870       return self.getDomain().getDim()       initializes a new Poisson equation
1871    
1872         @param domain: domain of the PDE
1873         @type domain: L{Domain<escript.Domain>}
1874         @param debug: if True debug informations are printed.
1875    
    def getNumEquations(self):  
1876       """       """
1877       @brief returns the number of equations       super(Poisson, self).__init__(domain,1,1,debug)
1878         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1879                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1880                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1881         self.setSymmetryOn()
1882    
1883       def setValue(self,**coefficients):
1884       """       """
1885       if self.__numEquations>0:       sets new values to coefficients
1886           return self.__numEquations  
1887         @param coefficients: new values assigned to coefficients
1888         @keyword f: value for right hand side M{f}
1889         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1890         @keyword q: mask for location of constraints
1891         @type q: any type that can be casted to rank zeo L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1892                   depending of reduced order is used for the representation of the equation.
1893         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1894         """
1895         super(Poisson, self).setValue(**coefficients)
1896    
1897       def getCoefficientOfGeneralPDE(self,name):
1898         """
1899         return the value of the coefficient name of the general PDE
1900         @param name: name of the coefficient requested.
1901         @type name: C{string}
1902         @return: the value of the coefficient  name
1903         @rtype: L{Data<escript.Data>}
1904         @raise IllegalCoefficient: if name is not one of coefficients
1905                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1906         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1907         """
1908         if name == "A" :
1909             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1910         elif name == "B" :
1911             return escript.Data()
1912         elif name == "C" :
1913             return escript.Data()
1914         elif name == "D" :
1915             return escript.Data()
1916         elif name == "X" :
1917             return escript.Data()
1918         elif name == "Y" :
1919             return self.getCoefficient("f")
1920         elif name == "d" :
1921             return escript.Data()
1922         elif name == "y" :
1923             return escript.Data()
1924         elif name == "d_contact" :
1925             return escript.Data()
1926         elif name == "y_contact" :
1927             return escript.Data()
1928         elif name == "A_reduced" :
1929             return escript.Data()
1930         elif name == "B_reduced" :
1931             return escript.Data()
1932         elif name == "C_reduced" :
1933             return escript.Data()
1934         elif name == "D_reduced" :
1935             return escript.Data()
1936         elif name == "X_reduced" :
1937             return escript.Data()
1938         elif name == "Y_reduced" :
1939             return self.getCoefficient("f_reduced")
1940         elif name == "d_reduced" :
1941             return escript.Data()
1942         elif name == "y_reduced" :
1943             return escript.Data()
1944         elif name == "d_contact_reduced" :
1945             return escript.Data()
1946         elif name == "y_contact_reduced" :
1947             return escript.Data()
1948         elif name == "r" :
1949             return escript.Data()
1950         elif name == "q" :
1951             return self.getCoefficient("q")
1952       else:       else:
1953           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1954    
1955     def getNumSolutions(self):  class Helmholtz(LinearPDE):
1956       """
1957       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1958    
1959       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1960    
1961       with natural boundary conditons
1962    
1963       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1964    
1965       and constraints:
1966    
1967       M{u=r} where M{q>0}
1968    
1969       """
1970    
1971       def __init__(self,domain,debug=False):
1972       """       """
1973       @brief returns the number of unknowns       initializes a new Poisson equation
1974    
1975         @param domain: domain of the PDE
1976         @type domain: L{Domain<escript.Domain>}
1977         @param debug: if True debug informations are printed.
1978    
1979         """
1980         super(Helmholtz, self).__init__(domain,1,1,debug)
1981         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1982                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1983                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1984                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1985                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1986                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1989                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1990         self.setSymmetryOn()
1991    
1992       def setValue(self,**coefficients):
1993       """       """
1994       if self.__numSolutions>0:       sets new values to coefficients
1995          return self.__numSolutions  
1996         @param coefficients: new values assigned to coefficients
1997         @keyword omega: value for coefficient M{S{omega}}
1998         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1999         @keyword k: value for coefficeint M{k}
2000         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2001         @keyword f: value for right hand side M{f}
2002         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2003         @keyword alpha: value for right hand side M{S{alpha}}
2004         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2005         @keyword g: value for right hand side M{g}
2006         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2007         @keyword r: prescribed values M{r} for the solution in constraints.
2008         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2009                   depending of reduced order is used for the representation of the equation.
2010         @keyword q: mask for location of constraints
2011         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2012                   depending of reduced order is used for the representation of the equation.
2013         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2014         """
2015         super(Helmholtz, self).setValue(**coefficients)
2016    
2017       def getCoefficientOfGeneralPDE(self,name):
2018         """
2019         return the value of the coefficient name of the general PDE
2020    
2021         @param name: name of the coefficient requested.
2022         @type name: C{string}
2023         @return: the value of the coefficient  name
2024         @rtype: L{Data<escript.Data>}
2025         @raise IllegalCoefficient: if name is not one of coefficients
2026                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2027         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2028         """
2029         if name == "A" :
2030             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2031         elif name == "B" :
2032             return escript.Data()
2033         elif name == "C" :
2034             return escript.Data()
2035         elif name == "D" :
2036             return self.getCoefficient("omega")
2037         elif name == "X" :
2038             return escript.Data()
2039         elif name == "Y" :
2040             return self.getCoefficient("f")
2041         elif name == "d" :
2042             return self.getCoefficient("alpha")
2043         elif name == "y" :
2044             return self.getCoefficient("g")
2045         elif name == "d_contact" :
2046             return escript.Data()
2047         elif name == "y_contact" :
2048             return escript.Data()
2049         elif name == "A_reduced" :
2050             return escript.Data()
2051         elif name == "B_reduced" :
2052             return escript.Data()
2053         elif name == "C_reduced" :
2054             return escript.Data()
2055         elif name == "D_reduced" :
2056             return escript.Data()
2057         elif name == "X_reduced" :
2058             return escript.Data()
2059         elif name == "Y_reduced" :
2060             return self.getCoefficient("f_reduced")
2061         elif name == "d_reduced" :
2062             return escript.Data()
2063         elif name == "y_reduced" :
2064            return self.getCoefficient("g_reduced")
2065         elif name == "d_contact_reduced" :
2066             return escript.Data()
2067         elif name == "y_contact_reduced" :
2068             return escript.Data()
2069         elif name == "r" :
2070             return self.getCoefficient("r")
2071         elif name == "q" :
2072             return self.getCoefficient("q")
2073       else:       else:
2074          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2075    
2076    class LameEquation(LinearPDE):
2077       """
2078       Class to define a Lame equation problem:
2079    
2080     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"  
2081    
2082        return None     with natural boundary conditons:
2083    
2084     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  
2085    
2086              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}     and constraints:
2087    
2088         @param u argument of the operator     M{u[i]=r[i]} where M{q[i]>0}
2089    
2090         """     """
        raise SystemError,"getFlux is not implemented yet"  
        return None  
2091    
2092     def applyOperator(self,u):     def __init__(self,domain,debug=False):
2093         """        super(LameEquation, self).__init__(domain,\
2094         @brief applies the operator of the PDE to a given solution u in weak from                                           domain.getDim(),domain.getDim(),debug)
2095          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2096                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2097                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2098                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2099                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2100                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2101                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2102          self.setSymmetryOn()
2103    
2104       def setValues(self,**coefficients):
2105         """
2106         sets new values to coefficients
2107    
2108         @param coefficients: new values assigned to coefficients
2109         @keyword lame_mu: value for coefficient M{S{mu}}
2110         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2111         @keyword lame_lambda: value for coefficient M{S{lambda}}
2112         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2113         @keyword F: value for internal force M{F}
2114         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2115         @keyword sigma: value for initial stress M{S{sigma}}
2116         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2117         @keyword f: value for extrenal force M{f}
2118         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2119         @keyword r: prescribed values M{r} for the solution in constraints.
2120         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2121                   depending of reduced order is used for the representation of the equation.
2122         @keyword q: mask for location of constraints
2123         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2124                   depending of reduced order is used for the representation of the equation.
2125         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2126         """
2127         super(LameEquation, self).setValues(**coefficients)
2128    
2129       def getCoefficientOfGeneralPDE(self,name):
2130         """
2131         return the value of the coefficient name of the general PDE
2132    
2133         @param name: name of the coefficient requested.
2134         @type name: C{string}
2135         @return: the value of the coefficient  name
2136         @rtype: L{Data<escript.Data>}
2137         @raise IllegalCoefficient: if name is not one of coefficients
2138                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2139         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2140         """
2141         if name == "A" :
2142             out =self.createCoefficientOfGeneralPDE("A")
2143             for i in range(self.getDim()):
2144               for j in range(self.getDim()):
2145                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2146                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2147                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2148             return out
2149         elif name == "B" :
2150             return escript.Data()
2151         elif name == "C" :
2152             return escript.Data()
2153         elif name == "D" :
2154             return escript.Data()
2155         elif name == "X" :
2156             return self.getCoefficient("sigma")
2157         elif name == "Y" :
2158             return self.getCoefficient("F")
2159         elif name == "d" :
2160             return escript.Data()
2161         elif name == "y" :
2162             return self.getCoefficient("f")
2163         elif name == "d_contact" :
2164             return escript.Data()
2165         elif name == "y_contact" :
2166             return escript.Data()
2167         elif name == "A_reduced" :
2168             return escript.Data()
2169         elif name == "B_reduced" :
2170             return escript.Data()
2171         elif name == "C_reduced" :
2172             return escript.Data()
2173         elif name == "D_reduced" :
2174             return escript.Data()
2175         elif name == "X_reduced" :
2176             return escript.Data()
2177         elif name == "Y_reduced" :
2178             return escript.Data()
2179         elif name == "d_reduced" :
2180             return escript.Data()
2181         elif name == "y_reduced" :
2182             return escript.Data()
2183         elif name == "d_contact_reduced" :
2184             return escript.Data()
2185         elif name == "y_contact_reduced" :
2186             return escript.Data()
2187         elif name == "r" :
2188             return self.getCoefficient("r")
2189         elif name == "q" :
2190             return self.getCoefficient("q")
2191         else:
2192            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2193    
2194         @param u argument of the operator  def LinearSinglePDE(domain,debug=False):
2195       """
2196       defines a single linear PDEs
2197    
2198         """     @param domain: domain of the PDE
2199         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())     @type domain: L{Domain<escript.Domain>}
2200                                                                                                                                                                 @param debug: if True debug informations are printed.
2201     def getResidual(self,u):     @rtype: L{LinearPDE}
2202         """     """
2203         @brief return the residual of u in the weak from     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2204    
2205         @param u  def LinearPDESystem(domain,debug=False):
2206         """     """
2207         return self.applyOperator(u)-self.getRightHandSide()     defines a system of linear PDEs
2208    
2209  class Poisson(LinearPDE):     @param domain: domain of the PDE
2210       @type domain: L{Domain<escript.Domain>}
2211       @param debug: if True debug informations are printed.
2212       @rtype: L{LinearPDE}
2213     """     """
2214     @brief Class to define a Poisson equstion problem:     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2215                                                                                                                                                                
2216     class to define a linear PDE of the form  class TransportPDE(object):
2217                                                                                                                                                                     """
2218          -u_{,jj} = f       Warning: This is still a very experimental. The class is still changing!
2219                                                                                                                                                                
2220       with boundary conditons:       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2221                                                                                                                                                                    
2222          n_j*u_{,j} = 0       u=r where q>0
2223                                                                                                                                                                    
2224      and constraints:       all coefficients are constant over time.
2225                                                                                                                                                                
2226           u=0 where q>0       typical usage:
2227                                                                                                                                                                
2228     """           p=TransportPDE(dom)
2229             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2230     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2231         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))           t=0
2232         self._setValue(A=numarray.identity(self.getDomain().getDim()))           dt=0.1
2233         self.setSymmetryOn()           while (t<1.):
2234         self.setValue(f,q)                u=p.solve(dt)
2235    
2236     def setValue(self,f=escript.Data(),q=escript.Data()):       """
2237         self._setValue(Y=f,q=q)       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2238            self.__domain=domain
2239                                                                                                                                                                      self.__num_equations=num_equations
2240  # $Log$          self.__useSUPG=useSUPG
2241  # Revision 1.3  2004/12/17 07:43:10  jgs          self.__trace=trace
2242  # *** empty log message ***          self.__theta=theta
2243  #          self.__matrix_type=0
2244  # Revision 1.1.2.3  2004/12/16 00:12:34  gross          self.__reduced=True
2245  # __init__ of LinearPDE does not accept any coefficients anymore          self.__reassemble=True
2246  #          if self.__useSUPG:
2247  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2248  # *** empty log message ***             self.__pde.setSymmetryOn()
2249  #             self.__pde.setReducedOrderOn()
2250  # Revision 1.1.2.1  2004/12/12 22:53:47  gross          else:
2251  # linearPDE has been renamed LinearPDE             self.__transport_problem=self.__getNewTransportProblem()
2252  #          self.setTolerance()
2253  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross          self.__M=escript.Data()
2254  # GMRES added          self.__A=escript.Data()
2255  #          self.__B=escript.Data()
2256  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross          self.__C=escript.Data()
2257  # options for GMRES and PRES20 added          self.__D=escript.Data()
2258  #          self.__X=escript.Data()
2259  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross          self.__Y=escript.Data()
2260  # some small changes          self.__d=escript.Data()
2261  #          self.__y=escript.Data()
2262  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross          self.__d_contact=escript.Data()
2263  # Finley solves 4M unknowns now          self.__y_contact=escript.Data()
2264  #          self.__r=escript.Data()
2265  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross          self.__q=escript.Data()
2266  # poisson solver added  
2267  #       def trace(self,text):
2268  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross               if self.__trace: print text
2269  # 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       def getSafeTimeStepSize(self):
2270  #          if self.__useSUPG:
2271  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross              if self.__reassemble:
2272  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed                 h=self.__domain.getSize()
2273  #                 dt=None
2274  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs                 if not self.__A.isEmpty():
2275  # initial import of project esys2                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2276  #                    if dt == None:
2277  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs                       dt = dt2
2278  # committing Lutz's and Paul's changes to brach jgs                    else:
2279  #                       dt=1./(1./dt+1./dt2)
2280  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane                 if not self.__B.isEmpty():
2281  # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.                    dt2=util.inf(h*self.__M/util.length(self.__B))
2282  #                    if dt == None:
2283  # Revision 1.3  2004/09/23 00:53:23  jgs                       dt = dt2
2284  # minor fixes                    else:
2285  #                       dt=1./(1./dt+1./dt2)
2286  # Revision 1.1  2004/08/28 12:58:06  gross                 if not  self.__C.isEmpty():
2287  # SimpleSolve is not running yet: problem with == of functionsspace                    dt2=util.inf(h*self.__M/util.length(self.__C))
2288  #                    if dt == None:
2289  #                       dt = dt2
2290                      else:
2291                         dt=1./(1./dt+1./dt2)
2292                   if not self.__D.isEmpty():
2293                      dt2=util.inf(self.__M/util.length(self.__D))
2294                      if dt == None:
2295                         dt = dt2
2296                      else:
2297                         dt=1./(1./dt+1./dt2)
2298                   self.__dt = dt/2
2299                return self.__dt
2300            else:
2301                return self.__getTransportProblem().getSafeTimeStepSize()
2302         def getDomain(self):
2303            return self.__domain
2304         def getTheta(self):
2305            return self.__theta
2306         def getNumEquations(self):
2307            return self.__num_equations
2308         def setReducedOn(self):
2309              if not self.reduced():
2310                  if self.__useSUPG:
2311                     self.__pde.setReducedOrderOn()
2312                  else:
2313                     self.__transport_problem=self.__getNewTransportProblem()
2314              self.__reduced=True
2315         def setReducedOff(self):
2316              if self.reduced():
2317                  if self.__useSUPG:
2318                     self.__pde.setReducedOrderOff()
2319                  else:
2320                     self.__transport_problem=self.__getNewTransportProblem()
2321              self.__reduced=False
2322         def reduced(self):
2323             return self.__reduced
2324         def getFunctionSpace(self):
2325            if self.reduced():
2326               return escript.ReducedSolution(self.getDomain())
2327            else:
2328               return escript.Solution(self.getDomain())
2329    
2330         def setTolerance(self,tol=1.e-8):
2331            self.__tolerance=tol
2332            if self.__useSUPG:
2333                  self.__pde.setTolerance(self.__tolerance)
2334    
2335         def __getNewTransportProblem(self):
2336           """
2337           returns an instance of a new operator
2338           """
2339           self.trace("New Transport problem is allocated.")
2340           return self.getDomain().newTransportProblem( \
2341                                   self.getTheta(),
2342                                   self.getNumEquations(), \
2343                                   self.getFunctionSpace(), \
2344                                   self.__matrix_type)
2345              
2346         def __getNewSolutionVector(self):
2347             if self.getNumEquations() ==1 :
2348                    out=escript.Data(0.0,(),self.getFunctionSpace())
2349             else:
2350                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2351             return out
2352    
2353         def __getTransportProblem(self):
2354           if self.__reassemble:
2355                 self.__source=self.__getNewSolutionVector()
2356                 self.__transport_problem.reset()
2357                 self.getDomain().addPDEToTransportProblem(
2358                             self.__transport_problem,
2359                             self.__source,
2360                             self.__M,
2361                             self.__A,
2362                             self.__B,
2363                             self.__C,
2364                             self.__D,
2365                             self.__X,
2366                             self.__Y,
2367                             self.__d,
2368                             self.__y,
2369                             self.__d_contact,
2370                             self.__y_contact)
2371                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2372                 self.__reassemble=False
2373           return self.__transport_problem
2374         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2375                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2376                 if not M==None:
2377                      self.__reassemble=True
2378                      self.__M=M
2379                 if not A==None:
2380                      self.__reassemble=True
2381                      self.__A=A
2382                 if not B==None:
2383                      self.__reassemble=True
2384                      self.__B=B
2385                 if not C==None:
2386                      self.__reassemble=True
2387                      self.__C=C
2388                 if not D==None:
2389                      self.__reassemble=True
2390                      self.__D=D
2391                 if not X==None:
2392                      self.__reassemble=True
2393                      self.__X=X
2394                 if not Y==None:
2395                      self.__reassemble=True
2396                      self.__Y=Y
2397                 if not d==None:
2398                      self.__reassemble=True
2399                      self.__d=d
2400                 if not y==None:
2401                      self.__reassemble=True
2402                      self.__y=y
2403                 if not d_contact==None:
2404                      self.__reassemble=True
2405                      self.__d_contact=d_contact
2406                 if not y_contact==None:
2407                      self.__reassemble=True
2408                      self.__y_contact=y_contact
2409                 if not q==None:
2410                      self.__reassemble=True
2411                      self.__q=q
2412                 if not r==None:
2413                      self.__reassemble=True
2414                      self.__r=r
2415    
2416         def setInitialSolution(self,u):
2417                 if self.__useSUPG:
2418                     self.__u=util.interpolate(u,self.getFunctionSpace())
2419                 else:
2420                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2421    
2422         def solve(self,dt,**kwarg):
2423               if self.__useSUPG:
2424                    if self.__reassemble:
2425                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2426                        self.__reassemble=False
2427                    dt2=self.getSafeTimeStepSize()
2428                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2429                    dt2=dt/nn
2430                    nnn=0
2431                    u=self.__u
2432                    self.trace("number of substeps is %d."%nn)
2433                    while nnn<nn :
2434                        self.__setSUPG(u,u,dt2/2)
2435                        u_half=self.__pde.getSolution(verbose=True)
2436                        self.__setSUPG(u,u_half,dt2)
2437                        u=self.__pde.getSolution(verbose=True)
2438                        nnn+=1
2439                    self.__u=u
2440                    return self.__u
2441               else:
2442                   kwarg["tolerance"]=self.__tolerance
2443                   tp=self.__getTransportProblem()
2444                   return tp.solve(self.__source,dt,kwarg)
2445         def __setSUPG(self,u0,u,dt):
2446                g=util.grad(u)
2447                X=0
2448                Y=self.__M*u0
2449                X=0
2450                self.__pde.setValue(r=u0)
2451                if not self.__A.isEmpty():
2452                   X=X+dt*util.matrixmult(self.__A,g)
2453                if not self.__B.isEmpty():
2454                   X=X+dt*self.__B*u
2455                if not  self.__C.isEmpty():
2456                   Y=Y+dt*util.inner(self.__C,g)
2457                if not self.__D.isEmpty():
2458                   Y=Y+dt*self.__D*u
2459                if not self.__X.isEmpty():
2460                   X=X+dt*self.__X
2461                if not self.__Y.isEmpty():
2462                   Y=Y+dt*self.__Y
2463                self.__pde.setValue(X=X,Y=Y)
2464                if not self.__y.isEmpty():
2465                   self.__pde.setValue(y=dt*self.__y)
2466                if not self.__y_contact.isEmpty():
2467                   self.__pde.setValue(y=dt*self.__y_contact)
2468                self.__pde.setValue(r=u0)

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