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trunk/esys2/escript/py_src/linearPDEs.py revision 102 by jgs, Wed Dec 15 07:08:39 2004 UTC trunk/escript/py_src/linearPDEs.py revision 430 by gross, Wed Jan 11 06:40:50 2006 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
2    
3  ## @file linearPDEs.py  #
4    #      COPYRIGHT ACcESS 2004 -  All Rights Reserved
5    #
6    #   This software is the property of ACcESS.  No part of this code
7    #   may be copied in any form or by any means without the expressed written
8    #   consent of ACcESS.  Copying, use or modification of this software
9    #   by any unauthorised person is illegal unless that
10    #   person has a software license agreement with ACcESS.
11    #
12  """  """
13  @brief Functions and classes for linear PDEs  The module provides an interface to define and solve linear partial
14    differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
15    solver capabilities in itself but hands the PDE over to
16    the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
17    The general interface is provided through the L{LinearPDE} class. The
18    L{AdvectivePDE} which is derived from the L{LinearPDE} class
19    provides an interface to PDE dominated by its advective terms. The L{Poisson},
20    L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}
21    classs which are also derived form the L{LinearPDE} class should be used
22    to define of solve these sepecial PDEs.
23    
24    @var __author__: name of author
25    @var __licence__: licence agreement
26    @var __url__: url entry point on documentation
27    @var __version__: version
28    @var __date__: date of the version
29  """  """
30    
31  import escript  import escript
32  import util  import util
33  import numarray  import numarray
34    
35  def identifyDomain(domain=None,data={}):  __author__="Lutz Gross, l.gross@uq.edu.au"
36       """  __licence__="contact: esys@access.uq.edu.au"
37       @brief Return the Domain which is equal to the input domain (if not None)  __url__="http://www.iservo.edu.au/esys/escript"
38       and is the domain of all Data objects in the dictionary data.  __version__="$Revision$"
39       An exception is raised if this is not possible  __date__="$Date$"
40    
41       @param domain  
42       @param data  class IllegalCoefficient(ValueError):
43       """     """
44       # get the domain used by any Data object in the list data:     raised if an illegal coefficient of the general ar particular PDE is requested.
45       data_domain=None     """
46       for d in data.itervalues():  
47            if isinstance(d,escript.Data):  class IllegalCoefficientValue(ValueError):
48               if not d.isEmpty(): data_domain=d.getDomain()     """
49       # check if domain and data_domain are identical?     raised if an incorrect value for a coefficient is used.
50       if domain == None:     """
51           if data_domain == None:  
52                raise ValueError,"Undefined PDE domain. Specify a domain or use a Data class object as coefficient"  class UndefinedPDEError(ValueError):
53       else:     """
54           if data_domain == None:     raised if a PDE is not fully defined yet.
55                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  
   
   
 def _CompTuple2(t1,t2):  
    """  
    @brief  
   
    @param t1  
    @param t2  
    """  
    dif=t1[0]+t1[1]-(t2[0]+t2[1])  
    if dif<0: return 1  
    elif dif>0: return -1  
    else: return 0  
56    
57  class PDECoefficientType:  class PDECoefficient(object):
58      """      """
59      @brief      A class for describing a PDE coefficient
60    
61        @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
62        @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
63        @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
64        @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
65        @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
66        @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
67        @cvar BY_SOLUTION: indicator that the dimension of the coefficient shape is defined by the number PDE solutions
68        @cvar BY_DIM: indicator that the dimension of the coefficient shape is defined by the spatial dimension
69        @cvar OPERATOR: indicator that the the coefficient alters the operator of the PDE
70        @cvar RIGHTHANDSIDE: indicator that the the coefficient alters the right hand side of the PDE
71        @cvar BOTH: indicator that the the coefficient alters the operator as well as the right hand side of the PDE
72    
73      """      """
     # identifier for location of Data objects defining coefficients  
74      INTERIOR=0      INTERIOR=0
75      BOUNDARY=1      BOUNDARY=1
76      CONTACT=2      CONTACT=2
77      CONTINUOUS=3      SOLUTION=3
78      # identifier in the pattern of coefficients:      REDUCED=4
79      # 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
80      # number of unknowns.      BY_SOLUTION=6
81      EQUATION=3      BY_DIM=7
82      SOLUTION=4      OPERATOR=10
83      DIM=5      RIGHTHANDSIDE=11
84      # indicator for what is altered if the coefficient is altered:      BOTH=12
85      OPERATOR=5  
     RIGHTHANDSIDE=6  
     BOTH=7  
86      def __init__(self,where,pattern,altering):      def __init__(self,where,pattern,altering):
87         """         """
88         @brief Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
89    
90           @param where: describes where the coefficient lives
91           @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}
92           @param pattern: describes the shape of the coefficient and how the shape is build for a given
93                  spatial dimension and numbers of equation and solution in then PDE. For instance,
94                  (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
95                  is instanciated as shape (3,2,2) in case of a three equations and two solution components
96                  on a 2-dimensional domain. In the case of single equation and a single solution component
97                  the shape compoments marked by L{BY_EQUATION} or L{BY_SOLUTION} are dropped. In this case
98                  the example would be read as (2,).
99           @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
100           @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
101           @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
102    
103         """         """
104           super(PDECoefficient, self).__init__()
105         self.what=where         self.what=where
106         self.pattern=pattern         self.pattern=pattern
107         self.altering=altering         self.altering=altering
108           self.resetValue()
109    
110      def getFunctionSpace(self,domain):      def resetValue(self):
111         """         """
112         @brief defines the FunctionSpace of the coefficient on the domain         resets coefficient value to default
   
        @param domain  
113         """         """
114         if self.what==self.INTERIOR: return escript.Function(domain)         self.value=escript.Data()
115         elif self.what==self.BOUNDARY: return escript.FunctionOnBoundary(domain)  
116         elif self.what==self.CONTACT: return escript.FunctionOnContactZero(domain)      def getFunctionSpace(self,domain,reducedEquationOrder=False,reducedSolutionOrder=False):
117         elif self.what==self.CONTINUOUS: return escript.ContinuousFunction(domain)         """
118           defines the L{FunctionSpace<escript.FunctionSpace>} of the coefficient
119    
120           @param domain: domain on which the PDE uses the coefficient
121           @type domain: L{Domain<escript.Domain>}
122           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
123           @type domain: C{bool}
124           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
125           @type domain: C{bool}
126           @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
127           @rtype:  L{FunctionSpace<escript.FunctionSpace>}
128           """
129           if self.what==self.INTERIOR:
130                return escript.Function(domain)
131           elif self.what==self.BOUNDARY:
132                return escript.FunctionOnBoundary(domain)
133           elif self.what==self.CONTACT:
134                return escript.FunctionOnContactZero(domain)
135           elif self.what==self.SOLUTION:
136                if reducedEquationOrder and reducedSolutionOrder:
137                    return escript.ReducedSolution(domain)
138                else:
139                    return escript.Solution(domain)
140           elif self.what==self.REDUCED:
141                return escript.ReducedSolution(domain)
142    
143        def getValue(self):
144           """
145           returns the value of the coefficient
146    
147           @return:  value of the coefficient
148           @rtype:  L{Data<escript.Data>}
149           """
150           return self.value
151    
152        def setValue(self,domain,numEquations=1,numSolutions=1,reducedEquationOrder=False,reducedSolutionOrder=False,newValue=None):
153           """
154           set the value of the coefficient to a new value
155    
156           @param domain: domain on which the PDE uses the coefficient
157           @type domain: L{Domain<escript.Domain>}
158           @param numEquations: number of equations of the PDE
159           @type numEquations: C{int}
160           @param numSolutions: number of components of the PDE solution
161           @type numSolutions: C{int}
162           @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
163           @type domain: C{bool}
164           @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
165           @type domain: C{bool}
166           @param newValue: number of components of the PDE solution
167           @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
168           @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
169           """
170           if newValue==None:
171               newValue=escript.Data()
172           elif isinstance(newValue,escript.Data):
173               if not newValue.isEmpty():
174                  try:
175                     newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
176                  except:
177                     raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
178           else:
179               newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
180           if not newValue.isEmpty():
181               if not self.getShape(domain,numEquations,numSolutions)==newValue.getShape():
182                   raise IllegalCoefficientValue,"Expected shape of coefficient is %s but actual shape is %s."%(self.getShape(domain,numEquations,numSolutions),newValue.getShape())
183           self.value=newValue
184    
185      def isAlteringOperator(self):      def isAlteringOperator(self):
186          """          """
187      @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
188    
189            @return:  True if the operator of the PDE is changed when the coefficient is changed
190            @rtype:  C{bool}
191      """      """
192          if self.altering==self.OPERATOR or self.altering==self.BOTH:          if self.altering==self.OPERATOR or self.altering==self.BOTH:
193              return not None              return not None
# Line 119  class PDECoefficientType: Line 196  class PDECoefficientType:
196    
197      def isAlteringRightHandSide(self):      def isAlteringRightHandSide(self):
198          """          """
199      @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
200    
201        @rtype:  C{bool}
202            @return:  True if the right hand side of the PDE is changed when the coefficient is changed
203      """      """
204          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:          if self.altering==self.RIGHTHANDSIDE or self.altering==self.BOTH:
205              return not None              return not None
206          else:          else:
207              return None              return None
208    
209      def estimateNumEquationsAndNumSolutions(self,shape=(),dim=3):      def estimateNumEquationsAndNumSolutions(self,domain,shape=()):
210         """         """
211         @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
212    
213         @param shape         @param domain: domain on which the PDE uses the coefficient
214         @param dim         @type domain: L{Domain<escript.Domain>}
215           @param shape: suggested shape of the coefficient
216           @type shape: C{tuple} of C{int} values
217           @return: the number of equations and number of solutions of the PDE is the coefficient has shape s.
218                     If no appropriate numbers could be identified, C{None} is returned
219           @rtype: C{tuple} of two C{int} values or C{None}
220         """         """
221           dim=domain.getDim()
222         if len(shape)>0:         if len(shape)>0:
223             num=max(shape)+1             num=max(shape)+1
224         else:         else:
225             num=1             num=1
226         search=[]         search=[]
227         for u in range(num):         if self.definesNumEquation() and self.definesNumSolutions():
228            for e in range(num):            for u in range(num):
229               search.append((e,u))               for e in range(num):
230         search.sort(_CompTuple2)                  search.append((e,u))
231         for item in search:            search.sort(self.__CompTuple2)
232               s=self.buildShape(item[0],item[1],dim)            for item in search:
233                 s=self.getShape(domain,item[0],item[1])
234               if len(s)==0 and len(shape)==0:               if len(s)==0 and len(shape)==0:
235                   return (1,1)                   return (1,1)
236               else:               else:
237                   if s==shape: return item                   if s==shape: return item
238           elif self.definesNumEquation():
239              for e in range(num,0,-1):
240                 s=self.getShape(domain,e,0)
241                 if len(s)==0 and len(shape)==0:
242                     return (1,None)
243                 else:
244                     if s==shape: return (e,None)
245    
246           elif self.definesNumSolutions():
247              for u in range(num,0,-1):
248                 s=self.getShape(domain,0,u)
249                 if len(s)==0 and len(shape)==0:
250                     return (None,1)
251                 else:
252                     if s==shape: return (None,u)
253         return None         return None
254        def definesNumSolutions(self):
255           """
256           checks if the coefficient allows to estimate the number of solution components
257    
258      def buildShape(self,e=1,u=1,dim=3):         @return: True if the coefficient allows an estimate of the number of solution components
259          """         @rtype: C{bool}
260      @brief builds the required shape for a given number of equations e, number of unknowns u and spatial dimension dim         """
261           for i in self.pattern:
262                 if i==self.BY_SOLUTION: return True
263           return False
264    
265      @param e      def definesNumEquation(self):
266      @param u         """
267      @param dim         checks if the coefficient allows to estimate the number of equations
268      """  
269          s=()         @return: True if the coefficient allows an estimate of the number of equations
270          for i in self.pattern:         @rtype: C{bool}
271               if i==self.EQUATION:         """
272                  if e>1: s=s+(e,)         for i in self.pattern:
273               elif i==self.SOLUTION:               if i==self.BY_EQUATION: return True
274                  if u>1: s=s+(u,)         return False
275    
276        def __CompTuple2(self,t1,t2):
277          """
278          Compare two tuples of possible number of equations and number of solutions
279    
280          @param t1: The first tuple
281          @param t2: The second tuple
282    
283          """
284    
285          dif=t1[0]+t1[1]-(t2[0]+t2[1])
286          if dif<0: return 1
287          elif dif>0: return -1
288          else: return 0
289    
290        def getShape(self,domain,numEquations=1,numSolutions=1):
291           """
292           builds the required shape of the coefficient
293    
294           @param domain: domain on which the PDE uses the coefficient
295           @type domain: L{Domain<escript.Domain>}
296           @param numEquations: number of equations of the PDE
297           @type numEquations: C{int}
298           @param numSolutions: number of components of the PDE solution
299           @type numSolutions: C{int}
300           @return: shape of the coefficient
301           @rtype: C{tuple} of C{int} values
302           """
303           dim=domain.getDim()
304           s=()
305           for i in self.pattern:
306                 if i==self.BY_EQUATION:
307                    if numEquations>1: s=s+(numEquations,)
308                 elif i==self.BY_SOLUTION:
309                    if numSolutions>1: s=s+(numSolutions,)
310               else:               else:
311                  s=s+(dim,)                  s=s+(dim,)
312          return s         return s
313    
314  _PDECoefficientTypes={  class LinearPDE(object):
 "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),  
 }  
   
 class LinearPDE:  
315     """     """
316     @brief Class to define a linear PDE     This class is used to define a general linear, steady, second order PDE
317         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  
318    
319       -(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:
320    
321       with boundary conditons:     M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}
322    
323          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_{ik}u_k = - n_j*X_{ij} + y_i     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
324       ie. summation over indexes appearing twice in a term of a sum is performed, is used.
325       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
326       L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.
327       M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.
328    
329      and contact conditions     The following natural boundary conditions are considered:
330    
331          n_j*(A_{ijkl}u_{k,l}+B_{ijk}u_k)_{,j} + d_contact_{ik}[u_k] = - n_j*X_{ij} + y_contact_i     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}
332    
333      and constraints:     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
334       Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are
335       each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
336    
          u_i=r_i where q_i>0  
337    
338     """     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
    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  
339    
340     def __init__(self,**args):     M{u=r}  where M{q>0}
      """  
      @brief initializes a new linear PDE.  
341    
342       @param args     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
343       """     The constraints override any other condition set by the PDE or the boundary condition.
344    
345       The PDE is symmetrical if
346    
347       M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}
348    
349       For a system of PDEs and a solution with several components the PDE has the form
350    
351       M{-grad(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])[j]+C[i,k,l]*grad(u[k])[l]+D[i,k]*u[k] =-grad(X[i,j])[j]+Y[i] }
352    
353       M{A} is a ramk four, M{B} and M{C} are each a rank three, M{D} and M{X} are each a rank two and M{Y} is a rank one.
354       The natural boundary conditions take the form:
355    
356       M{n[j]*(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}
357    
      # initialize attributes  
      self.__debug=None  
      self.__domain=None  
      self.__numEquations=0  
      self.__numSolutions=0  
      self.cleanCoefficients()  
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
   
      # check the arguments  
      coef={}  
      for arg in args.iterkeys():  
           if arg=="domain":  
               self.__domain=args[arg]  
           elif arg=="numEquations":  
               self.__numEquations=args[arg]  
           elif arg=="numSolutions":  
               self.__numSolutions=args[arg]  
           elif _PDECoefficientTypes.has_key(arg):  
               coef[arg]=args[arg]  
           else:  
               raise ValueError,"Illegal argument %s"%arg  
358    
359       # get the domain of the PDE     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
360       self.__domain=identifyDomain(self.__domain,coef)  
361    
362       M{u[i]=r[i]}  where  M{q[i]>0}
363    
364       M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
365    
366       The system of PDEs is symmetrical if
367    
368            - M{A[i,j,k,l]=A[k,l,i,j]}
369            - M{B[i,j,k]=C[k,i,j]}
370            - M{D[i,k]=D[i,k]}
371            - M{d[i,k]=d[k,i]}
372    
373       L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
374       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
375       defined as
376    
377       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}
378    
379       For the case of single solution component and single PDE M{J} is defined
380    
381       M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}
382    
383       In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
384       calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
385       the contact condition takes the form
386    
387       M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}
388    
389       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
390       of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
391       L{jump<util.jump>}.
392       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>}.
393       In case of a single PDE and a single component solution the contact condition takes the form
394    
395       M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}
396    
397       In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar
398       both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
399    
400       @cvar DEFAULT: The default method used to solve the system of linear equations
401       @cvar DIRECT: The direct solver based on LDU factorization
402       @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
403       @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
404       @cvar CR: The conjugate residual method
405       @cvar CGS: The conjugate gardient square method
406       @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
407       @cvar SSOR: The symmetric overrealaxtion method
408       @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
409       @cvar ILUT: The incomplete LU factorization preconditioner with will in
410       @cvar JACOBI: The Jacobi preconditioner
411       @cvar GMRES: The Gram-Schmidt minimum residual method
412       @cvar PRES20: Special GMRES with restart after 20 steps and truncation after 5 residuals
413       @cvar LUMPING: Matrix lumping.
414       @cvar NO_REORDERING: No matrix reordering allowed
415       @cvar MINIMUM_FILL_IN: Reorder matrix to reduce fill-in during factorization
416       @cvar NESTED_DISSECTION: Reorder matrix to improve load balancing during factorization
417       @cvar PASO: PASO solver package
418       @cvar SCSL: SGI SCSL solver library
419       @cvar MKL: Intel's MKL solver library
420       @cvar UMFPACK: the UMFPACK library
421       @cvar ITERATIVE: The default iterative solver
422       @cvar AMG: algebraic multi grid
423       @cvar RILU: recursive ILU
424    
425       """
426       DEFAULT= 0
427       DIRECT= 1
428       CHOLEVSKY= 2
429       PCG= 3
430       CR= 4
431       CGS= 5
432       BICGSTAB= 6
433       SSOR= 7
434       ILU0= 8
435       ILUT= 9
436       JACOBI= 10
437       GMRES= 11
438       PRES20= 12
439       LUMPING= 13
440       NO_REORDERING= 17
441       MINIMUM_FILL_IN= 18
442       NESTED_DISSECTION= 19
443       SCSL= 14
444       MKL= 15
445       UMFPACK= 16
446       ITERATIVE= 20
447       PASO= 21
448       AMG= 22
449       RILU = 23
450    
451       __TOL=1.e-13
452       __PACKAGE_KEY="package"
453       __METHOD_KEY="method"
454       __SYMMETRY_KEY="symmetric"
455       __TOLERANCE_KEY="tolerance"
456       __PRECONDITIONER_KEY="preconditioner"
457    
458    
459       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
460         """
461         initializes a new linear PDE
462    
463         @param domain: domain of the PDE
464         @type domain: L{Domain<escript.Domain>}
465         @param numEquations: number of equations. If numEquations==None the number of equations
466                              is exracted from the PDE coefficients.
467         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
468                              is exracted from the PDE coefficients.
469         @param debug: if True debug informations are printed.
470    
471         """
472         super(LinearPDE, self).__init__()
473         #
474         #   the coefficients of the general PDE:
475         #
476         self.__COEFFICIENTS_OF_GENEARL_PDE={
477           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
478           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
479           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
480           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
481           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
482           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
483           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
484           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
485           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
486           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
487           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
488           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
489    
490         # COEFFICIENTS can be overwritten by subclasses:
491         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
492         self.__altered_coefficients=False
493         # initialize attributes
494         self.__debug=debug
495         self.__domain=domain
496         self.__numEquations=numEquations
497         self.__numSolutions=numSolutions
498         self.__resetSystem()
499    
500       # set some default values:       # set some default values:
501       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
502       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
503       self.__tolerance=1.e-8       self.__tolerance=1.e-8
504       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
505       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
506         self.__preconditioner=self.DEFAULT
507         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
508       self.__sym=False       self.__sym=False
      self.__lumping=False  
      self.__numEquations=0  
      self.__numSolutions=0  
      # now we can set the ceofficients:  
      self._setCoefficient(**coef)  
509    
510     def getCoefficient(self,name):       self.resetCoefficients()
511         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
512       # =============================================================================
513       #    general stuff:
514       # =============================================================================
515       def __str__(self):
516         """
517         returns string representation of the PDE
518    
519         @return: a simple representation of the PDE
520         @rtype: C{str}
521         """
522         return "<LinearPDE %d>"%id(self)
523       # =============================================================================
524       #    debug :
525       # =============================================================================
526       def setDebugOn(self):
527       """       """
528       @brief return the value of the coefficient name       switches on debugging
529         """
530         self.__debug=not None
531    
532       @param name     def setDebugOff(self):
533       """       """
534       return self.__coefficient[name]       switches off debugging
535         """
536         self.__debug=None
537    
538     def setValue(self,**coefficients):     def trace(self,text):
539        """       """
540        @brief sets new values to coefficients       print the text message if debugging is swiched on.
541         @param text: message
542         @type text: C{string}
543         """
544         if self.__debug: print "%s: %s"%(str(self),text)
545    
546        @param coefficients     # =============================================================================
547        """     # some service functions:
548        self._setCoefficient(**coefficients)     # =============================================================================
549             def getDomain(self):
550         """
551         returns the domain of the PDE
552    
553     def _setCoefficient(self,**coefficients):       @return: the domain of the PDE
554        """       @rtype: L{Domain<escript.Domain>}
555        @brief sets new values to coefficients       """
556         return self.__domain
557    
558        @param coefficients     def getDim(self):
559        """       """
560               returns the spatial dimension of the PDE
       # get the dictionary of the coefficinets been altered:  
       alteredCoefficients={}  
       for i,d in coefficients.iteritems():  
          if self.hasCoefficient(i):  
             if d == None:  
                 alteredCoefficients[i]=escript.Data()  
             elif isinstance(d,escript.Data):  
                 if d.isEmpty():  
                   alteredCoefficients[i]=escript.Data()  
                 else:  
                   alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
             else:  
                 if self.__numEquations>0 and  self.__numSolutions>0:  
                    alteredCoefficients[i]=escript.Data(d,self.getShapeOfCoefficient(i),self.getFunctionSpaceOfCoefficient(i))  
                 else:  
                    alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
          else:  
             raise ValueError,"Attempt to set undefined coefficient %s"%i  
       # if numEquations and numSolutions is undefined we try identify their values based on the coefficients:  
       if self.__numEquations<1 or self.__numSolutions<1:  
             numEquations,numSolutions=identifyNumEquationsAndSolutions(self.getDomain().getDim(),alteredCoefficients)  
             if self.__numEquations<1 and numEquations>0: self.__numEquations=numEquations  
             if self.__numSolutions<1 and numSolutions>0: self.__numSolutions=numSolutions  
             if self.debug() and self.__numEquations>0: print "PDE Debug: identified number of equations is ",self.__numEquations  
             if self.debug() and self.__numSolutions>0: print "PDE Debug: identified number of solutions is ",self.__numSolutions  
561    
562        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
563        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
564           for i in self.__coefficient.iterkeys():       """
565               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()  
566    
567     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
568       """       """
569       @brief return the shape of the coefficient name       returns the number of equations
570    
571       @param name       @return: the number of equations
572         @rtype: C{int}
573         @raise UndefinedPDEError: if the number of equations is not be specified yet.
574       """       """
575       if self.hasCoefficient(name):       if self.__numEquations==None:
576          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
577       else:       else:
578          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
579    
580     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
581       """       """
582       @brief return the atoms of the coefficient name       returns the number of unknowns
583    
584       @param name       @return: the number of unknowns
585         @rtype: C{int}
586         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
587       """       """
588       if self.hasCoefficient(name):       if self.__numSolutions==None:
589          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
590       else:       else:
591          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
592    
593     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
594       """       """
595       @brief annonced that coefficient name has been changed       return status for order reduction for equation
596    
597       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
598         @rtype: L{bool}
599       """       """
600       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  
601    
602     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
603        """       """
604        @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  
605    
606        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
607        """       @rtype: L{bool}
608        return self.__coefficient.has_key(name)       """
609         return self.__reduce_solution_order
610    
611     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
612       """       """
613       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
614    
615         @return: representation space of equation
616         @rtype: L{FunctionSpace<escript.FunctionSpace>}
617       """       """
618       return self.__row_function_space       if self.reduceEquationOrder():
619             return escript.ReducedSolution(self.getDomain())
620         else:
621             return escript.Solution(self.getDomain())
622    
623     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
624       """       """
625       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
626    
627         @return: representation space of solution
628         @rtype: L{FunctionSpace<escript.FunctionSpace>}
629       """       """
630       return self.__column_function_space       if self.reduceSolutionOrder():
631             return escript.ReducedSolution(self.getDomain())
632         else:
633             return escript.Solution(self.getDomain())
634    
635     # ===== debug ==============================================================  
636     def setDebugOn(self):     def getOperator(self):
637         """
638         provides access to the operator of the PDE
639    
640         @return: the operator of the PDE
641         @rtype: L{Operator<escript.Operator>}
642         """
643         m=self.getSystem()[0]
644         if self.isUsingLumping():
645             return self.copyConstraint(1./m)
646         else:
647             return m
648    
649       def getRightHandSide(self):
650         """
651         provides access to the right hand side of the PDE
652         @return: the right hand side of the PDE
653         @rtype: L{Data<escript.Data>}
654         """
655         r=self.getSystem()[1]
656         if self.isUsingLumping():
657             return self.copyConstraint(r)
658         else:
659             return r
660    
661       def applyOperator(self,u=None):
662         """
663         applies the operator of the PDE to a given u or the solution of PDE if u is not present.
664    
665         @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
666                   the current solution is used.
667         @type u: L{Data<escript.Data>} or None
668         @return: image of u
669         @rtype: L{Data<escript.Data>}
670         """
671         if u==None:
672              return self.getOperator()*self.getSolution()
673         else:
674            self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
675    
676       def getResidual(self,u=None):
677         """
678         return the residual of u or the current solution if u is not present.
679    
680         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
681                   the current solution is used.
682         @type u: L{Data<escript.Data>} or None
683         @return: residual of u
684         @rtype: L{Data<escript.Data>}
685         """
686         return self.applyOperator(u)-self.getRightHandSide()
687    
688       def checkSymmetry(self,verbose=True):
689          """
690          test the PDE for symmetry.
691    
692          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
693          @type verbose: C{bool}
694          @return:  True if the PDE is symmetric.
695          @rtype: L{Data<escript.Data>}
696          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
697          """
698          verbose=verbose or self.__debug
699          out=True
700          if self.getNumSolutions()!=self.getNumEquations():
701             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
702             out=False
703          else:
704             A=self.getCoefficientOfGeneralPDE("A")
705             if not A.isEmpty():
706                tol=util.Lsup(A)*self.__TOL
707                if self.getNumSolutions()>1:
708                   for i in range(self.getNumEquations()):
709                      for j in range(self.getDim()):
710                         for k in range(self.getNumSolutions()):
711                            for l in range(self.getDim()):
712                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
713                                   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)
714                                   out=False
715                else:
716                   for j in range(self.getDim()):
717                      for l in range(self.getDim()):
718                         if util.Lsup(A[j,l]-A[l,j])>tol:
719                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
720                            out=False
721             B=self.getCoefficientOfGeneralPDE("B")
722             C=self.getCoefficientOfGeneralPDE("C")
723             if B.isEmpty() and not C.isEmpty():
724                if verbose: print "non-symmetric PDE because B is not present but C is"
725                out=False
726             elif not B.isEmpty() and C.isEmpty():
727                if verbose: print "non-symmetric PDE because C is not present but B is"
728                out=False
729             elif not B.isEmpty() and not C.isEmpty():
730                tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.
731                if self.getNumSolutions()>1:
732                   for i in range(self.getNumEquations()):
733                       for j in range(self.getDim()):
734                          for k in range(self.getNumSolutions()):
735                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
736                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
737                                  out=False
738                else:
739                   for j in range(self.getDim()):
740                      if util.Lsup(B[j]-C[j])>tol:
741                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
742                         out=False
743             if self.getNumSolutions()>1:
744               D=self.getCoefficientOfGeneralPDE("D")
745               if not D.isEmpty():
746                 tol=util.Lsup(D)*self.__TOL
747                 for i in range(self.getNumEquations()):
748                    for k in range(self.getNumSolutions()):
749                      if util.Lsup(D[i,k]-D[k,i])>tol:
750                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
751                          out=False
752               d=self.getCoefficientOfGeneralPDE("d")
753               if not d.isEmpty():
754                 tol=util.Lsup(d)*self.__TOL
755                 for i in range(self.getNumEquations()):
756                    for k in range(self.getNumSolutions()):
757                      if util.Lsup(d[i,k]-d[k,i])>tol:
758                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
759                          out=False
760               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
761               if not d_contact.isEmpty():
762                 tol=util.Lsup(d_contact)*self.__TOL
763                 for i in range(self.getNumEquations()):
764                    for k in range(self.getNumSolutions()):
765                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
766                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
767                          out=False
768          return out
769    
770       def getSolution(self,**options):
771         """         """
772         @brief         returns the solution of the PDE. If the solution is not valid the PDE is solved.
773    
774           @return: the solution
775           @rtype: L{Data<escript.Data>}
776           @param options: solver options
777           @keyword verbose: True to get some information during PDE solution
778           @type verbose: C{bool}
779           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
780                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
781           @keyword iter_max: maximum number of iteration steps allowed.
782           @keyword drop_tolerance: threshold for drupping in L{ILUT}
783           @keyword drop_storage: maximum of allowed memory in L{ILUT}
784           @keyword truncation: maximum number of residuals in L{GMRES}
785           @keyword restart: restart cycle length in L{GMRES}
786         """         """
787         self.__debug=not None         if not self.__solution_isValid:
788              mat,f=self.getSystem()
789              if self.isUsingLumping():
790                 self.__solution=self.copyConstraint(f*mat)
791              else:
792                 options[self.__TOLERANCE_KEY]=self.getTolerance()
793                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
794                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
795                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
796                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
797                 self.trace("PDE is resolved.")
798                 self.trace("solver options: %s"%str(options))
799                 self.__solution=mat.solve(f,options)
800              self.__solution_isValid=True
801           return self.__solution
802    
803     def setDebugOff(self):     def getFlux(self,u=None):
804         """
805         returns the flux M{J} for a given M{u}
806    
807         M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
808    
809         or
810    
811         M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
812    
813         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
814         @type u: L{Data<escript.Data>} or None
815         @return: flux
816         @rtype: L{Data<escript.Data>}
817         """
818         if u==None: u=self.getSolution()
819         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
820       # =============================================================================
821       #   solver settings:
822       # =============================================================================
823       def setSolverMethod(self,solver=None,preconditioner=None):
824         """         """
825         @brief         sets a new solver
826    
827           @param solver: sets a new solver method.
828           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}.
829           @param preconditioner: sets a new solver method.
830           @type solver: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}
831         """         """
832         self.__debug=None         if solver==None: solve=self.DEFAULT
833           if preconditioner==None: preconditioner=self.DEFAULT
834           if not (solver,preconditioner)==self.getSolverMethod():
835               self.__solver_method=solver
836               self.__preconditioner=preconditioner
837               self.__checkMatrixType()
838               self.trace("New solver is %s"%self.getSolverMethodName())
839    
840     def debug(self):     def getSolverMethodName(self):
841         """         """
842         @brief returns true if the PDE is in the debug mode         returns the name of the solver currently used
843    
844           @return: the name of the solver currently used.
845           @rtype: C{string}
846         """         """
        return self.__debug  
847    
848     #===== Lumping ===========================         m=self.getSolverMethod()
849     def setLumpingOn(self):         p=self.getSolverPackage()
850        """         method=""
851        @brief indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
852        """         elif m[0]==self.DIRECT: method= "DIRECT"
853        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
854           raise SystemError,"Lumping is not working yet! Talk to the experts"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
855           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.PCG: method= "PCG"
856           self.__rebuildOperator()         elif m[0]==self.CR: method= "CR"
857           self.__lumping=True         elif m[0]==self.CGS: method= "CGS"
858           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
859           elif m[0]==self.SSOR: method= "SSOR"
860           elif m[0]==self.GMRES: method= "GMRES"
861           elif m[0]==self.PRES20: method= "PRES20"
862           elif m[0]==self.LUMPING: method= "LUMPING"
863           if m[1]==self.DEFAULT: method+="+DEFAULT"
864           elif m[1]==self.JACOBI: method+= "+JACOBI"
865           elif m[1]==self.ILU0: method+= "+ILU0"
866           elif m[1]==self.ILUT: method+= "+ILUT"
867           elif m[1]==self.SSOR: method+= "+SSOR"
868           if p==self.DEFAULT: package="DEFAULT"
869           elif p==self.PASO: package= "PASO"
870           elif p==self.MKL: package= "MKL"
871           elif p==self.SCSL: package= "SCSL"
872           elif p==self.UMFPACK: package= "UMFPACK"
873           else : method="unknown"
874           return "%s solver of %s package"%(method,package)
875    
    def setLumpingOff(self):  
       """  
       @brief switches off matrix lumping  
       """  
       if self.isUsingLumping():  
          if self.debug() : print "PDE Debug: lumping is set off"  
          self.__rebuildOperator()  
          self.__lumping=False  
876    
877     def setLumping(self,flag=False):     def getSolverMethod(self):
878        """         """
879        @brief set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
880    
881     def isUsingLumping(self):         @return: the solver method currently be used.
882        """         @rtype: C{int}
883        @brief         """
884        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
885    
886     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
887         """         """
888         @brief sets a new solver         sets a new solver package
889    
890           @param solver: sets a new solver method.
891           @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
892         """         """
893         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
894           if not package==self.getSolverPackage():
895             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
896             self.__checkMatrixType()             self.__checkMatrixType()
897               self.trace("New solver is %s"%self.getSolverMethodName())
898    
899     def getSolverMethod(self):     def getSolverPackage(self):
900         """         """
901         @brief returns the solver method         returns the package of the solver
902    
903           @return: the solver package currently being used.
904           @rtype: C{int}
905         """         """
906         return self.__solver_method         return self.__solver_package
907    
908       def isUsingLumping(self):
909          """
910          checks if matrix lumping is used a solver method
911    
912          @return: True is lumping is currently used a solver method.
913          @rtype: C{bool}
914          """
915          return self.getSolverMethod()[0]==self.LUMPING
916    
    #============ tolerance business =========================================================  
917     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
918         """         """
919         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
920    
921           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
922    
923           defines the stopping criterion.
924    
925           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
926                       the system will be resolved.
927           @type tol: positive C{float}
928           @raise ValueException: if tolerance is not positive.
929         """         """
930         if not tol>0:         if not tol>0:
931             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
932         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
933         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
934         self.__tolerance=tol         self.__tolerance=tol
935         return         return
936    
937     def getTolerance(self):     def getTolerance(self):
938         """         """
939         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
940    
941           @return: tolerance currently used.
942           @rtype: C{float}
943         """         """
944         return self.__tolerance         return self.__tolerance
945    
946     #===== symmetry  flag ==========================     # =============================================================================
947       #    symmetry  flag:
948       # =============================================================================
949     def isSymmetric(self):     def isSymmetric(self):
950        """        """
951        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
952    
953          @return: True is a symmetric PDE is indicated, otherwise False is returned
954          @rtype: C{bool}
955        """        """
956        return self.__sym        return self.__sym
957    
958     def setSymmetryOn(self):     def setSymmetryOn(self):
959        """        """
960        @brief sets the symmetry flag to true        sets the symmetry flag.
961        """        """
962        if not self.isSymmetric():        if not self.isSymmetric():
963           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
964           self.__sym=True           self.__sym=True
965           self.__checkMatrixType()           self.__checkMatrixType()
966    
967     def setSymmetryOff(self):     def setSymmetryOff(self):
968        """        """
969        @brief sets the symmetry flag to false        removes the symmetry flag.
970        """        """
971        if self.isSymmetric():        if self.isSymmetric():
972           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
973           self.__sym=False           self.__sym=False
974           self.__checkMatrixType()           self.__checkMatrixType()
975    
976     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
977       """        """
978       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
979    
980       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
981       """        @type flag: C{bool}
982       if flag:        """
983          self.setSymmetryOn()        if flag:
984       else:           self.setSymmetryOn()
985          self.setSymmetryOff()        else:
986             self.setSymmetryOff()
987    
988     #===== order reduction ==========================     # =============================================================================
989       # function space handling for the equation as well as the solution
990       # =============================================================================
991     def setReducedOrderOn(self):     def setReducedOrderOn(self):
992       """       """
993       @brief switches to on reduced order       switches on reduced order for solution and equation representation
994    
995         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
996       """       """
997       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
998       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
999    
1000     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1001       """       """
1002       @brief switches to full order       switches off reduced order for solution and equation representation
1003    
1004         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1005       """       """
1006       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1007       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1008    
1009     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1010       """       """
1011       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1012         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1013       @param flag                    if flag is not present order reduction is switched off
1014         @type flag: C{bool}
1015         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1016       """       """
1017       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1018       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1019    
1020     #===== order reduction solution ==========================  
1021     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1022       """       """
1023       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1024    
1025         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1026       """       """
1027       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1028       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1029           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1030           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1031           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1032             self.__resetSystem()
1033    
1034     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1035       """       """
1036       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1037    
1038         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1039       """       """
1040       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1041       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1042           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1043           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1044           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1045             self.__resetSystem()
1046    
1047     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1048       """       """
1049       @brief sets order for test functions according to flag       sets order for test functions according to flag
1050    
1051       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1052                      if flag is not present order reduction is switched off
1053         @type flag: C{bool}
1054         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1055       """       """
1056       if flag:       if flag:
1057          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1058       else:       else:
1059          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1060                                                                                                                                                              
    #===== order reduction equation ==========================  
1061     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1062       """       """
1063       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1064    
1065         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1066       """       """
1067       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1068       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1069           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1070           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1071           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1072             self.__resetSystem()
1073    
1074     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1075       """       """
1076       @brief switches to full order for test functions       switches off reduced order for equation representation
1077    
1078         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1079       """       """
1080       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1081       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1082           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1083           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1084           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1085             self.__resetSystem()
1086    
1087     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1088       """       """
1089       @brief sets order for test functions according to flag       sets order for test functions according to flag
1090    
1091       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1092                      if flag is not present order reduction is switched off
1093         @type flag: C{bool}
1094         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1095       """       """
1096       if flag:       if flag:
1097          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1098       else:       else:
1099          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1100    
1101     # ==== initialization =====================================================================     # =============================================================================
1102     def __makeNewOperator(self):     # private method:
1103       # =============================================================================
1104       def __checkMatrixType(self):
1105         """
1106         reassess the matrix type and, if a new matrix is needed, resets the system.
1107         """
1108         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1109         if not new_matrix_type==self.__matrix_type:
1110             self.trace("Matrix type is now %d."%new_matrix_type)
1111             self.__matrix_type=new_matrix_type
1112             self.__resetSystem()
1113       #
1114       #   rebuild switches :
1115       #
1116       def __invalidateSolution(self):
1117           """
1118           indicates the PDE has to be resolved if the solution is requested
1119           """
1120           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1121           self.__solution_isValid=False
1122    
1123       def __invalidateOperator(self):
1124           """
1125           indicates the operator has to be rebuilt next time it is used
1126           """
1127           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1128           self.__invalidateSolution()
1129           self.__operator_is_Valid=False
1130    
1131       def __invalidateRightHandSide(self):
1132           """
1133           indicates the right hand side has to be rebuild next time it is used
1134         """         """
1135         @brief         if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1136           self.__invalidateSolution()
1137           self.__righthandside_isValid=False
1138    
1139       def __invalidateSystem(self):
1140         """         """
1141           annonced that everthing has to be rebuild:
1142           """
1143           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1144           self.__invalidateSolution()
1145           self.__invalidateOperator()
1146           self.__invalidateRightHandSide()
1147    
1148       def __resetSystem(self):
1149           """
1150           annonced that everthing has to be rebuild:
1151           """
1152           self.trace("New System is built from scratch.")
1153           self.__operator=escript.Operator()
1154           self.__operator_is_Valid=False
1155           self.__righthandside=escript.Data()
1156           self.__righthandside_isValid=False
1157           self.__solution=escript.Data()
1158           self.__solution_isValid=False
1159       #
1160       #    system initialization:
1161       #
1162       def __getNewOperator(self):
1163           """
1164           returns an instance of a new operator
1165           """
1166           self.trace("New operator is allocated.")
1167         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1168                             self.getNumEquations(), \                             self.getNumEquations(), \
1169                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 641  class LinearPDE: Line 1171  class LinearPDE:
1171                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1172                             self.__matrix_type)                             self.__matrix_type)
1173    
1174     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1175         """         """
1176         @brief         returns an instance of a new right hand side
1177         """         """
1178         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1179           if self.getNumEquations()>1:
1180               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1181           else:
1182               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1183    
1184     def __makeNewSolution(self):     def __getNewSolution(self):
1185         """         """
1186         @brief         returns an instance of a new solution
1187         """         """
1188         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1189           if self.getNumSolutions()>1:
1190               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1191           else:
1192               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1193    
1194     def __getFreshOperator(self):     def __makeFreshSolution(self):
1195         """         """
1196         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1197         """         """
1198         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1199             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1200         else:         else:
1201             self.__operator.setValue(0.)             self.__solution*=0
1202             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1203         return self.__operator         return self.__solution
1204    
1205     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1206         """         """
1207         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1208         """         """
1209         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1210             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1211         else:         else:
1212             print "fix self.__righthandside*=0"             self.__righthandside*=0
1213             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1214             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1215    
1216     # ==== rebuild switches =====================================================================     def __makeFreshOperator(self):
    def __rebuildSolution(self,deep=False):  
1217         """         """
1218         @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
1219         """         """
1220         if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."         if self.__operator.isEmpty():
1221         self.__solution_isValid=False             self.__operator=self.__getNewOperator()
1222         if deep: self.__solution=escript.Data(deep)         else:
1223               self.__operator.resetValues()
1224               self.trace("Operator reset to zero")
1225           return self.__operator
1226    
1227     def __rebuildOperator(self,deep=False):     def __applyConstraint(self):
1228         """         """
1229         @brief indicates the operator has to be rebuilt next time it is used         applies the constraints defined by q and r to the system
1230         """         """
1231         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if not self.isUsingLumping():
1232         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1233         self.__operator_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1234         if deep: self.__operator=escript.Operator()            if not q.isEmpty() and not self.__operator.isEmpty():
1235                 # q is the row and column mask to indicate where constraints are set:
1236                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1237                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1238                 u=self.__getNewSolution()
1239                 if r.isEmpty():
1240                    r_s=self.__getNewSolution()
1241                 else:
1242                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1243                 u.copyWithMask(r_s,col_q)
1244                 if not self.__righthandside.isEmpty():
1245                    self.__righthandside-=self.__operator*u
1246                    self.__righthandside=self.copyConstraint(self.__righthandside)
1247                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1248       # =============================================================================
1249       # function giving access to coefficients of the general PDE:
1250       # =============================================================================
1251       def getCoefficientOfGeneralPDE(self,name):
1252         """
1253         return the value of the coefficient name of the general PDE.
1254    
1255         @note: This method is called by the assembling routine it can be overwritten
1256               to map coefficients of a particular PDE to the general PDE.
1257         @param name: name of the coefficient requested.
1258         @type name: C{string}
1259         @return: the value of the coefficient  name
1260         @rtype: L{Data<escript.Data>}
1261         @raise IllegalCoefficient: if name is not one of coefficients
1262                      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}.
1263         """
1264         if self.hasCoefficientOfGeneralPDE(name):
1265            return self.getCoefficient(name)
1266         else:
1267            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1268    
1269     def __rebuildRightHandSide(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
1270         """       """
1271         @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.
        """  
        if self.__righthandside_isValid and self.debug() : print "PDE Debug: Right hand side has to be rebuilt."  
        self.__rebuildSolution(deep)  
        self.__righthandside_isValid=False  
        if not self.__homogeneous_constraint: self.__rebuildOperator()  
        if deep: self.__righthandside=escript.Data()  
1272    
1273     def __rebuildSystem(self,deep=False):       @param name: name of the coefficient enquired.
1274         """       @type name: C{string}
1275         @brief annonced that all coefficient name has been changed       @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1276         """       @rtype: C{bool}
1277         self.__rebuildSolution(deep)  
1278         self.__rebuildOperator(deep)       """
1279         self.__rebuildRightHandSide(deep)       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1280      
1281     def __checkMatrixType(self):     def createCoefficientOfGeneralPDE(self,name):
1282       """       """
1283       @brief reassess the matrix type and, if needed, initiates an operator rebuild       returns a new instance of a coefficient for coefficient name of the general PDE
1284    
1285         @param name: name of the coefficient requested.
1286         @type name: C{string}
1287         @return: a coefficient name initialized to 0.
1288         @rtype: L{Data<escript.Data>}
1289         @raise IllegalCoefficient: if name is not one of coefficients
1290                      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}.
1291       """       """
1292       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       if self.hasCoefficientOfGeneralPDE(name):
1293       if not new_matrix_type==self.__matrix_type:          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1294           if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type       else:
1295           self.__matrix_type=new_matrix_type          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1296           self.__rebuildOperator(deep=True)  
1297       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1298         """
1299         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1300    
1301         @param name: name of the coefficient enquired.
1302         @type name: C{string}
1303         @return: the function space to be used for coefficient name
1304         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1305         @raise IllegalCoefficient: if name is not one of coefficients
1306                      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}.
1307         """
1308         if self.hasCoefficientOfGeneralPDE(name):
1309            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1310         else:
1311            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1312    
1313       def getShapeOfCoefficientOfGeneralPDE(self,name):
1314         """
1315         return the shape of the coefficient name of the general PDE
1316    
1317     #============ assembling =======================================================       @param name: name of the coefficient enquired.
1318     def __copyConstraint(self,u):       @type name: C{string}
1319         @return: the shape of the coefficient name
1320         @rtype: C{tuple} of C{int}
1321         @raise IllegalCoefficient: if name is not one of coefficients
1322                      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}.
1323         """
1324         if self.hasCoefficientOfGeneralPDE(name):
1325            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1326         else:
1327            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1328    
1329       # =============================================================================
1330       # functions giving access to coefficients of a particular PDE implementation:
1331       # =============================================================================
1332       def getCoefficient(self,name):
1333         """
1334         returns the value of the coefficient name
1335    
1336         @param name: name of the coefficient requested.
1337         @type name: C{string}
1338         @return: the value of the coefficient name
1339         @rtype: L{Data<escript.Data>}
1340         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1341         """
1342         if self.hasCoefficient(name):
1343             return self.COEFFICIENTS[name].getValue()
1344         else:
1345            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1346    
1347       def hasCoefficient(self,name):
1348         """
1349         return True if name is the name of a coefficient
1350    
1351         @param name: name of the coefficient enquired.
1352         @type name: C{string}
1353         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1354         @rtype: C{bool}
1355         """
1356         return self.COEFFICIENTS.has_key(name)
1357    
1358       def createCoefficient(self, name):
1359         """
1360         create a L{Data<escript.Data>} object corresponding to coefficient name
1361    
1362         @return: a coefficient name initialized to 0.
1363         @rtype: L{Data<escript.Data>}
1364         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1365         """
1366         if self.hasCoefficient(name):
1367            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1368         else:
1369            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1370    
1371       def getFunctionSpaceForCoefficient(self,name):
1372         """
1373         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1374    
1375         @param name: name of the coefficient enquired.
1376         @type name: C{string}
1377         @return: the function space to be used for coefficient name
1378         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1379         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1380         """
1381         if self.hasCoefficient(name):
1382            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1383         else:
1384            raise ValueError,"unknown coefficient %s requested"%name
1385       def getShapeOfCoefficient(self,name):
1386         """
1387         return the shape of the coefficient name
1388    
1389         @param name: name of the coefficient enquired.
1390         @type name: C{string}
1391         @return: the shape of the coefficient name
1392         @rtype: C{tuple} of C{int}
1393         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1394         """
1395         if self.hasCoefficient(name):
1396            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1397         else:
1398            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1399    
1400       def resetCoefficients(self):
1401         """
1402         resets all coefficients to there default values.
1403         """
1404         for i in self.COEFFICIENTS.iterkeys():
1405             self.COEFFICIENTS[i].resetValue()
1406    
1407       def alteredCoefficient(self,name):
1408         """
1409         announce that coefficient name has been changed
1410    
1411         @param name: name of the coefficient enquired.
1412         @type name: C{string}
1413         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1414         @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.
1415         """
1416         if self.hasCoefficient(name):
1417            self.trace("Coefficient %s has been altered."%name)
1418            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1419               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1420               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1421         else:
1422            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1423    
1424       def copyConstraint(self,u):
1425        """        """
1426        @brief copies the constrint condition into u        copies the constraint into u and returns u.
1427    
1428          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1429          @type u: L{Data<escript.Data>}
1430          @return: the input u modified by the constraints.
1431          @rtype: L{Data<escript.Data>}
1432          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1433        """        """
1434        q=self.getCoefficient("q")        q=self.getCoefficientOfGeneralPDE("q")
1435        r=self.getCoefficient("r")        r=self.getCoefficientOfGeneralPDE("r")
1436        if not q.isEmpty():        if not q.isEmpty():
1437            if r.isEmpty():           if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1438               r2=escript.Data(0,u.getShape(),u.getFunctionSpace())           if r.isEmpty():
1439            else:               r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1440               r2=escript.Data(r,u.getFunctionSpace())           else:
1441            u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))               r=escript.Data(r,u.getFunctionSpace())
1442             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1443     def __applyConstraint(self,rhs_update=True):        return u
        """  
        @brief applies the constraints  defined by q and r to the system  
        """  
        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.)  
   
    def getOperator(self):  
        """  
        @brief returns the operator of the PDE  
        """  
        if not self.__operator_isValid:  
            # some Constraints are applying for a lumpled stifness matrix:  
            if self.isUsingLumping():  
               if self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():  
                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"  
               if not self.getCoefficient("A").isEmpty():  
                        raise Warning,"Lumped matrix does not allow coefficient A"  
               if not self.getCoefficient("B").isEmpty():  
                        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()  
   
            self.getDomain().addPDEToSystem(mat,escript.Data(), \  
                         self.getCoefficient("A"), \  
                         self.getCoefficient("B"), \  
                         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  
1444    
1445     def getRightHandSide(self,ignoreConstraint=False):     def setValue(self,**coefficients):
1446         """        """
1447         @brief returns the right hand side of the PDE        sets new values to coefficients
1448    
1449         @param ignoreConstraint        @param coefficients: new values assigned to coefficients
1450         """        @keyword A: value for coefficient A.
1451         if not self.__righthandside_isValid:        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1452             if self.debug() : print "PDE Debug: New right hand side is built."        @keyword B: value for coefficient B
1453             self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1454                           self.getCoefficient("X"), \        @keyword C: value for coefficient C
1455                           self.getCoefficient("Y"),\        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1456                           self.getCoefficient("y"),\        @keyword D: value for coefficient D
1457                           self.getCoefficient("y_contact"))        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1458             self.__righthandside_isValid=True        @keyword X: value for coefficient X
1459             if ignoreConstraint: self.__copyConstraint(self.__righthandside)        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1460         return self.__righthandside        @keyword Y: value for coefficient Y
1461          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1462          @keyword d: value for coefficient d
1463          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1464          @keyword y: value for coefficient y
1465          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1466          @keyword d_contact: value for coefficient d_contact
1467          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1468                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1469          @keyword y_contact: value for coefficient y_contact
1470          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1471                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1472          @keyword r: values prescribed to the solution at the locations of constraints
1473          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1474                   depending of reduced order is used for the solution.
1475          @keyword q: mask for location of constraints
1476          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1477                   depending of reduced order is used for the representation of the equation.
1478          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1479          """
1480          # check if the coefficients are  legal:
1481          for i in coefficients.iterkeys():
1482             if not self.hasCoefficient(i):
1483                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1484          # if the number of unknowns or equations is still unknown we try to estimate them:
1485          if self.__numEquations==None or self.__numSolutions==None:
1486             for i,d in coefficients.iteritems():
1487                if hasattr(d,"shape"):
1488                    s=d.shape
1489                elif hasattr(d,"getShape"):
1490                    s=d.getShape()
1491                else:
1492                    s=numarray.array(d).shape
1493                if s!=None:
1494                    # get number of equations and number of unknowns:
1495                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1496                    if res==None:
1497                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1498                    else:
1499                        if self.__numEquations==None: self.__numEquations=res[0]
1500                        if self.__numSolutions==None: self.__numSolutions=res[1]
1501          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1502          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1503          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1504          for i,d in coefficients.iteritems():
1505            try:
1506               self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1507            except IllegalCoefficientValue,m:
1508               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1509            self.alteredCoefficient(i)
1510    
1511          self.__altered_coefficients=True
1512          # check if the systrem is inhomogeneous:
1513          if len(coefficients)>0 and not self.isUsingLumping():
1514             q=self.getCoefficientOfGeneralPDE("q")
1515             r=self.getCoefficientOfGeneralPDE("r")
1516             homogeneous_constraint=True
1517             if not q.isEmpty() and not r.isEmpty():
1518                 if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1519                   self.trace("Inhomogeneous constraint detected.")
1520                   self.__invalidateSystem()
1521    
1522     def getSystem(self):     def getSystem(self):
1523         """         """
1524         @brief         return the operator and right hand side of the PDE
1525    
1526           @return: the discrete version of the PDE
1527           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1528         """         """
1529         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."  
1530            if self.isUsingLumping():            if self.isUsingLumping():
1531                self.getRightHandSide(ignoreConstraint=True)                if not self.__operator_is_Valid:
1532                self.getOperator()                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1533                     if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Using coefficient A in lumped matrix can produce wrong results"
1534                     if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"
1535                     if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Using coefficient C in lumped matrix can produce wrong results"
1536                     mat=self.__getNewOperator()
1537                     self.getDomain().addPDEToSystem(mat,escript.Data(), \
1538                               self.getCoefficientOfGeneralPDE("A"), \
1539                               self.getCoefficientOfGeneralPDE("B"), \
1540                               self.getCoefficientOfGeneralPDE("C"), \
1541                               self.getCoefficientOfGeneralPDE("D"), \
1542                               escript.Data(), \
1543                               escript.Data(), \
1544                               self.getCoefficientOfGeneralPDE("d"), \
1545                               escript.Data(),\
1546                               self.getCoefficientOfGeneralPDE("d_contact"), \
1547                               escript.Data())
1548                     self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))
1549                     del mat
1550                     self.trace("New lumped operator has been built.")
1551                     self.__operator_is_Valid=True
1552                  if not self.__righthandside_isValid:
1553                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1554                                   self.getCoefficientOfGeneralPDE("X"), \
1555                                   self.getCoefficientOfGeneralPDE("Y"),\
1556                                   self.getCoefficientOfGeneralPDE("y"),\
1557                                   self.getCoefficientOfGeneralPDE("y_contact"))
1558                     self.trace("New right hand side as been built.")
1559                     self.__righthandside_isValid=True
1560            else:            else:
1561                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1562                              self.getCoefficient("A"), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1563                              self.getCoefficient("B"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1564                              self.getCoefficient("C"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1565                              self.getCoefficient("D"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1566                              self.getCoefficient("X"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1567                              self.getCoefficient("Y"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1568                              self.getCoefficient("d"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1569                              self.getCoefficient("y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1570                              self.getCoefficient("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1571                              self.getCoefficient("y_contact"))                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1572            self.__operator_isValid=True                                 self.getCoefficientOfGeneralPDE("y_contact"))
1573            self.__righthandside_isValid=True                   self.__applyConstraint()
1574            self.__applyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1575            self.__copyConstraint(self.__righthandside)                   self.trace("New system has been built.")
1576         elif not self.__operator_isValid:                   self.__operator_is_Valid=True
1577            self.getOperator()                   self.__righthandside_isValid=True
1578         elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1579            self.getRightHandSide()                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1580                                   self.getCoefficientOfGeneralPDE("X"), \
1581                                   self.getCoefficientOfGeneralPDE("Y"),\
1582                                   self.getCoefficientOfGeneralPDE("y"),\
1583                                   self.getCoefficientOfGeneralPDE("y_contact"))
1584                     self.__righthandside=self.copyConstraint(self.__righthandside)
1585                     self.trace("New right hand side has been built.")
1586                     self.__righthandside_isValid=True
1587                 elif not self.__operator_is_Valid:
1588                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1589                                self.getCoefficientOfGeneralPDE("A"), \
1590                                self.getCoefficientOfGeneralPDE("B"), \
1591                                self.getCoefficientOfGeneralPDE("C"), \
1592                                self.getCoefficientOfGeneralPDE("D"), \
1593                                escript.Data(), \
1594                                escript.Data(), \
1595                                self.getCoefficientOfGeneralPDE("d"), \
1596                                escript.Data(),\
1597                                self.getCoefficientOfGeneralPDE("d_contact"), \
1598                                escript.Data())
1599                     self.__applyConstraint()
1600                     self.trace("New operator has been built.")
1601                     self.__operator_is_Valid=True
1602         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1603    
    def solve(self,**options):  
       """  
       @brief solve the PDE  
1604    
1605        @param options  class Poisson(LinearPDE):
1606        """     """
1607        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  
1608    
1609     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief returns the solution of the PDE  
1610    
1611         @param options     with natural boundary conditons
1612         """  
1613         if not self.__solution_isValid:     M{n[j]*grad(u)[j] = 0 }
1614             if self.debug() : print "PDE Debug: PDE is resolved."  
1615             self.__solution=self.solve(**options)     and constraints:
1616             self.__solution_isValid=True  
1617         return self.__solution     M{u=0} where M{q>0}
1618     #============ some serivice functions  =====================================================  
1619     def getDomain(self):     """
1620       """  
1621       @brief returns the domain of the PDE     def __init__(self,domain,debug=False):
1622       """       """
1623       return self.__domain       initializes a new Poisson equation
1624    
1625         @param domain: domain of the PDE
1626         @type domain: L{Domain<escript.Domain>}
1627         @param debug: if True debug informations are printed.
1628    
    def getNumEquations(self):  
1629       """       """
1630       @brief returns the number of equations       super(Poisson, self).__init__(domain,1,1,debug)
1631         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1632                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1633         self.setSymmetryOn()
1634    
1635       def setValue(self,**coefficients):
1636       """       """
1637       if self.__numEquations>0:       sets new values to coefficients
1638           return self.__numEquations  
1639         @param coefficients: new values assigned to coefficients
1640         @keyword f: value for right hand side M{f}
1641         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1642         @keyword q: mask for location of constraints
1643         @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>}
1644                   depending of reduced order is used for the representation of the equation.
1645         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1646         """
1647         super(Poisson, self).setValue(**coefficients)
1648    
1649       def getCoefficientOfGeneralPDE(self,name):
1650         """
1651         return the value of the coefficient name of the general PDE
1652         @param name: name of the coefficient requested.
1653         @type name: C{string}
1654         @return: the value of the coefficient  name
1655         @rtype: L{Data<escript.Data>}
1656         @raise IllegalCoefficient: if name is not one of coefficients
1657                      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}.
1658         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1659         """
1660         if name == "A" :
1661             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1662         elif name == "B" :
1663             return escript.Data()
1664         elif name == "C" :
1665             return escript.Data()
1666         elif name == "D" :
1667             return escript.Data()
1668         elif name == "X" :
1669             return escript.Data()
1670         elif name == "Y" :
1671             return self.getCoefficient("f")
1672         elif name == "d" :
1673             return escript.Data()
1674         elif name == "y" :
1675             return escript.Data()
1676         elif name == "d_contact" :
1677             return escript.Data()
1678         elif name == "y_contact" :
1679             return escript.Data()
1680         elif name == "r" :
1681             return escript.Data()
1682         elif name == "q" :
1683             return self.getCoefficient("q")
1684       else:       else:
1685           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1686    
1687     def getNumSolutions(self):  class Helmholtz(LinearPDE):
1688       """
1689       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1690    
1691       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1692    
1693       with natural boundary conditons
1694    
1695       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1696    
1697       and constraints:
1698    
1699       M{u=r} where M{q>0}
1700    
1701       """
1702    
1703       def __init__(self,domain,debug=False):
1704       """       """
1705       @brief returns the number of unknowns       initializes a new Poisson equation
1706    
1707         @param domain: domain of the PDE
1708         @type domain: L{Domain<escript.Domain>}
1709         @param debug: if True debug informations are printed.
1710    
1711         """
1712         super(Helmholtz, self).__init__(domain,1,1,debug)
1713         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1714                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1715                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1716                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1717                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1718                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1719                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1720         self.setSymmetryOn()
1721    
1722       def setValue(self,**coefficients):
1723       """       """
1724       if self.__numSolutions>0:       sets new values to coefficients
1725          return self.__numSolutions  
1726         @param coefficients: new values assigned to coefficients
1727         @keyword omega: value for coefficient M{S{omega}}
1728         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1729         @keyword k: value for coefficeint M{k}
1730         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1731         @keyword f: value for right hand side M{f}
1732         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1733         @keyword alpha: value for right hand side M{S{alpha}}
1734         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1735         @keyword g: value for right hand side M{g}
1736         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1737         @keyword r: prescribed values M{r} for the solution in constraints.
1738         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1739                   depending of reduced order is used for the representation of the equation.
1740         @keyword q: mask for location of constraints
1741         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1742                   depending of reduced order is used for the representation of the equation.
1743         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1744         """
1745         super(Helmholtz, self).setValue(**coefficients)
1746    
1747       def getCoefficientOfGeneralPDE(self,name):
1748         """
1749         return the value of the coefficient name of the general PDE
1750    
1751         @param name: name of the coefficient requested.
1752         @type name: C{string}
1753         @return: the value of the coefficient  name
1754         @rtype: L{Data<escript.Data>}
1755         @raise IllegalCoefficient: if name is not one of coefficients
1756                      "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}.
1757         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1758         """
1759         if name == "A" :
1760             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1761         elif name == "B" :
1762             return escript.Data()
1763         elif name == "C" :
1764             return escript.Data()
1765         elif name == "D" :
1766             return self.getCoefficient("omega")
1767         elif name == "X" :
1768             return escript.Data()
1769         elif name == "Y" :
1770             return self.getCoefficient("f")
1771         elif name == "d" :
1772             return self.getCoefficient("alpha")
1773         elif name == "y" :
1774             return self.getCoefficient("g")
1775         elif name == "d_contact" :
1776             return escript.Data()
1777         elif name == "y_contact" :
1778             return escript.Data()
1779         elif name == "r" :
1780             return self.getCoefficient("r")
1781         elif name == "q" :
1782             return self.getCoefficient("q")
1783         else:
1784            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1785    
1786    class LameEquation(LinearPDE):
1787       """
1788       Class to define a Lame equation problem:
1789    
1790       M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[j])[i])[j] = F_i -grad(S{sigma}[i,j])[j] }
1791    
1792       with natural boundary conditons:
1793    
1794       M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) - S{lambda}*grad(u[j])[i]) = f_i -n[j]*S{sigma}[i,j] }
1795    
1796       and constraints:
1797    
1798       M{u[i]=r[i]} where M{q[i]>0}
1799    
1800       """
1801    
1802       def __init__(self,domain,debug=False):
1803          super(LameEquation, self).__init__(domain,\
1804                                             domain.getDim(),domain.getDim(),debug)
1805          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1806                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1807                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1808                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1809                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1810                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1811                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1812          self.setSymmetryOn()
1813    
1814       def setValue(self,**coefficients):
1815         """
1816         sets new values to coefficients
1817    
1818         @param coefficients: new values assigned to coefficients
1819         @keyword lame_mu: value for coefficient M{S{mu}}
1820         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1821         @keyword lame_lambda: value for coefficient M{S{lambda}}
1822         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1823         @keyword F: value for internal force M{F}
1824         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1825         @keyword sigma: value for initial stress M{S{sigma}}
1826         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1827         @keyword f: value for extrenal force M{f}
1828         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1829         @keyword r: prescribed values M{r} for the solution in constraints.
1830         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1831                   depending of reduced order is used for the representation of the equation.
1832         @keyword q: mask for location of constraints
1833         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1834                   depending of reduced order is used for the representation of the equation.
1835         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1836         """
1837         super(LameEquation, self).setValue(**coefficients)
1838    
1839       def getCoefficientOfGeneralPDE(self,name):
1840         """
1841         return the value of the coefficient name of the general PDE
1842    
1843         @param name: name of the coefficient requested.
1844         @type name: C{string}
1845         @return: the value of the coefficient  name
1846         @rtype: L{Data<escript.Data>}
1847         @raise IllegalCoefficient: if name is not one of coefficients
1848                      "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}.
1849         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1850         """
1851         if name == "A" :
1852             out =self.createCoefficientOfGeneralPDE("A")
1853             for i in range(self.getDim()):
1854               for j in range(self.getDim()):
1855                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1856                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1857                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1858             return out
1859         elif name == "B" :
1860             return escript.Data()
1861         elif name == "C" :
1862             return escript.Data()
1863         elif name == "D" :
1864             return escript.Data()
1865         elif name == "X" :
1866             return self.getCoefficient("sigma")
1867         elif name == "Y" :
1868             return self.getCoefficient("F")
1869         elif name == "d" :
1870             return escript.Data()
1871         elif name == "y" :
1872             return self.getCoefficient("f")
1873         elif name == "d_contact" :
1874             return escript.Data()
1875         elif name == "y_contact" :
1876             return escript.Data()
1877         elif name == "r" :
1878             return self.getCoefficient("r")
1879         elif name == "q" :
1880             return self.getCoefficient("q")
1881       else:       else:
1882          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1883    
1884    class AdvectivePDE(LinearPDE):
1885       """
1886       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1887       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1888    
1889       In the following we set
1890    
1891       M{Z[j]=C[j]-B[j]}
1892    
1893       or
1894    
1895       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1896    
1897       To measure the dominance of the advective terms over the diffusive term M{A} the
1898       X{Pelclet number} M{P} is used. It is defined as
1899    
1900       M{P=h|Z|/(2|A|)}
1901    
1902       where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1903       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1904    
1905     def checkSymmetry(self):     From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1906    
1907       M{S{Xi}=S{xi}(P) h/|Z|}
1908    
1909       where M{S{xi}} is a suitable function of the Peclet number.
1910    
1911       In the case of a single PDE the coefficient are up-dated in the following way:
1912             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1913             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1914             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1915             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1916    
1917       Similar for the case of a systems of PDEs:
1918             - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}
1919             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1920             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1921             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1922    
1923       where M{S{delta}} is L{kronecker}.
1924       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1925       but with the intension to stabilize the solution.
1926    
1927       """
1928       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1929        """        """
1930        @brief returns if the Operator is symmetric. This is a very expensive operation!!! The symmetry flag is not altered.        creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1931    
1932          @param domain: domain of the PDE
1933          @type domain: L{Domain<escript.Domain>}
1934          @param numEquations: number of equations. If numEquations==None the number of equations
1935                               is exracted from the PDE coefficients.
1936          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1937                               is exracted from the PDE coefficients.
1938          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1939                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1940          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1941          @param debug: if True debug informations are printed.
1942          """
1943          super(AdvectivePDE, self).__init__(domain,\
1944                                             numEquations,numSolutions,debug)
1945          if xi==None:
1946             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1947          else:
1948             self.__xi=xi
1949          self.__Xi=escript.Data()
1950    
1951       def setValue(**coefficients):
1952        """        """
1953        raise SystemError,"checkSymmetry is not implemented yet"        sets new values to coefficients
1954    
1955        return None        @param coefficients: new values assigned to coefficients
1956          @keyword A: value for coefficient A.
1957          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1958          @keyword B: value for coefficient B
1959          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1960          @keyword C: value for coefficient C
1961          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1962          @keyword D: value for coefficient D
1963          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1964          @keyword X: value for coefficient X
1965          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1966          @keyword Y: value for coefficient Y
1967          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1968          @keyword d: value for coefficient d
1969          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1970          @keyword y: value for coefficient y
1971          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1972          @keyword d_contact: value for coefficient d_contact
1973          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1974                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1975          @keyword y_contact: value for coefficient y_contact
1976          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1977                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1978          @keyword r: values prescribed to the solution at the locations of constraints
1979          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1980                   depending of reduced order is used for the solution.
1981          @keyword q: mask for location of constraints
1982          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1983                   depending of reduced order is used for the representation of the equation.
1984          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1985    
1986          """
1987          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
1988          super(AdvectivePDE, self).setValue(**coefficients)
1989    
1990       def ELMAN_RAMAGE(self,P):
1991         """
1992         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
1993         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
1994              - M{S{xi}(P)=0} for M{P<1}
1995              - M{S{xi}(P)=(1-1/P)/2} otherwise
1996    
1997         @param P: Preclet number
1998         @type P: L{Scalar<escript.Scalar>}
1999         @return: up-wind weightimg factor
2000         @rtype: L{Scalar<escript.Scalar>}
2001         """
2002         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2003    
2004       def SIMPLIFIED_BROOK_HUGHES(self,P):
2005         """
2006         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2007         The original methods is
2008    
2009         M{S{xi}(P)=coth(P)-1/P}
2010    
2011         As the evaluation of M{coth} is expensive we are using the approximation:
2012    
2013             - M{S{xi}(P)=P/3} where M{P<3}
2014             - M{S{xi}(P)=1/2} otherwise
2015    
2016         @param P: Preclet number
2017         @type P: L{Scalar<escript.Scalar>}
2018         @return: up-wind weightimg factor
2019         @rtype: L{Scalar<escript.Scalar>}
2020         """
2021         c=util.whereNegative(P-3.)
2022         return P/6.*c+1./2.*(1.-c)
2023    
2024       def HALF(self,P):
2025         """
2026         Predefined function to set value M{1/2} for M{S{xi}}
2027    
2028         @param P: Preclet number
2029         @type P: L{Scalar<escript.Scalar>}
2030         @return: up-wind weightimg factor
2031         @rtype: L{Scalar<escript.Scalar>}
2032         """
2033         return escript.Scalar(0.5,P.getFunctionSpace())
2034    
2035       def __calculateXi(self,peclet_factor,flux,h):
2036           flux=util.Lsup(flux)
2037           if flux_max>0.:
2038              return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2039           else:
2040              return 0.
2041    
2042     def getFlux(self,u):     def __getXi(self):
2043         """        if self.__Xi.isEmpty():
2044         @brief returns the flux J_ij for a given u           B=self.getCoefficient("B")
2045             C=self.getCoefficient("C")
2046             A=self.getCoefficient("A")
2047             h=self.getDomain().getSize()
2048             self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2049             if not C.isEmpty() or not B.isEmpty():
2050                if not C.isEmpty() and not B.isEmpty():
2051                    flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2052                    if self.getNumEquations()>1:
2053                       if self.getNumSolutions()>1:
2054                          for i in range(self.getNumEquations()):
2055                             for k in range(self.getNumSolutions()):
2056                                for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2057                          # flux=C-util.reorderComponents(B,[0,2,1])
2058                       else:
2059                          for i in range(self.getNumEquations()):
2060                             for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2061                          # flux=C-B
2062                    else:
2063                       if self.getNumSolutions()>1:
2064                          for k in range(self.getNumSolutions()):
2065                             for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2066                          # flux=C-util.reorderComponents(B,[1,0])
2067                       else:
2068                          for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2069                          #flux=C-B
2070                    length_of_flux=util.sqrt(flux2)
2071                elif C.isEmpty():
2072                  length_of_flux=util.length(B)
2073                  #flux=B
2074                else:
2075                  length_of_flux=util.length(C)
2076                  #flux=C
2077    
2078              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}              #length_of_flux=util.length(flux)
2079                flux_max=util.Lsup(length_of_flux)
2080                if flux_max>0.:
2081                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2082                   length_of_A=util.length(A)
2083                   A_max=util.Lsup(length_of_A)
2084                   if A_max>0:
2085                        inv_A=1./(length_of_A+A_max*self.__TOL)
2086                   else:
2087                        inv_A=1./self.__TOL
2088                   peclet_number=length_of_flux*h/2*inv_A
2089                   xi=self.__xi(peclet_number)
2090                   self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2091                   self.trace("preclet number = %e"%util.Lsup(peclet_number))
2092          return self.__Xi
2093    
2094    
2095       def getCoefficientOfGeneralPDE(self,name):
2096         """
2097         return the value of the coefficient name of the general PDE
2098    
2099         @param name: name of the coefficient requested.
2100         @type name: C{string}
2101         @return: the value of the coefficient name
2102         @rtype: L{Data<escript.Data>}
2103         @raise IllegalCoefficient: if name is not one of coefficients
2104                      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}.
2105         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2106         """
2107         if not self.getNumEquations() == self.getNumSolutions():
2108              raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
2109    
2110         if name == "A" :
2111             A=self.getCoefficient("A")
2112             B=self.getCoefficient("B")
2113             C=self.getCoefficient("C")
2114             if B.isEmpty() and C.isEmpty():
2115                Aout=A
2116             else:
2117                if A.isEmpty():
2118                   Aout=self.createNewCoefficient("A")
2119                else:
2120                   Aout=A[:]
2121                Xi=self.__getXi()
2122                if self.getNumEquations()>1:
2123                    for i in range(self.getNumEquations()):
2124                       for j in range(self.getDim()):
2125                          for k in range(self.getNumSolutions()):
2126                             for l in range(self.getDim()):
2127                                if not C.isEmpty() and not B.isEmpty():
2128                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2129                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2130                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k])
2131                                elif C.isEmpty():
2132                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2133                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2134                                else:
2135                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2136                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2137                else:
2138                    for j in range(self.getDim()):
2139                       for l in range(self.getDim()):
2140                          if not C.isEmpty() and not B.isEmpty():
2141                              Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])
2142                          elif C.isEmpty():
2143                              Aout[j,l]+=Xi*B[j]*B[l]
2144                          else:
2145                              Aout[j,l]+=Xi*C[j]*C[l]
2146                     # if not C.isEmpty() and not B.isEmpty():
2147                     #    tmp=C-B
2148                     #    Aout=Aout+Xi*util.outer(tmp,tmp)
2149                     # elif C.isEmpty():
2150                     #    Aout=Aout+Xi*util.outer(B,B)
2151                     # else:
2152                     # Aout=Aout+Xi*util.outer(C,C)
2153             return Aout
2154         elif name == "B" :
2155             B=self.getCoefficient("B")
2156             C=self.getCoefficient("C")
2157             D=self.getCoefficient("D")
2158             if C.isEmpty() or D.isEmpty():
2159                Bout=B
2160             else:
2161                Xi=self.__getXi()
2162                if B.isEmpty():
2163                    Bout=self.createNewCoefficient("B")
2164                else:
2165                    Bout=B[:]
2166                if self.getNumEquations()>1:
2167                   for k in range(self.getNumSolutions()):
2168                      for p in range(self.getNumEquations()):
2169                         tmp=Xi*D[p,k]
2170                         for i in range(self.getNumEquations()):
2171                            for j in range(self.getDim()):
2172                               Bout[i,j,k]+=tmp*C[p,i,j]
2173                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2174                else:
2175                   tmp=Xi*D
2176                   for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2177                   # Bout=Bout+Xi*D*C
2178             return Bout
2179         elif name == "C" :
2180             B=self.getCoefficient("B")
2181             C=self.getCoefficient("C")
2182             D=self.getCoefficient("D")
2183             if B.isEmpty() or D.isEmpty():
2184                Cout=C
2185             else:
2186                Xi=self.__getXi()
2187                if C.isEmpty():
2188                    Cout=self.createNewCoefficient("C")
2189                else:
2190                    Cout=C[:]
2191                if self.getNumEquations()>1:
2192                   for k in range(self.getNumSolutions()):
2193                       for p in range(self.getNumEquations()):
2194                          tmp=Xi*D[p,k]
2195                          for i in range(self.getNumEquations()):
2196                            for l in range(self.getDim()):
2197                                     Cout[i,k,l]+=tmp*B[p,l,i]
2198                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2199                else:
2200                   tmp=Xi*D
2201                   for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2202                   # Cout=Cout+tmp*D*B
2203             return Cout
2204         elif name == "D" :
2205             return self.getCoefficient("D")
2206         elif name == "X" :
2207             X=self.getCoefficient("X")
2208             Y=self.getCoefficient("Y")
2209             B=self.getCoefficient("B")
2210             C=self.getCoefficient("C")
2211             if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):
2212                Xout=X
2213             else:
2214                if X.isEmpty():
2215                    Xout=self.createNewCoefficient("X")
2216                else:
2217                    Xout=X[:]
2218                Xi=self.__getXi()
2219                if self.getNumEquations()>1:
2220                     for p in range(self.getNumEquations()):
2221                        tmp=Xi*Y[p]
2222                        for i in range(self.getNumEquations()):
2223                           for j in range(self.getDim()):
2224                              if not C.isEmpty() and not B.isEmpty():
2225                                 Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2226                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2227                              elif C.isEmpty():
2228                                 Xout[i,j]-=tmp*B[p,j,i]
2229                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2230                              else:
2231                                 Xout[i,j]+=tmp*C[p,i,j]
2232                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2233                else:
2234                     tmp=Xi*Y
2235                     for j in range(self.getDim()):
2236                        if not C.isEmpty() and not B.isEmpty():
2237                           Xout[j]+=tmp*(C[j]-B[j])
2238                           # Xout=Xout+Xi*Y*(C-B)
2239                        elif C.isEmpty():
2240                           Xout[j]-=tmp*B[j]
2241                           # Xout=Xout-Xi*Y*B
2242                        else:
2243                           Xout[j]+=tmp*C[j]
2244                           # Xout=Xout+Xi*Y*C
2245             return Xout
2246         elif name == "Y" :
2247             return self.getCoefficient("Y")
2248         elif name == "d" :
2249             return self.getCoefficient("d")
2250         elif name == "y" :
2251             return self.getCoefficient("y")
2252         elif name == "d_contact" :
2253             return self.getCoefficient("d_contact")
2254         elif name == "y_contact" :
2255             return self.getCoefficient("y_contact")
2256         elif name == "r" :
2257             return self.getCoefficient("r")
2258         elif name == "q" :
2259             return self.getCoefficient("q")
2260         else:
2261            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2262    
2263         @param u argument of the operator  class AdvectionDiffusion(LinearPDE):
2264       """
2265       Class to define PDE equation of the unisotropic advection-diffusion problem, which is genear L{LinearPDE} of the form
2266    
2267         """     M{S{omega}*u + inner(v,grad(u))- grad(matrixmult(k_bar,grad(u))[j])[j] = f}
        raise SystemError,"getFlux is not implemented yet"  
        return None  
2268    
2269     def applyOperator(self,u):     with natural boundary conditons
        """  
        @brief applies the operator of the PDE to a given solution u in weak from  
2270    
2271         @param u argument of the operator     M{n[j]*matrixmult(k,grad(u))[j] = g- S{alpha}u }
2272    
2273         """     and constraints:
        return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())  
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        @brief return the residual of u in the weak from  
2274    
2275         @param u     M{u=r} where M{q>0}
2276         """  
2277         return self.applyOperator(u)-self.getRightHandSide()     and
2278    
2279       M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}
2280    
 class Poisson(LinearPDE):  
2281     """     """
2282     @brief Class to define a Poisson equstion problem:  
2283                                                                                                                                                                   def __init__(self,domain,debug=False):
2284     class to define a linear PDE of the form       """
2285                                                                                                                                                                     initializes a new Poisson equation
2286          -u_{,jj} = f  
2287                                                                                                                                                                     @param domain: domain of the PDE
2288       with boundary conditons:       @type domain: L{Domain<escript.Domain>}
2289                                                                                                                                                                     @param debug: if True debug informations are printed.
2290          n_j*u_{,j} = 0  
2291                                                                                                                                                                     """
2292      and constraints:       super(AdvectionDiffusion, self).__init__(domain,1,1,debug)
2293                                                                                                                                                                     self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2294           u=0 where q>0                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
2295                                                                                                                                                                                        "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2296     """                          "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2297                            "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2298     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2299         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2300         self._setCoefficient(A=numarray.identity(self.getDomain().getDim()))                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2301         self.setSymmetryOn()                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2302         self.setValue(f,q)  
2303       def setValue(self,**coefficients):
2304     def setValue(self,f=escript.Data(),q=escript.Data()):       """
2305         self._setCoefficient(Y=f,q=q)       sets new values to coefficients
2306    
2307                                                                                                                                                                   @param coefficients: new values assigned to coefficients
2308         @keyword omega: value for coefficient M{S{omega}}
2309         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2310         @keyword k: value for coefficient M{k}
2311         @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.
2312         @keyword v: value for coefficient M{v}
2313         @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2314         @keyword upwind: value for upwind term M{upwind}
2315         @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2316         @keyword f: value for right hand side M{f}
2317         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2318         @keyword alpha: value for right hand side M{S{alpha}}
2319         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2320         @keyword g: value for right hand side M{g}
2321         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2322         @keyword r: prescribed values M{r} for the solution in constraints.
2323         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2324                   depending of reduced order is used for the representation of the equation.
2325         @keyword q: mask for location of constraints
2326         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2327                   depending of reduced order is used for the representation of the equation.
2328         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2329         """
2330         super(AdvectionDiffusion, self).setValue(**coefficients)
2331    
2332       def getCoefficientOfGeneralPDE(self,name):
2333         """
2334         return the value of the coefficient name of the general PDE
2335    
2336         @param name: name of the coefficient requested.
2337         @type name: C{string}
2338         @return: the value of the coefficient  name
2339         @rtype: L{Data<escript.Data>}
2340         @raise IllegalCoefficient: if name is not one of coefficients
2341                      "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}.
2342         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2343         """
2344         if name == "A" :
2345             return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))
2346         elif name == "B" :
2347             return escript.Data()
2348         elif name == "C" :
2349             return self.getCoefficient("v")
2350         elif name == "D" :
2351             return self.getCoefficient("omega")
2352         elif name == "X" :
2353             return escript.Data()
2354         elif name == "Y" :
2355             return self.getCoefficient("f")
2356         elif name == "d" :
2357             return self.getCoefficient("alpha")
2358         elif name == "y" :
2359             return self.getCoefficient("g")
2360         elif name == "d_contact" :
2361             return escript.Data()
2362         elif name == "y_contact" :
2363             return escript.Data()
2364         elif name == "r" :
2365             return self.getCoefficient("r")
2366         elif name == "q" :
2367             return self.getCoefficient("q")
2368         else:
2369            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2370    
2371    
2372  # $Log$  # $Log$
2373  # Revision 1.2  2004/12/15 07:08:27  jgs  # Revision 1.14  2005/09/22 01:54:57  jgs
2374  # *** empty log message ***  # Merge of development branch dev-02 back to main trunk on 2005-09-22
2375    #
2376    # Revision 1.13  2005/09/15 03:44:19  jgs
2377    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2378    #
2379    # Revision 1.12  2005/09/01 03:31:28  jgs
2380    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2381    #
2382    # Revision 1.11  2005/08/23 01:24:28  jgs
2383    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2384    #
2385    # Revision 1.10  2005/08/12 01:45:36  jgs
2386    # erge of development branch dev-02 back to main trunk on 2005-08-12
2387    #
2388    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2389    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2390    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2391    # modified to instead use portable/cooperative "super" calls to extend base
2392    # class methods.
2393    #
2394    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2395    # Removed redundant if-loop.
2396    #
2397    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2398    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2399    #
2400    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2401    # the solver from finley are put into the standalone package paso now
2402    #
2403    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2404    # in the case of lumping no new system is allocated if the constraint is changed.
2405    #
2406    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2407    # test for Lumping added
2408    #
2409    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2410    # bug in format fixed.
2411    #
2412    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2413    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2414    #
2415    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2416    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2417    #
2418    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2419    # gneric unit testing for linearPDE
2420    #
2421    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2422    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2423    #
2424    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2425    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2426    #
2427    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2428    # epydoc mark up partially fixed
2429    #
2430    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2431    # some problems with LinearPDEs fixed.
2432    #
2433    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2434    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2435    #
2436    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2437    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2438    #
2439    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2440    # new functions in util and a new pde type in linearPDEs
2441    #
2442    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2443    # Lame equation: (linear elastic, isotropic) added
2444    #
2445    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2446    # some extensions to modellib and linearPDEs
2447    #
2448    # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2449    # Fixed up some docstrings.  Moved module-level functions to top of file so
2450    # that epydoc and doxygen can pick them up properly.
2451    #
2452    # Revision 1.1.2.22  2005/05/12 11:41:30  gross
2453    # some basic Models have been added
2454    #
2455    # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane
2456    # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of
2457    # file so that the AdvectivePDE class is picked up by doxygen.  Some
2458    # reformatting of docstrings.  Addition of code to make equations come out
2459    # as proper LaTeX.
2460    #
2461    # Revision 1.1.2.20  2005/04/15 07:09:08  gross
2462    # some problems with functionspace and linearPDEs fixed.
2463    #
2464    # Revision 1.1.2.19  2005/03/04 05:27:07  gross
2465    # bug in SystemPattern fixed.
2466    #
2467    # Revision 1.1.2.18  2005/02/08 06:16:45  gross
2468    # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed
2469    #
2470    # Revision 1.1.2.17  2005/02/08 05:56:19  gross
2471    # Reference Number handling added
2472    #
2473    # Revision 1.1.2.16  2005/02/07 04:41:28  gross
2474    # some function exposed to python to make mesh merging running
2475    #
2476    # Revision 1.1.2.15  2005/02/03 00:14:44  gross
2477    # timeseries add and ESySParameter.py renames esysXML.py for consistence
2478    #
2479    # Revision 1.1.2.14  2005/02/01 06:44:10  gross
2480    # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working
2481    #
2482    # Revision 1.1.2.13  2005/01/25 00:47:07  gross
2483    # updates in the documentation
2484    #
2485    # Revision 1.1.2.12  2005/01/12 01:28:04  matt
2486    # Added createCoefficient method for linearPDEs.
2487    #
2488    # Revision 1.1.2.11  2005/01/11 01:55:34  gross
2489    # a problem in linearPDE class fixed
2490    #
2491    # Revision 1.1.2.10  2005/01/07 01:13:29  gross
2492    # some bugs in linearPDE fixed
2493    #
2494    # Revision 1.1.2.9  2005/01/06 06:24:58  gross
2495    # some bugs in slicing fixed
2496    #
2497    # Revision 1.1.2.8  2005/01/05 04:21:40  gross
2498    # FunctionSpace checking/matchig in slicing added
2499    #
2500    # Revision 1.1.2.7  2004/12/29 10:03:41  gross
2501    # bug in setValue fixed
2502    #
2503    # Revision 1.1.2.6  2004/12/29 05:29:59  gross
2504    # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()
2505    #
2506    # Revision 1.1.2.5  2004/12/29 00:18:41  gross
2507    # AdvectivePDE added
2508    #
2509    # Revision 1.1.2.4  2004/12/24 06:05:41  gross
2510    # some changes in linearPDEs to add AdevectivePDE
2511    #
2512    # Revision 1.1.2.3  2004/12/16 00:12:34  gross
2513    # __init__ of LinearPDE does not accept any coefficient anymore
2514  #  #
2515  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs
2516  # *** empty log message ***  # *** empty log message ***
# Line 1013  class Poisson(LinearPDE): Line 2554  class Poisson(LinearPDE):
2554  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2555  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2556  #  #
 #  

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