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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 1787 by artak, Mon Sep 15 01:36:34 2008 UTC
# Line 1  Line 1 
1    #
2  # $Id$  # $Id$
3    #
4  ## @file linearPDEs.py  #######################################################
5    #
6    #           Copyright 2003-2007 by ACceSS MNRF
7    #       Copyright 2007 by University of Queensland
8    #
9    #                http://esscc.uq.edu.au
10    #        Primary Business: Queensland, Australia
11    #  Licensed under the Open Software License version 3.0
12    #     http://www.opensource.org/licenses/osl-3.0.php
13    #
14    #######################################################
15    #
16    
17  """  """
18  @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 TFQMR: Transport Free Quasi Minimal Residual method.
449       @cvar MINRES: Minimum residual method.
450       @cvar SSOR: The symmetric overrealaxtion method
451       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
452       @cvar ILUT: The incomplete LU factorization preconditioner with will in
453       @cvar JACOBI: The Jacobi preconditioner
454       @cvar GMRES: The Gram-Schmidt minimum residual method
455       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
456       @cvar LUMPING: Matrix lumping.
457       @cvar NO_REORDERING: No matrix reordering allowed
458       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
459       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
460       @cvar PASO: PASO solver package
461       @cvar SCSL: SGI SCSL solver library
462       @cvar MKL: Intel's MKL solver library
463       @cvar UMFPACK: the UMFPACK library
464       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
465       @cvar ITERATIVE: The default iterative solver
466       @cvar AMG: algebraic multi grid
467       @cvar RILU: recursive ILU
468    
469       """
470       DEFAULT= 0
471       DIRECT= 1
472       CHOLEVSKY= 2
473       PCG= 3
474       CR= 4
475       CGS= 5
476       BICGSTAB= 6
477       SSOR= 7
478       ILU0= 8
479       ILUT= 9
480       JACOBI= 10
481       GMRES= 11
482       PRES20= 12
483       LUMPING= 13
484       NO_REORDERING= 17
485       MINIMUM_FILL_IN= 18
486       NESTED_DISSECTION= 19
487       SCSL= 14
488       MKL= 15
489       UMFPACK= 16
490       ITERATIVE= 20
491       PASO= 21
492       AMG= 22
493       RILU = 23
494       TRILINOS = 24
495       NONLINEAR_GMRES = 25
496       TFQMR = 26
497       MINRES = 27
498    
499       SMALL_TOLERANCE=1.e-13
500       __PACKAGE_KEY="package"
501       __METHOD_KEY="method"
502       __SYMMETRY_KEY="symmetric"
503       __TOLERANCE_KEY="tolerance"
504       __PRECONDITIONER_KEY="preconditioner"
505    
506    
507       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
508         """
509         initializes a new linear PDE
510    
511         @param domain: domain of the PDE
512         @type domain: L{Domain<escript.Domain>}
513         @param numEquations: number of equations. If numEquations==None the number of equations
514                              is exracted from the PDE coefficients.
515         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
516                              is exracted from the PDE coefficients.
517         @param debug: if True debug informations are printed.
518    
519         """
520         super(LinearPDE, self).__init__()
521         #
522         #   the coefficients of the general PDE:
523         #
524         self.__COEFFICIENTS_OF_GENEARL_PDE={
525           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
526           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
527           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
528           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
529           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
530           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
531           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
532           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
533           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
535           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
536           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
537           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
538           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
540           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
541           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
542           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
543           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
544           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
545           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
546           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
547    
548         # COEFFICIENTS can be overwritten by subclasses:
549         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
550         self.__altered_coefficients=False
551       # initialize attributes       # initialize attributes
552       self.__debug=None       self.__debug=debug
553       self.__domain=domain       self.__domain=domain
554       self.__numEquations=numEquations       self.__numEquations=numEquations
555       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
556       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
557    
558       # set some default values:       # set some default values:
559       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
560       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
561       self.__tolerance=1.e-8       self.__tolerance=1.e-8
562       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
563       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
564         self.__preconditioner=self.DEFAULT
565         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
566       self.__sym=False       self.__sym=False
      self.__lumping=False  
567    
568     def getCoefficient(self,name):       self.resetCoefficients()
569         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
570       # =============================================================================
571       #    general stuff:
572       # =============================================================================
573       def __str__(self):
574         """
575         returns string representation of the PDE
576    
577         @return: a simple representation of the PDE
578         @rtype: C{str}
579         """
580         return "<LinearPDE %d>"%id(self)
581       # =============================================================================
582       #    debug :
583       # =============================================================================
584       def setDebugOn(self):
585         """
586         switches on debugging
587       """       """
588       @brief return the value of the coefficient name       self.__debug=not None
589    
590       @param name     def setDebugOff(self):
591         """
592         switches off debugging
593       """       """
594       return self.__coefficient[name]       self.__debug=None
595    
596     def setValue(self,**coefficients):     def trace(self,text):
597        """       """
598        @brief sets new values to coefficients       print the text message if debugging is swiched on.
599         @param text: message
600         @type text: C{string}
601         """
602         if self.__debug: print "%s: %s"%(str(self),text)
603    
604        @param coefficients     # =============================================================================
605        """     # some service functions:
606        self._setValue(**coefficients)     # =============================================================================
607             def getDomain(self):
608         """
609         returns the domain of the PDE
610    
611     def _setValue(self,**coefficients):       @return: the domain of the PDE
612        """       @rtype: L{Domain<escript.Domain>}
613        @brief sets new values to coefficients       """
614         return self.__domain
615    
616        @param coefficients     def getDim(self):
617        """       """
618               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  
619    
620        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
621        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
622           for i in self.__coefficient.iterkeys():       """
623               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()  
624    
625     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
626       """       """
627       @brief return the shape of the coefficient name       returns the number of equations
628    
629       @param name       @return: the number of equations
630         @rtype: C{int}
631         @raise UndefinedPDEError: if the number of equations is not be specified yet.
632       """       """
633       if self.hasCoefficient(name):       if self.__numEquations==None:
634          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
635       else:       else:
636          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
637    
638     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
639       """       """
640       @brief return the atoms of the coefficient name       returns the number of unknowns
641    
642       @param name       @return: the number of unknowns
643         @rtype: C{int}
644         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
645       """       """
646       if self.hasCoefficient(name):       if self.__numSolutions==None:
647          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
648       else:       else:
649          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
650    
651     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
652       """       """
653       @brief annonced that coefficient name has been changed       return status for order reduction for equation
654    
655       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
656         @rtype: L{bool}
657       """       """
658       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  
659    
660     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
661        """       """
662        @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  
663    
664        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
665        """       @rtype: L{bool}
666        return self.__coefficient.has_key(name)       """
667         return self.__reduce_solution_order
668    
669     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
670       """       """
671       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
672    
673         @return: representation space of equation
674         @rtype: L{FunctionSpace<escript.FunctionSpace>}
675       """       """
676       return self.__row_function_space       if self.reduceEquationOrder():
677             return escript.ReducedSolution(self.getDomain())
678         else:
679             return escript.Solution(self.getDomain())
680    
681     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
682       """       """
683       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
684    
685         @return: representation space of solution
686         @rtype: L{FunctionSpace<escript.FunctionSpace>}
687       """       """
688       return self.__column_function_space       if self.reduceSolutionOrder():
689             return escript.ReducedSolution(self.getDomain())
690         else:
691             return escript.Solution(self.getDomain())
692    
    # ===== debug ==============================================================  
    def setDebugOn(self):  
        """  
        @brief  
        """  
        self.__debug=not None  
693    
694     def setDebugOff(self):     def getOperator(self):
695         """       """
696         @brief       provides access to the operator of the PDE
        """  
        self.__debug=None  
697    
698     def debug(self):       @return: the operator of the PDE
699         """       @rtype: L{Operator<escript.Operator>}
700         @brief returns true if the PDE is in the debug mode       """
701         """       m=self.getSystem()[0]
702         return self.__debug       if self.isUsingLumping():
703             return self.copyConstraint(1./m)
704         else:
705             return m
706    
707     #===== Lumping ===========================     def getRightHandSide(self):
708     def setLumpingOn(self):       """
709        """       provides access to the right hand side of the PDE
710        @brief indicates to use matrix lumping       @return: the right hand side of the PDE
711        """       @rtype: L{Data<escript.Data>}
712        if not self.isUsingLumping():       """
713           raise SystemError,"Lumping is not working yet! Talk to the experts"       r=self.getSystem()[1]
714           if self.debug() : print "PDE Debug: lumping is set on"       if self.isUsingLumping():
715           self.__rebuildOperator()           return self.copyConstraint(r)
716           self.__lumping=True       else:
717             return r
718    
719     def setLumpingOff(self):     def applyOperator(self,u=None):
720        """       """
721        @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  
722    
723     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}
724        """                 the current solution is used.
725        @brief set the matrix lumping flag to flag       @type u: L{Data<escript.Data>} or None
726        """       @return: image of u
727        if flag:       @rtype: L{Data<escript.Data>}
728           self.setLumpingOn()       """
729        else:       if u==None:
730           self.setLumpingOff()          return self.getOperator()*self.getSolution()
731         else:
732            return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
733    
734     def isUsingLumping(self):     def getResidual(self,u=None):
735         """
736         return the residual of u or the current solution if u is not present.
737    
738         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
739                   the current solution is used.
740         @type u: L{Data<escript.Data>} or None
741         @return: residual of u
742         @rtype: L{Data<escript.Data>}
743         """
744         return self.applyOperator(u)-self.getRightHandSide()
745    
746       def checkSymmetry(self,verbose=True):
747        """        """
748        @brief        test the PDE for symmetry.
749    
750          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
751          @type verbose: C{bool}
752          @return:  True if the PDE is symmetric.
753          @rtype: L{Data<escript.Data>}
754          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
755        """        """
756        return self.__lumping        verbose=verbose or self.__debug
757          out=True
758          if self.getNumSolutions()!=self.getNumEquations():
759             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
760             out=False
761          else:
762             A=self.getCoefficientOfGeneralPDE("A")
763             if not A.isEmpty():
764                tol=util.Lsup(A)*self.SMALL_TOLERANCE
765                if self.getNumSolutions()>1:
766                   for i in range(self.getNumEquations()):
767                      for j in range(self.getDim()):
768                         for k in range(self.getNumSolutions()):
769                            for l in range(self.getDim()):
770                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
771                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
772                                   out=False
773                else:
774                   for j in range(self.getDim()):
775                      for l in range(self.getDim()):
776                         if util.Lsup(A[j,l]-A[l,j])>tol:
777                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
778                            out=False
779             B=self.getCoefficientOfGeneralPDE("B")
780             C=self.getCoefficientOfGeneralPDE("C")
781             if B.isEmpty() and not C.isEmpty():
782                if verbose: print "non-symmetric PDE because B is not present but C is"
783                out=False
784             elif not B.isEmpty() and C.isEmpty():
785                if verbose: print "non-symmetric PDE because C is not present but B is"
786                out=False
787             elif not B.isEmpty() and not C.isEmpty():
788                tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
789                if self.getNumSolutions()>1:
790                   for i in range(self.getNumEquations()):
791                       for j in range(self.getDim()):
792                          for k in range(self.getNumSolutions()):
793                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
794                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
795                                  out=False
796                else:
797                   for j in range(self.getDim()):
798                      if util.Lsup(B[j]-C[j])>tol:
799                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
800                         out=False
801             if self.getNumSolutions()>1:
802               D=self.getCoefficientOfGeneralPDE("D")
803               if not D.isEmpty():
804                 tol=util.Lsup(D)*self.SMALL_TOLERANCE
805                 for i in range(self.getNumEquations()):
806                    for k in range(self.getNumSolutions()):
807                      if util.Lsup(D[i,k]-D[k,i])>tol:
808                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
809                          out=False
810               d=self.getCoefficientOfGeneralPDE("d")
811               if not d.isEmpty():
812                 tol=util.Lsup(d)*self.SMALL_TOLERANCE
813                 for i in range(self.getNumEquations()):
814                    for k in range(self.getNumSolutions()):
815                      if util.Lsup(d[i,k]-d[k,i])>tol:
816                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
817                          out=False
818               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
819               if not d_contact.isEmpty():
820                 tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
821                 for i in range(self.getNumEquations()):
822                    for k in range(self.getNumSolutions()):
823                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
824                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
825                          out=False
826             # and now the reduced coefficients
827             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
828             if not A_reduced.isEmpty():
829                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
830                if self.getNumSolutions()>1:
831                   for i in range(self.getNumEquations()):
832                      for j in range(self.getDim()):
833                         for k in range(self.getNumSolutions()):
834                            for l in range(self.getDim()):
835                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
836                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
837                                   out=False
838                else:
839                   for j in range(self.getDim()):
840                      for l in range(self.getDim()):
841                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
842                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
843                            out=False
844             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
845             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
846             if B_reduced.isEmpty() and not C_reduced.isEmpty():
847                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
848                out=False
849             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
850                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
851                out=False
852             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
853                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
854                if self.getNumSolutions()>1:
855                   for i in range(self.getNumEquations()):
856                       for j in range(self.getDim()):
857                          for k in range(self.getNumSolutions()):
858                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
859                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
860                                  out=False
861                else:
862                   for j in range(self.getDim()):
863                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
864                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
865                         out=False
866             if self.getNumSolutions()>1:
867               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
868               if not D_reduced.isEmpty():
869                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
870                 for i in range(self.getNumEquations()):
871                    for k in range(self.getNumSolutions()):
872                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
873                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
874                          out=False
875               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
876               if not d_reduced.isEmpty():
877                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
878                 for i in range(self.getNumEquations()):
879                    for k in range(self.getNumSolutions()):
880                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
881                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
882                          out=False
883               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
884               if not d_contact_reduced.isEmpty():
885                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
886                 for i in range(self.getNumEquations()):
887                    for k in range(self.getNumSolutions()):
888                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
889                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
890                          out=False
891          return out
892    
893     #============ method business =========================================================     def getSolution(self,**options):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
894         """         """
895         @brief sets a new solver         returns the solution of the PDE. If the solution is not valid the PDE is solved.
896    
897           @return: the solution
898           @rtype: L{Data<escript.Data>}
899           @param options: solver options
900           @keyword verbose: True to get some information during PDE solution
901           @type verbose: C{bool}
902           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
903                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
904           @keyword iter_max: maximum number of iteration steps allowed.
905           @keyword drop_tolerance: threshold for drupping in L{ILUT}
906           @keyword drop_storage: maximum of allowed memory in L{ILUT}
907           @keyword truncation: maximum number of residuals in L{GMRES}
908           @keyword restart: restart cycle length in L{GMRES}
909         """         """
910         if not solver==self.getSolverMethod():         if not self.__solution_isValid:
911              mat,f=self.getSystem()
912              if self.isUsingLumping():
913                 self.__solution=self.copyConstraint(f*mat)
914              else:
915                 options[self.__TOLERANCE_KEY]=self.getTolerance()
916                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
917                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
918                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
919                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
920                 self.trace("PDE is resolved.")
921                 self.trace("solver options: %s"%str(options))
922                 self.__solution=mat.solve(f,options)
923              self.__solution_isValid=True
924           return self.__solution
925    
926       def getFlux(self,u=None):
927         """
928         returns the flux M{J} for a given M{u}
929    
930         M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
931    
932         or
933    
934         M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
935    
936         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
937         @type u: L{Data<escript.Data>} or None
938         @return: flux
939         @rtype: L{Data<escript.Data>}
940         """
941         if u==None: u=self.getSolution()
942         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
943               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
944               -util.self.getCoefficientOfGeneralPDE("X") \
945               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
946               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
947               -util.self.getCoefficientOfGeneralPDE("X_reduced")
948       # =============================================================================
949       #   solver settings:
950       # =============================================================================
951       def setSolverMethod(self,solver=None,preconditioner=None):
952           """
953           sets a new solver
954    
955           @param solver: sets a new solver method.
956           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{TFQMR}, L{MINRES}, L{PRES20}, L{LUMPING}, L{AMG}
957           @param preconditioner: sets a new solver method.
958           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
959           """
960           if solver==None: solver=self.__solver_method
961           if preconditioner==None: preconditioner=self.__preconditioner
962           if solver==None: solver=self.DEFAULT
963           if preconditioner==None: preconditioner=self.DEFAULT
964           if not (solver,preconditioner)==self.getSolverMethod():
965             self.__solver_method=solver             self.__solver_method=solver
966             if self.debug() : print "PDE Debug: New solver is %s"%solver             self.__preconditioner=preconditioner
967             self.__checkMatrixType()             self.__checkMatrixType()
968               self.trace("New solver is %s"%self.getSolverMethodName())
969    
970       def getSolverMethodName(self):
971           """
972           returns the name of the solver currently used
973    
974           @return: the name of the solver currently used.
975           @rtype: C{string}
976           """
977    
978           m=self.getSolverMethod()
979           p=self.getSolverPackage()
980           method=""
981           if m[0]==self.DEFAULT: method="DEFAULT"
982           elif m[0]==self.DIRECT: method= "DIRECT"
983           elif m[0]==self.ITERATIVE: method= "ITERATIVE"
984           elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
985           elif m[0]==self.PCG: method= "PCG"
986           elif m[0]==self.TFQMR: method= "TFQMR"
987           elif m[0]==self.MINRES: method= "MINRES"
988           elif m[0]==self.CR: method= "CR"
989           elif m[0]==self.CGS: method= "CGS"
990           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
991           elif m[0]==self.SSOR: method= "SSOR"
992           elif m[0]==self.GMRES: method= "GMRES"
993           elif m[0]==self.PRES20: method= "PRES20"
994           elif m[0]==self.LUMPING: method= "LUMPING"
995           elif m[0]==self.AMG: method= "AMG"
996           if m[1]==self.DEFAULT: method+="+DEFAULT"
997           elif m[1]==self.JACOBI: method+= "+JACOBI"
998           elif m[1]==self.ILU0: method+= "+ILU0"
999           elif m[1]==self.ILUT: method+= "+ILUT"
1000           elif m[1]==self.SSOR: method+= "+SSOR"
1001           elif m[1]==self.AMG: method+= "+AMG"
1002           elif m[1]==self.RILU: method+= "+RILU"
1003           if p==self.DEFAULT: package="DEFAULT"
1004           elif p==self.PASO: package= "PASO"
1005           elif p==self.MKL: package= "MKL"
1006           elif p==self.SCSL: package= "SCSL"
1007           elif p==self.UMFPACK: package= "UMFPACK"
1008           elif p==self.TRILINOS: package= "TRILINOS"
1009           else : method="unknown"
1010           return "%s solver of %s package"%(method,package)
1011    
1012    
1013     def getSolverMethod(self):     def getSolverMethod(self):
1014         """         """
1015         @brief returns the solver method         returns the solver method
1016    
1017           @return: the solver method currently be used.
1018           @rtype: C{int}
1019           """
1020           return self.__solver_method,self.__preconditioner
1021    
1022       def setSolverPackage(self,package=None):
1023         """         """
1024         return self.__solver_method         sets a new solver package
1025    
1026           @param package: sets a new solver method.
1027           @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1028           """
1029           if package==None: package=self.DEFAULT
1030           if not package==self.getSolverPackage():
1031               self.__solver_package=package
1032               self.__checkMatrixType()
1033               self.trace("New solver is %s"%self.getSolverMethodName())
1034    
1035       def getSolverPackage(self):
1036           """
1037           returns the package of the solver
1038    
1039           @return: the solver package currently being used.
1040           @rtype: C{int}
1041           """
1042           return self.__solver_package
1043    
1044       def isUsingLumping(self):
1045          """
1046          checks if matrix lumping is used a solver method
1047    
1048          @return: True is lumping is currently used a solver method.
1049          @rtype: C{bool}
1050          """
1051          return self.getSolverMethod()[0]==self.LUMPING
1052    
    #============ tolerance business =========================================================  
1053     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1054         """         """
1055         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
1056    
1057           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
1058    
1059           defines the stopping criterion.
1060    
1061           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1062                       the system will be resolved.
1063           @type tol: positive C{float}
1064           @raise ValueError: if tolerance is not positive.
1065         """         """
1066         if not tol>0:         if not tol>0:
1067             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1068         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1069         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
1070         self.__tolerance=tol         self.__tolerance=tol
1071         return         return
1072    
1073     def getTolerance(self):     def getTolerance(self):
1074         """         """
1075         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
1076    
1077           @return: tolerance currently used.
1078           @rtype: C{float}
1079         """         """
1080         return self.__tolerance         return self.__tolerance
1081    
1082     #===== symmetry  flag ==========================     # =============================================================================
1083       #    symmetry  flag:
1084       # =============================================================================
1085     def isSymmetric(self):     def isSymmetric(self):
1086        """        """
1087        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
1088    
1089          @return: True is a symmetric PDE is indicated, otherwise False is returned
1090          @rtype: C{bool}
1091        """        """
1092        return self.__sym        return self.__sym
1093    
1094     def setSymmetryOn(self):     def setSymmetryOn(self):
1095        """        """
1096        @brief sets the symmetry flag to true        sets the symmetry flag.
1097        """        """
1098        if not self.isSymmetric():        if not self.isSymmetric():
1099           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
1100           self.__sym=True           self.__sym=True
1101           self.__checkMatrixType()           self.__checkMatrixType()
1102    
1103     def setSymmetryOff(self):     def setSymmetryOff(self):
1104        """        """
1105        @brief sets the symmetry flag to false        removes the symmetry flag.
1106        """        """
1107        if self.isSymmetric():        if self.isSymmetric():
1108           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
1109           self.__sym=False           self.__sym=False
1110           self.__checkMatrixType()           self.__checkMatrixType()
1111    
1112     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
1113       """        """
1114       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
1115    
1116       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
1117       """        @type flag: C{bool}
1118       if flag:        """
1119          self.setSymmetryOn()        if flag:
1120       else:           self.setSymmetryOn()
1121          self.setSymmetryOff()        else:
1122             self.setSymmetryOff()
1123    
1124     #===== order reduction ==========================     # =============================================================================
1125       # function space handling for the equation as well as the solution
1126       # =============================================================================
1127     def setReducedOrderOn(self):     def setReducedOrderOn(self):
1128       """       """
1129       @brief switches to on reduced order       switches on reduced order for solution and equation representation
1130    
1131         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1132       """       """
1133       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1134       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1135    
1136     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1137       """       """
1138       @brief switches to full order       switches off reduced order for solution and equation representation
1139    
1140         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1141       """       """
1142       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1143       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1144    
1145     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1146       """       """
1147       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1148         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1149       @param flag                    if flag is not present order reduction is switched off
1150         @type flag: C{bool}
1151         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1152       """       """
1153       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1154       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1155    
1156     #===== order reduction solution ==========================  
1157     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1158       """       """
1159       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1160    
1161         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1162       """       """
1163       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1164       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1165           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1166           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1167           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1168             self.__resetSystem()
1169    
1170     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1171       """       """
1172       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1173    
1174         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1175       """       """
1176       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1177       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1178           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1179           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1180           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1181             self.__resetSystem()
1182    
1183     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1184       """       """
1185       @brief sets order for test functions according to flag       sets order for test functions according to flag
1186    
1187       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1188                      if flag is not present order reduction is switched off
1189         @type flag: C{bool}
1190         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1191       """       """
1192       if flag:       if flag:
1193          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1194       else:       else:
1195          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1196                                                                                                                                                              
    #===== order reduction equation ==========================  
1197     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1198       """       """
1199       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1200    
1201         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1202       """       """
1203       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1204       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1205           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1206           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1207           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1208             self.__resetSystem()
1209    
1210     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1211       """       """
1212       @brief switches to full order for test functions       switches off reduced order for equation representation
1213    
1214         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1215       """       """
1216       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1217       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1218           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1219           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1220           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1221             self.__resetSystem()
1222    
1223     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1224       """       """
1225       @brief sets order for test functions according to flag       sets order for test functions according to flag
1226    
1227       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1228                      if flag is not present order reduction is switched off
1229         @type flag: C{bool}
1230         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1231       """       """
1232       if flag:       if flag:
1233          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1234       else:       else:
1235          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1236    
1237     # ==== initialization =====================================================================     # =============================================================================
1238     def __makeNewOperator(self):     # private method:
1239       # =============================================================================
1240       def __checkMatrixType(self):
1241         """
1242         reassess the matrix type and, if a new matrix is needed, resets the system.
1243         """
1244         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1245         if not new_matrix_type==self.__matrix_type:
1246             self.trace("Matrix type is now %d."%new_matrix_type)
1247             self.__matrix_type=new_matrix_type
1248             self.__resetSystem()
1249       #
1250       #   rebuild switches :
1251       #
1252       def __invalidateSolution(self):
1253           """
1254           indicates the PDE has to be resolved if the solution is requested
1255           """
1256           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1257           self.__solution_isValid=False
1258    
1259       def __invalidateOperator(self):
1260           """
1261           indicates the operator has to be rebuilt next time it is used
1262           """
1263           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1264           self.__invalidateSolution()
1265           self.__operator_is_Valid=False
1266    
1267       def __invalidateRightHandSide(self):
1268           """
1269           indicates the right hand side has to be rebuild next time it is used
1270           """
1271           if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1272           self.__invalidateSolution()
1273           self.__righthandside_isValid=False
1274    
1275       def __invalidateSystem(self):
1276           """
1277           annonced that everthing has to be rebuild:
1278           """
1279           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1280           self.__invalidateSolution()
1281           self.__invalidateOperator()
1282           self.__invalidateRightHandSide()
1283    
1284       def __resetSystem(self):
1285           """
1286           annonced that everthing has to be rebuild:
1287           """
1288           self.trace("New System is built from scratch.")
1289           self.__operator=escript.Operator()
1290           self.__operator_is_Valid=False
1291           self.__righthandside=escript.Data()
1292           self.__righthandside_isValid=False
1293           self.__solution=escript.Data()
1294           self.__solution_isValid=False
1295       #
1296       #    system initialization:
1297       #
1298       def __getNewOperator(self):
1299         """         """
1300         @brief         returns an instance of a new operator
1301         """         """
1302           self.trace("New operator is allocated.")
1303         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1304                             self.getNumEquations(), \                             self.getNumEquations(), \
1305                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 617  class LinearPDE: Line 1307  class LinearPDE:
1307                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1308                             self.__matrix_type)                             self.__matrix_type)
1309    
1310     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1311         """         """
1312         @brief         returns an instance of a new right hand side
1313         """         """
1314         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1315           if self.getNumEquations()>1:
1316               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1317           else:
1318               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1319    
1320     def __makeNewSolution(self):     def __getNewSolution(self):
1321         """         """
1322         @brief         returns an instance of a new solution
1323         """         """
1324         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1325           if self.getNumSolutions()>1:
1326               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1327           else:
1328               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1329    
1330     def __getFreshOperator(self):     def __makeFreshSolution(self):
1331         """         """
1332         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1333         """         """
1334         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1335             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1336         else:         else:
1337             self.__operator.setValue(0.)             self.__solution*=0
1338             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1339         return self.__operator         return self.__solution
1340    
1341     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1342         """         """
1343         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1344         """         """
1345         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1346             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1347         else:         else:
1348             print "fix self.__righthandside*=0"             self.__righthandside.setToZero()
1349             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1350             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1351    
1352     # ==== rebuild switches =====================================================================     def __makeFreshOperator(self):
    def __rebuildSolution(self,deep=False):  
1353         """         """
1354         @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
1355         """         """
1356         if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."         if self.__operator.isEmpty():
1357         self.__solution_isValid=False             self.__operator=self.__getNewOperator()
1358         if deep: self.__solution=escript.Data(deep)         else:
1359               self.__operator.resetValues()
1360               self.trace("Operator reset to zero")
1361           return self.__operator
1362    
1363     def __rebuildOperator(self,deep=False):     def __applyConstraint(self):
1364         """         """
1365         @brief indicates the operator has to be rebuilt next time it is used         applies the constraints defined by q and r to the system
1366         """         """
1367         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if not self.isUsingLumping():
1368         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1369         self.__operator_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1370         if deep: self.__operator=escript.Operator()            if not q.isEmpty() and not self.__operator.isEmpty():
1371                 # q is the row and column mask to indicate where constraints are set:
1372                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1373                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1374                 u=self.__getNewSolution()
1375                 if r.isEmpty():
1376                    r_s=self.__getNewSolution()
1377                 else:
1378                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1379                 u.copyWithMask(r_s,col_q)
1380                 if not self.__righthandside.isEmpty():
1381                    self.__righthandside-=self.__operator*u
1382                    self.__righthandside=self.copyConstraint(self.__righthandside)
1383                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1384       # =============================================================================
1385       # function giving access to coefficients of the general PDE:
1386       # =============================================================================
1387       def getCoefficientOfGeneralPDE(self,name):
1388         """
1389         return the value of the coefficient name of the general PDE.
1390    
1391         @note: This method is called by the assembling routine it can be overwritten
1392               to map coefficients of a particular PDE to the general PDE.
1393         @param name: name of the coefficient requested.
1394         @type name: C{string}
1395         @return: the value of the coefficient  name
1396         @rtype: L{Data<escript.Data>}
1397         @raise IllegalCoefficient: if name is not one of coefficients
1398                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1399                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1400         """
1401         if self.hasCoefficientOfGeneralPDE(name):
1402            return self.getCoefficient(name)
1403         else:
1404            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1405    
1406     def __rebuildRightHandSide(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
1407         """       """
1408         @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.
1409         """  
1410         if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."       @param name: name of the coefficient enquired.
1411         self.__rebuildSolution(deep)       @type name: C{string}
1412         self.__righthandside_isValid=False       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1413         if not self.__homogeneous_constraint: self.__rebuildOperator()       @rtype: C{bool}
        if deep: self.__righthandside=escript.Data()  
1414    
    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):  
1415       """       """
1416       @brief reassess the matrix type and, if needed, initiates an operator rebuild       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1417    
1418       def createCoefficientOfGeneralPDE(self,name):
1419       """       """
1420       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)  
1421    
1422     #============ assembling =======================================================       @param name: name of the coefficient requested.
1423     def __copyConstraint(self,u):       @type name: C{string}
1424        """       @return: a coefficient name initialized to 0.
1425        @brief copies the constrint condition into u       @rtype: L{Data<escript.Data>}
1426        """       @raise IllegalCoefficient: if name is not one of coefficients
1427        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},
1428        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}.
1429        if not q.isEmpty():       """
1430            if r.isEmpty():       if self.hasCoefficientOfGeneralPDE(name):
1431               r2=escript.Data(0,u.getShape(),u.getFunctionSpace())          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1432            else:       else:
1433               r2=escript.Data(r,u.getFunctionSpace())          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
           u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))  
1434    
1435     def __applyConstraint(self,rhs_update=True):     def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1436         """       """
1437         @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.)  
1438    
1439     def getOperator(self):       @param name: name of the coefficient enquired.
1440         """       @type name: C{string}
1441         @brief returns the operator of the PDE       @return: the function space to be used for coefficient name
1442         """       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1443         if not self.__operator_isValid:       @raise IllegalCoefficient: if name is not one of coefficients
1444             # 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},
1445             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}.
1446                if self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():       """
1447                         raise TypeError,"Lumped matrix requires same order for equations and unknowns"       if self.hasCoefficientOfGeneralPDE(name):
1448                if not self.getCoefficient("A").isEmpty():          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1449                         raise Warning,"Lumped matrix does not allow coefficient A"       else:
1450                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()  
1451    
1452             self.getDomain().addPDEToSystem(mat,escript.Data(), \     def getShapeOfCoefficientOfGeneralPDE(self,name):
1453                          self.getCoefficient("A"), \       """
1454                          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  
1455    
1456     def getRightHandSide(self,ignoreConstraint=False):       @param name: name of the coefficient enquired.
1457         """       @type name: C{string}
1458         @brief returns the right hand side of the PDE       @return: the shape of the coefficient name
1459         @rtype: C{tuple} of C{int}
1460         @raise IllegalCoefficient: if name is not one of coefficients
1461                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1462                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1463         """
1464         if self.hasCoefficientOfGeneralPDE(name):
1465            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1466         else:
1467            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1468    
1469         @param ignoreConstraint     # =============================================================================
1470         """     # functions giving access to coefficients of a particular PDE implementation:
1471         if not self.__righthandside_isValid:     # =============================================================================
1472             if self.debug() : print "PDE Debug: New right hand side is built."     def getCoefficient(self,name):
1473             self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \       """
1474                           self.getCoefficient("X"), \       returns the value of the coefficient name
1475                           self.getCoefficient("Y"),\  
1476                           self.getCoefficient("y"),\       @param name: name of the coefficient requested.
1477                           self.getCoefficient("y_contact"))       @type name: C{string}
1478             self.__righthandside_isValid=True       @return: the value of the coefficient name
1479             if ignoreConstraint: self.__copyConstraint(self.__righthandside)       @rtype: L{Data<escript.Data>}
1480         return self.__righthandside       @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1481         """
1482         if self.hasCoefficient(name):
1483             return self.COEFFICIENTS[name].getValue()
1484         else:
1485            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1486    
1487       def hasCoefficient(self,name):
1488         """
1489         return True if name is the name of a coefficient
1490    
1491         @param name: name of the coefficient enquired.
1492         @type name: C{string}
1493         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1494         @rtype: C{bool}
1495         """
1496         return self.COEFFICIENTS.has_key(name)
1497    
1498       def createCoefficient(self, name):
1499         """
1500         create a L{Data<escript.Data>} object corresponding to coefficient name
1501    
1502         @return: a coefficient name initialized to 0.
1503         @rtype: L{Data<escript.Data>}
1504         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1505         """
1506         if self.hasCoefficient(name):
1507            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1508         else:
1509            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1510    
1511       def getFunctionSpaceForCoefficient(self,name):
1512         """
1513         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1514    
1515         @param name: name of the coefficient enquired.
1516         @type name: C{string}
1517         @return: the function space to be used for coefficient name
1518         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1519         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1520         """
1521         if self.hasCoefficient(name):
1522            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1523         else:
1524            raise ValueError,"unknown coefficient %s requested"%name
1525       def getShapeOfCoefficient(self,name):
1526         """
1527         return the shape of the coefficient name
1528    
1529         @param name: name of the coefficient enquired.
1530         @type name: C{string}
1531         @return: the shape of the coefficient name
1532         @rtype: C{tuple} of C{int}
1533         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1534         """
1535         if self.hasCoefficient(name):
1536            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1537         else:
1538            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1539    
1540       def resetCoefficients(self):
1541         """
1542         resets all coefficients to there default values.
1543         """
1544         for i in self.COEFFICIENTS.iterkeys():
1545             self.COEFFICIENTS[i].resetValue()
1546    
1547       def alteredCoefficient(self,name):
1548         """
1549         announce that coefficient name has been changed
1550    
1551         @param name: name of the coefficient enquired.
1552         @type name: C{string}
1553         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1554         @note: if name is q or r, the method will not trigger a rebuilt of the system as constraints are applied to the solved system.
1555         """
1556         if self.hasCoefficient(name):
1557            self.trace("Coefficient %s has been altered."%name)
1558            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1559               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1560               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1561         else:
1562            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1563    
1564       def copyConstraint(self,u):
1565          """
1566          copies the constraint into u and returns u.
1567    
1568          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1569          @type u: L{Data<escript.Data>}
1570          @return: the input u modified by the constraints.
1571          @rtype: L{Data<escript.Data>}
1572          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1573          """
1574          q=self.getCoefficientOfGeneralPDE("q")
1575          r=self.getCoefficientOfGeneralPDE("r")
1576          if not q.isEmpty():
1577             if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1578             if r.isEmpty():
1579                 r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1580             else:
1581                 r=escript.Data(r,u.getFunctionSpace())
1582             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1583          return u
1584    
1585       def setValue(self,**coefficients):
1586          """
1587          sets new values to coefficients
1588    
1589          @param coefficients: new values assigned to coefficients
1590          @keyword A: value for coefficient A.
1591          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1592          @keyword A_reduced: value for coefficient A_reduced.
1593          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1594          @keyword B: value for coefficient B
1595          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1596          @keyword B_reduced: value for coefficient B_reduced
1597          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1598          @keyword C: value for coefficient C
1599          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1600          @keyword C_reduced: value for coefficient C_reduced
1601          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1602          @keyword D: value for coefficient D
1603          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1604          @keyword D_reduced: value for coefficient D_reduced
1605          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1606          @keyword X: value for coefficient X
1607          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1608          @keyword X_reduced: value for coefficient X_reduced
1609          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1610          @keyword Y: value for coefficient Y
1611          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1612          @keyword Y_reduced: value for coefficient Y_reduced
1613          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1614          @keyword d: value for coefficient d
1615          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1616          @keyword d_reduced: value for coefficient d_reduced
1617          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1618          @keyword y: value for coefficient y
1619          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1620          @keyword d_contact: value for coefficient d_contact
1621          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1622          @keyword d_contact_reduced: value for coefficient d_contact_reduced
1623          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1624          @keyword y_contact: value for coefficient y_contact
1625          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1626          @keyword y_contact_reduced: value for coefficient y_contact_reduced
1627          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1628          @keyword r: values prescribed to the solution at the locations of constraints
1629          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1630                   depending of reduced order is used for the solution.
1631          @keyword q: mask for location of constraints
1632          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1633                   depending of reduced order is used for the representation of the equation.
1634          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1635          """
1636          # check if the coefficients are  legal:
1637          for i in coefficients.iterkeys():
1638             if not self.hasCoefficient(i):
1639                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1640          # if the number of unknowns or equations is still unknown we try to estimate them:
1641          if self.__numEquations==None or self.__numSolutions==None:
1642             for i,d in coefficients.iteritems():
1643                if hasattr(d,"shape"):
1644                    s=d.shape
1645                elif hasattr(d,"getShape"):
1646                    s=d.getShape()
1647                else:
1648                    s=numarray.array(d).shape
1649                if s!=None:
1650                    # get number of equations and number of unknowns:
1651                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1652                    if res==None:
1653                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1654                    else:
1655                        if self.__numEquations==None: self.__numEquations=res[0]
1656                        if self.__numSolutions==None: self.__numSolutions=res[1]
1657          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1658          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1659          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1660          for i,d in coefficients.iteritems():
1661            try:
1662               self.COEFFICIENTS[i].setValue(self.getDomain(),
1663                                             self.getNumEquations(),self.getNumSolutions(),
1664                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1665               self.alteredCoefficient(i)
1666            except IllegalCoefficientFunctionSpace,m:
1667                # if the function space is wrong then we try the reduced version:
1668                i_red=i+"_reduced"
1669                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1670                    try:
1671                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1672                                                          self.getNumEquations(),self.getNumSolutions(),
1673                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1674                        self.alteredCoefficient(i_red)
1675                    except IllegalCoefficientValue,m:
1676                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1677                    except IllegalCoefficientFunctionSpace,m:
1678                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1679                else:
1680                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1681            except IllegalCoefficientValue,m:
1682               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1683          self.__altered_coefficients=True
1684          # check if the systrem is inhomogeneous:
1685          if len(coefficients)>0 and not self.isUsingLumping():
1686             q=self.getCoefficientOfGeneralPDE("q")
1687             r=self.getCoefficientOfGeneralPDE("r")
1688             homogeneous_constraint=True
1689             if not q.isEmpty() and not r.isEmpty():
1690                 if util.Lsup(q*r)>0.:
1691                   self.trace("Inhomogeneous constraint detected.")
1692                   self.__invalidateSystem()
1693    
1694     def getSystem(self):     def getSystem(self):
1695         """         """
1696         @brief         return the operator and right hand side of the PDE
1697    
1698           @return: the discrete version of the PDE
1699           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1700         """         """
1701         if not self.__operator_isValid 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."  
1702            if self.isUsingLumping():            if self.isUsingLumping():
1703                self.getRightHandSide(ignoreConstraint=True)                if not self.__operator_is_Valid:
1704                self.getOperator()                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1705                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1706                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1707                          raise ValueError,"coefficient A in lumped matrix may not be present."
1708                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1709                          raise ValueError,"coefficient B in lumped matrix may not be present."
1710                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1711                          raise ValueError,"coefficient C in lumped matrix may not be present."
1712                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1713                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1714                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1715                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1716                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1717                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1718                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1719                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1720                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1721                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1722                     D=self.getCoefficientOfGeneralPDE("D")
1723                     d=self.getCoefficientOfGeneralPDE("d")
1724                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1725                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
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                     if not d.isEmpty():
1734                         if self.getNumSolutions()>1:
1735                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1736                         else:
1737                            d_times_e=d
1738                     else:
1739                        d_times_e=escript.Data()
1740          
1741                     if not D_reduced.isEmpty():
1742                         if self.getNumSolutions()>1:
1743                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1744                         else:
1745                            D_reduced_times_e=D_reduced
1746                     else:
1747                        D_reduced_times_e=escript.Data()
1748                     if not d_reduced.isEmpty():
1749                         if self.getNumSolutions()>1:
1750                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1751                         else:
1752                            d_reduced_times_e=d_reduced
1753                     else:
1754                        d_reduced_times_e=escript.Data()
1755    
1756                     self.__operator=self.__getNewRightHandSide()
1757                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1758                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1759                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1760                     else:
1761                        self.getDomain().addPDEToRHS(self.__operator, \
1762                                                     escript.Data(), \
1763                                                     D_times_e, \
1764                                                     d_times_e,\
1765                                                     escript.Data())
1766                        self.getDomain().addPDEToRHS(self.__operator, \
1767                                                     escript.Data(), \
1768                                                     D_reduced_times_e, \
1769                                                     d_reduced_times_e,\
1770                                                     escript.Data())
1771                     self.__operator=1./self.__operator
1772                     self.trace("New lumped operator has been built.")
1773                     self.__operator_is_Valid=True
1774                  if not self.__righthandside_isValid:
1775                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1776                                   self.getCoefficientOfGeneralPDE("X"), \
1777                                   self.getCoefficientOfGeneralPDE("Y"),\
1778                                   self.getCoefficientOfGeneralPDE("y"),\
1779                                   self.getCoefficientOfGeneralPDE("y_contact"))
1780                     self.getDomain().addPDEToRHS(self.__righthandside, \
1781                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1782                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1783                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1784                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1785                     self.trace("New right hand side as been built.")
1786                     self.__righthandside_isValid=True
1787            else:            else:
1788                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1789                              self.getCoefficient("A"), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1790                              self.getCoefficient("B"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1791                              self.getCoefficient("C"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1792                              self.getCoefficient("D"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1793                              self.getCoefficient("X"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1794                              self.getCoefficient("Y"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1795                              self.getCoefficient("d"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1796                              self.getCoefficient("y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1797                              self.getCoefficient("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1798                              self.getCoefficient("y_contact"))                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1799            self.__operator_isValid=True                                 self.getCoefficientOfGeneralPDE("y_contact"))
1800            self.__righthandside_isValid=True                   self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1801            self.__applyConstraint()                                 self.getCoefficientOfGeneralPDE("A_reduced"), \
1802            self.__copyConstraint(self.__righthandside)                                 self.getCoefficientOfGeneralPDE("B_reduced"), \
1803         elif not self.__operator_isValid:                                 self.getCoefficientOfGeneralPDE("C_reduced"), \
1804            self.getOperator()                                 self.getCoefficientOfGeneralPDE("D_reduced"), \
1805         elif not self.__righthandside_isValid:                                 self.getCoefficientOfGeneralPDE("X_reduced"), \
1806            self.getRightHandSide()                                 self.getCoefficientOfGeneralPDE("Y_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1808                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1809                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1810                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1811                     self.__applyConstraint()
1812                     self.__righthandside=self.copyConstraint(self.__righthandside)
1813                     self.trace("New system has been built.")
1814                     self.__operator_is_Valid=True
1815                     self.__righthandside_isValid=True
1816                 elif not self.__righthandside_isValid:
1817                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1818                                   self.getCoefficientOfGeneralPDE("X"), \
1819                                   self.getCoefficientOfGeneralPDE("Y"),\
1820                                   self.getCoefficientOfGeneralPDE("y"),\
1821                                   self.getCoefficientOfGeneralPDE("y_contact"))
1822                     self.getDomain().addPDEToRHS(self.__righthandside, \
1823                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1824                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1825                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1826                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1827                     self.__righthandside=self.copyConstraint(self.__righthandside)
1828                     self.trace("New right hand side has been built.")
1829                     self.__righthandside_isValid=True
1830                 elif not self.__operator_is_Valid:
1831                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1832                                self.getCoefficientOfGeneralPDE("A"), \
1833                                self.getCoefficientOfGeneralPDE("B"), \
1834                                self.getCoefficientOfGeneralPDE("C"), \
1835                                self.getCoefficientOfGeneralPDE("D"), \
1836                                escript.Data(), \
1837                                escript.Data(), \
1838                                self.getCoefficientOfGeneralPDE("d"), \
1839                                escript.Data(),\
1840                                self.getCoefficientOfGeneralPDE("d_contact"), \
1841                                escript.Data())
1842                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1843                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1844                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1845                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1846                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1847                                escript.Data(), \
1848                                escript.Data(), \
1849                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1850                                escript.Data(),\
1851                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1852                                escript.Data())
1853                     self.__applyConstraint()
1854                     self.trace("New operator has been built.")
1855                     self.__operator_is_Valid=True
1856         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1857    
    def solve(self,**options):  
       """  
       @brief solve the PDE  
1858    
1859        @param options  class Poisson(LinearPDE):
1860        """     """
1861        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  
1862    
1863     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief returns the solution of the PDE  
1864    
1865         @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  
1866    
1867     def getDim(self):     M{n[j]*grad(u)[j] = 0 }
1868       """  
1869       @brief returns the spatial dimension of the PDE     and constraints:
1870    
1871       M{u=0} where M{q>0}
1872    
1873       """
1874    
1875       def __init__(self,domain,debug=False):
1876       """       """
1877       return self.getDomain().getDim()       initializes a new Poisson equation
1878    
1879         @param domain: domain of the PDE
1880         @type domain: L{Domain<escript.Domain>}
1881         @param debug: if True debug informations are printed.
1882    
    def getNumEquations(self):  
1883       """       """
1884       @brief returns the number of equations       super(Poisson, self).__init__(domain,1,1,debug)
1885         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1886                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1887                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1888         self.setSymmetryOn()
1889    
1890       def setValue(self,**coefficients):
1891       """       """
1892       if self.__numEquations>0:       sets new values to coefficients
1893           return self.__numEquations  
1894         @param coefficients: new values assigned to coefficients
1895         @keyword f: value for right hand side M{f}
1896         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1897         @keyword q: mask for location of constraints
1898         @type q: any type that can be casted to rank zeo L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1899                   depending of reduced order is used for the representation of the equation.
1900         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1901         """
1902         super(Poisson, self).setValue(**coefficients)
1903    
1904       def getCoefficientOfGeneralPDE(self,name):
1905         """
1906         return the value of the coefficient name of the general PDE
1907         @param name: name of the coefficient requested.
1908         @type name: C{string}
1909         @return: the value of the coefficient  name
1910         @rtype: L{Data<escript.Data>}
1911         @raise IllegalCoefficient: if name is not one of coefficients
1912                      M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
1913         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1914         """
1915         if name == "A" :
1916             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1917         elif name == "B" :
1918             return escript.Data()
1919         elif name == "C" :
1920             return escript.Data()
1921         elif name == "D" :
1922             return escript.Data()
1923         elif name == "X" :
1924             return escript.Data()
1925         elif name == "Y" :
1926             return self.getCoefficient("f")
1927         elif name == "d" :
1928             return escript.Data()
1929         elif name == "y" :
1930             return escript.Data()
1931         elif name == "d_contact" :
1932             return escript.Data()
1933         elif name == "y_contact" :
1934             return escript.Data()
1935         elif name == "A_reduced" :
1936             return escript.Data()
1937         elif name == "B_reduced" :
1938             return escript.Data()
1939         elif name == "C_reduced" :
1940             return escript.Data()
1941         elif name == "D_reduced" :
1942             return escript.Data()
1943         elif name == "X_reduced" :
1944             return escript.Data()
1945         elif name == "Y_reduced" :
1946             return self.getCoefficient("f_reduced")
1947         elif name == "d_reduced" :
1948             return escript.Data()
1949         elif name == "y_reduced" :
1950             return escript.Data()
1951         elif name == "d_contact_reduced" :
1952             return escript.Data()
1953         elif name == "y_contact_reduced" :
1954             return escript.Data()
1955         elif name == "r" :
1956             return escript.Data()
1957         elif name == "q" :
1958             return self.getCoefficient("q")
1959       else:       else:
1960           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1961    
1962     def getNumSolutions(self):  class Helmholtz(LinearPDE):
1963       """
1964       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1965    
1966       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1967    
1968       with natural boundary conditons
1969    
1970       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1971    
1972       and constraints:
1973    
1974       M{u=r} where M{q>0}
1975    
1976       """
1977    
1978       def __init__(self,domain,debug=False):
1979       """       """
1980       @brief returns the number of unknowns       initializes a new Poisson equation
1981    
1982         @param domain: domain of the PDE
1983         @type domain: L{Domain<escript.Domain>}
1984         @param debug: if True debug informations are printed.
1985    
1986         """
1987         super(Helmholtz, self).__init__(domain,1,1,debug)
1988         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1989                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1993                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1994                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1995                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1996                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1997         self.setSymmetryOn()
1998    
1999       def setValue(self,**coefficients):
2000       """       """
2001       if self.__numSolutions>0:       sets new values to coefficients
2002          return self.__numSolutions  
2003         @param coefficients: new values assigned to coefficients
2004         @keyword omega: value for coefficient M{S{omega}}
2005         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2006         @keyword k: value for coefficeint M{k}
2007         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2008         @keyword f: value for right hand side M{f}
2009         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2010         @keyword alpha: value for right hand side M{S{alpha}}
2011         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2012         @keyword g: value for right hand side M{g}
2013         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2014         @keyword r: prescribed values M{r} for the solution in constraints.
2015         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2016                   depending of reduced order is used for the representation of the equation.
2017         @keyword q: mask for location of constraints
2018         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2019                   depending of reduced order is used for the representation of the equation.
2020         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2021         """
2022         super(Helmholtz, self).setValue(**coefficients)
2023    
2024       def getCoefficientOfGeneralPDE(self,name):
2025         """
2026         return the value of the coefficient name of the general PDE
2027    
2028         @param name: name of the coefficient requested.
2029         @type name: C{string}
2030         @return: the value of the coefficient  name
2031         @rtype: L{Data<escript.Data>}
2032         @raise IllegalCoefficient: if name is not one of coefficients
2033                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2034         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2035         """
2036         if name == "A" :
2037             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
2038         elif name == "B" :
2039             return escript.Data()
2040         elif name == "C" :
2041             return escript.Data()
2042         elif name == "D" :
2043             return self.getCoefficient("omega")
2044         elif name == "X" :
2045             return escript.Data()
2046         elif name == "Y" :
2047             return self.getCoefficient("f")
2048         elif name == "d" :
2049             return self.getCoefficient("alpha")
2050         elif name == "y" :
2051             return self.getCoefficient("g")
2052         elif name == "d_contact" :
2053             return escript.Data()
2054         elif name == "y_contact" :
2055             return escript.Data()
2056         elif name == "A_reduced" :
2057             return escript.Data()
2058         elif name == "B_reduced" :
2059             return escript.Data()
2060         elif name == "C_reduced" :
2061             return escript.Data()
2062         elif name == "D_reduced" :
2063             return escript.Data()
2064         elif name == "X_reduced" :
2065             return escript.Data()
2066         elif name == "Y_reduced" :
2067             return self.getCoefficient("f_reduced")
2068         elif name == "d_reduced" :
2069             return escript.Data()
2070         elif name == "y_reduced" :
2071            return self.getCoefficient("g_reduced")
2072         elif name == "d_contact_reduced" :
2073             return escript.Data()
2074         elif name == "y_contact_reduced" :
2075             return escript.Data()
2076         elif name == "r" :
2077             return self.getCoefficient("r")
2078         elif name == "q" :
2079             return self.getCoefficient("q")
2080       else:       else:
2081          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2082    
2083    class LameEquation(LinearPDE):
2084       """
2085       Class to define a Lame equation problem:
2086    
2087     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"  
2088    
2089        return None     with natural boundary conditons:
2090    
2091     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  
2092    
2093              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}     and constraints:
2094    
2095         @param u argument of the operator     M{u[i]=r[i]} where M{q[i]>0}
2096    
2097         """     """
        raise SystemError,"getFlux is not implemented yet"  
        return None  
2098    
2099     def applyOperator(self,u):     def __init__(self,domain,debug=False):
2100         """        super(LameEquation, self).__init__(domain,\
2101         @brief applies the operator of the PDE to a given solution u in weak from                                           domain.getDim(),domain.getDim(),debug)
2102          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2103                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
2104                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2105                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
2106                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2107                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2108                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2109          self.setSymmetryOn()
2110    
2111       def setValues(self,**coefficients):
2112         """
2113         sets new values to coefficients
2114    
2115         @param coefficients: new values assigned to coefficients
2116         @keyword lame_mu: value for coefficient M{S{mu}}
2117         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2118         @keyword lame_lambda: value for coefficient M{S{lambda}}
2119         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2120         @keyword F: value for internal force M{F}
2121         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
2122         @keyword sigma: value for initial stress M{S{sigma}}
2123         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
2124         @keyword f: value for extrenal force M{f}
2125         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
2126         @keyword r: prescribed values M{r} for the solution in constraints.
2127         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2128                   depending of reduced order is used for the representation of the equation.
2129         @keyword q: mask for location of constraints
2130         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2131                   depending of reduced order is used for the representation of the equation.
2132         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2133         """
2134         super(LameEquation, self).setValues(**coefficients)
2135    
2136       def getCoefficientOfGeneralPDE(self,name):
2137         """
2138         return the value of the coefficient name of the general PDE
2139    
2140         @param name: name of the coefficient requested.
2141         @type name: C{string}
2142         @return: the value of the coefficient  name
2143         @rtype: L{Data<escript.Data>}
2144         @raise IllegalCoefficient: if name is not one of coefficients
2145                      "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.
2146         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2147         """
2148         if name == "A" :
2149             out =self.createCoefficientOfGeneralPDE("A")
2150             for i in range(self.getDim()):
2151               for j in range(self.getDim()):
2152                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
2153                 out[i,j,j,i] += self.getCoefficient("lame_mu")
2154                 out[i,j,i,j] += self.getCoefficient("lame_mu")
2155             return out
2156         elif name == "B" :
2157             return escript.Data()
2158         elif name == "C" :
2159             return escript.Data()
2160         elif name == "D" :
2161             return escript.Data()
2162         elif name == "X" :
2163             return self.getCoefficient("sigma")
2164         elif name == "Y" :
2165             return self.getCoefficient("F")
2166         elif name == "d" :
2167             return escript.Data()
2168         elif name == "y" :
2169             return self.getCoefficient("f")
2170         elif name == "d_contact" :
2171             return escript.Data()
2172         elif name == "y_contact" :
2173             return escript.Data()
2174         elif name == "A_reduced" :
2175             return escript.Data()
2176         elif name == "B_reduced" :
2177             return escript.Data()
2178         elif name == "C_reduced" :
2179             return escript.Data()
2180         elif name == "D_reduced" :
2181             return escript.Data()
2182         elif name == "X_reduced" :
2183             return escript.Data()
2184         elif name == "Y_reduced" :
2185             return escript.Data()
2186         elif name == "d_reduced" :
2187             return escript.Data()
2188         elif name == "y_reduced" :
2189             return escript.Data()
2190         elif name == "d_contact_reduced" :
2191             return escript.Data()
2192         elif name == "y_contact_reduced" :
2193             return escript.Data()
2194         elif name == "r" :
2195             return self.getCoefficient("r")
2196         elif name == "q" :
2197             return self.getCoefficient("q")
2198         else:
2199            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2200    
2201         @param u argument of the operator  def LinearSinglePDE(domain,debug=False):
2202       """
2203       defines a single linear PDEs
2204    
2205         """     @param domain: domain of the PDE
2206         return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())     @type domain: L{Domain<escript.Domain>}
2207                                                                                                                                                                 @param debug: if True debug informations are printed.
2208     def getResidual(self,u):     @rtype: L{LinearPDE}
2209         """     """
2210         @brief return the residual of u in the weak from     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
2211    
2212         @param u  def LinearPDESystem(domain,debug=False):
2213         """     """
2214         return self.applyOperator(u)-self.getRightHandSide()     defines a system of linear PDEs
2215    
2216  class Poisson(LinearPDE):     @param domain: domain of the PDE
2217       @type domain: L{Domain<escript.Domain>}
2218       @param debug: if True debug informations are printed.
2219       @rtype: L{LinearPDE}
2220     """     """
2221     @brief Class to define a Poisson equstion problem:     return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2222                                                                                                                                                                
2223     class to define a linear PDE of the form  class TransportPDE(object):
2224                                                                                                                                                                     """
2225          -u_{,jj} = f       Warning: This is still a very experimental. The class is still changing!
2226                                                                                                                                                                
2227       with boundary conditons:       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2228                                                                                                                                                                    
2229          n_j*u_{,j} = 0       u=r where q>0
2230                                                                                                                                                                    
2231      and constraints:       all coefficients are constant over time.
2232                                                                                                                                                                
2233           u=0 where q>0       typical usage:
2234                                                                                                                                                                
2235     """           p=TransportPDE(dom)
2236             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2237     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2238         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))           t=0
2239         self._setValue(A=numarray.identity(self.getDomain().getDim()))           dt=0.1
2240         self.setSymmetryOn()           while (t<1.):
2241         self.setValue(f,q)                u=p.solve(dt)
2242    
2243     def setValue(self,f=escript.Data(),q=escript.Data()):       """
2244         self._setValue(Y=f,q=q)       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2245            self.__domain=domain
2246                                                                                                                                                                      self.__num_equations=num_equations
2247  # $Log$          self.__useSUPG=useSUPG
2248  # Revision 1.3  2004/12/17 07:43:10  jgs          self.__trace=trace
2249  # *** empty log message ***          self.__theta=theta
2250  #          self.__matrix_type=0
2251  # Revision 1.1.2.3  2004/12/16 00:12:34  gross          self.__reduced=True
2252  # __init__ of LinearPDE does not accept any coefficients anymore          self.__reassemble=True
2253  #          if self.__useSUPG:
2254  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2255  # *** empty log message ***             self.__pde.setSymmetryOn()
2256  #             self.__pde.setReducedOrderOn()
2257  # Revision 1.1.2.1  2004/12/12 22:53:47  gross          else:
2258  # linearPDE has been renamed LinearPDE             self.__transport_problem=self.__getNewTransportProblem()
2259  #          self.setTolerance()
2260  # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross          self.__M=escript.Data()
2261  # GMRES added          self.__A=escript.Data()
2262  #          self.__B=escript.Data()
2263  # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross          self.__C=escript.Data()
2264  # options for GMRES and PRES20 added          self.__D=escript.Data()
2265  #          self.__X=escript.Data()
2266  # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross          self.__Y=escript.Data()
2267  # some small changes          self.__d=escript.Data()
2268  #          self.__y=escript.Data()
2269  # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross          self.__d_contact=escript.Data()
2270  # Finley solves 4M unknowns now          self.__y_contact=escript.Data()
2271  #          self.__r=escript.Data()
2272  # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross          self.__q=escript.Data()
2273  # poisson solver added  
2274  #       def trace(self,text):
2275  # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross               if self.__trace: print text
2276  # 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):
2277  #          if self.__useSUPG:
2278  # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross              if self.__reassemble:
2279  # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed                 h=self.__domain.getSize()
2280  #                 dt=None
2281  # Revision 1.1.1.1  2004/10/26 06:53:56  jgs                 if not self.__A.isEmpty():
2282  # initial import of project esys2                    dt2=util.inf(h**2*self.__M/util.length(self.__A))
2283  #                    if dt == None:
2284  # Revision 1.3.2.3  2004/10/26 06:43:48  jgs                       dt = dt2
2285  # committing Lutz's and Paul's changes to brach jgs                    else:
2286  #                       dt=1./(1./dt+1./dt2)
2287  # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane                 if not self.__B.isEmpty():
2288  # 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))
2289  #                    if dt == None:
2290  # Revision 1.3  2004/09/23 00:53:23  jgs                       dt = dt2
2291  # minor fixes                    else:
2292  #                       dt=1./(1./dt+1./dt2)
2293  # Revision 1.1  2004/08/28 12:58:06  gross                 if not  self.__C.isEmpty():
2294  # SimpleSolve is not running yet: problem with == of functionsspace                    dt2=util.inf(h*self.__M/util.length(self.__C))
2295  #                    if dt == None:
2296  #                       dt = dt2
2297                      else:
2298                         dt=1./(1./dt+1./dt2)
2299                   if not self.__D.isEmpty():
2300                      dt2=util.inf(self.__M/util.length(self.__D))
2301                      if dt == None:
2302                         dt = dt2
2303                      else:
2304                         dt=1./(1./dt+1./dt2)
2305                   self.__dt = dt/2
2306                return self.__dt
2307            else:
2308                return self.__getTransportProblem().getSafeTimeStepSize()
2309         def getDomain(self):
2310            return self.__domain
2311         def getTheta(self):
2312            return self.__theta
2313         def getNumEquations(self):
2314            return self.__num_equations
2315         def setReducedOn(self):
2316              if not self.reduced():
2317                  if self.__useSUPG:
2318                     self.__pde.setReducedOrderOn()
2319                  else:
2320                     self.__transport_problem=self.__getNewTransportProblem()
2321              self.__reduced=True
2322         def setReducedOff(self):
2323              if self.reduced():
2324                  if self.__useSUPG:
2325                     self.__pde.setReducedOrderOff()
2326                  else:
2327                     self.__transport_problem=self.__getNewTransportProblem()
2328              self.__reduced=False
2329         def reduced(self):
2330             return self.__reduced
2331         def getFunctionSpace(self):
2332            if self.reduced():
2333               return escript.ReducedSolution(self.getDomain())
2334            else:
2335               return escript.Solution(self.getDomain())
2336    
2337         def setTolerance(self,tol=1.e-8):
2338            self.__tolerance=tol
2339            if self.__useSUPG:
2340                  self.__pde.setTolerance(self.__tolerance)
2341    
2342         def __getNewTransportProblem(self):
2343           """
2344           returns an instance of a new operator
2345           """
2346           self.trace("New Transport problem is allocated.")
2347           return self.getDomain().newTransportProblem( \
2348                                   self.getTheta(),
2349                                   self.getNumEquations(), \
2350                                   self.getFunctionSpace(), \
2351                                   self.__matrix_type)
2352              
2353         def __getNewSolutionVector(self):
2354             if self.getNumEquations() ==1 :
2355                    out=escript.Data(0.0,(),self.getFunctionSpace())
2356             else:
2357                    out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2358             return out
2359    
2360         def __getTransportProblem(self):
2361           if self.__reassemble:
2362                 self.__source=self.__getNewSolutionVector()
2363                 self.__transport_problem.reset()
2364                 self.getDomain().addPDEToTransportProblem(
2365                             self.__transport_problem,
2366                             self.__source,
2367                             self.__M,
2368                             self.__A,
2369                             self.__B,
2370                             self.__C,
2371                             self.__D,
2372                             self.__X,
2373                             self.__Y,
2374                             self.__d,
2375                             self.__y,
2376                             self.__d_contact,
2377                             self.__y_contact)
2378                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2379                 self.__reassemble=False
2380           return self.__transport_problem
2381         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2382                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2383                 if not M==None:
2384                      self.__reassemble=True
2385                      self.__M=M
2386                 if not A==None:
2387                      self.__reassemble=True
2388                      self.__A=A
2389                 if not B==None:
2390                      self.__reassemble=True
2391                      self.__B=B
2392                 if not C==None:
2393                      self.__reassemble=True
2394                      self.__C=C
2395                 if not D==None:
2396                      self.__reassemble=True
2397                      self.__D=D
2398                 if not X==None:
2399                      self.__reassemble=True
2400                      self.__X=X
2401                 if not Y==None:
2402                      self.__reassemble=True
2403                      self.__Y=Y
2404                 if not d==None:
2405                      self.__reassemble=True
2406                      self.__d=d
2407                 if not y==None:
2408                      self.__reassemble=True
2409                      self.__y=y
2410                 if not d_contact==None:
2411                      self.__reassemble=True
2412                      self.__d_contact=d_contact
2413                 if not y_contact==None:
2414                      self.__reassemble=True
2415                      self.__y_contact=y_contact
2416                 if not q==None:
2417                      self.__reassemble=True
2418                      self.__q=q
2419                 if not r==None:
2420                      self.__reassemble=True
2421                      self.__r=r
2422    
2423         def setInitialSolution(self,u):
2424                 if self.__useSUPG:
2425                     self.__u=util.interpolate(u,self.getFunctionSpace())
2426                 else:
2427                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2428    
2429         def solve(self,dt,**kwarg):
2430               if self.__useSUPG:
2431                    if self.__reassemble:
2432                        self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2433                        self.__reassemble=False
2434                    dt2=self.getSafeTimeStepSize()
2435                    nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2436                    dt2=dt/nn
2437                    nnn=0
2438                    u=self.__u
2439                    self.trace("number of substeps is %d."%nn)
2440                    while nnn<nn :
2441                        self.__setSUPG(u,u,dt2/2)
2442                        u_half=self.__pde.getSolution(verbose=True)
2443                        self.__setSUPG(u,u_half,dt2)
2444                        u=self.__pde.getSolution(verbose=True)
2445                        nnn+=1
2446                    self.__u=u
2447                    return self.__u
2448               else:
2449                   kwarg["tolerance"]=self.__tolerance
2450                   tp=self.__getTransportProblem()
2451                   return tp.solve(self.__source,dt,kwarg)
2452         def __setSUPG(self,u0,u,dt):
2453                g=util.grad(u)
2454                X=0
2455                Y=self.__M*u0
2456                X=0
2457                self.__pde.setValue(r=u0)
2458                if not self.__A.isEmpty():
2459                   X=X+dt*util.matrixmult(self.__A,g)
2460                if not self.__B.isEmpty():
2461                   X=X+dt*self.__B*u
2462                if not  self.__C.isEmpty():
2463                   Y=Y+dt*util.inner(self.__C,g)
2464                if not self.__D.isEmpty():
2465                   Y=Y+dt*self.__D*u
2466                if not self.__X.isEmpty():
2467                   X=X+dt*self.__X
2468                if not self.__Y.isEmpty():
2469                   Y=Y+dt*self.__Y
2470                self.__pde.setValue(X=X,Y=Y)
2471                if not self.__y.isEmpty():
2472                   self.__pde.setValue(y=dt*self.__y)
2473                if not self.__y_contact.isEmpty():
2474                   self.__pde.setValue(y=dt*self.__y_contact)
2475                self.__pde.setValue(r=u0)

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