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trunk/esys2/escript/py_src/linearPDEs.py revision 104 by jgs, Fri Dec 17 07:43:12 2004 UTC trunk/escript/py_src/linearPDEs.py revision 425 by gross, Tue Jan 10 04:10:39 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,domain,numEquations=0,numSolutions=0):     M{u=r}  where M{q>0}
341       """  
342       @brief initializes a new linear PDE.     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    
358    
359       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    
      @param args  
      """  
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    
423       """
424       DEFAULT= 0
425       DIRECT= 1
426       CHOLEVSKY= 2
427       PCG= 3
428       CR= 4
429       CGS= 5
430       BICGSTAB= 6
431       SSOR= 7
432       ILU0= 8
433       ILUT= 9
434       JACOBI= 10
435       GMRES= 11
436       PRES20= 12
437       LUMPING= 13
438       NO_REORDERING= 17
439       MINIMUM_FILL_IN= 18
440       NESTED_DISSECTION= 19
441       SCSL= 14
442       MKL= 15
443       UMFPACK= 16
444       ITERATIVE= 20
445       PASO= 21
446    
447       __TOL=1.e-13
448       __PACKAGE_KEY="package"
449       __METHOD_KEY="method"
450       __SYMMETRY_KEY="symmetric"
451       __TOLERANCE_KEY="tolerance"
452       __PRECONDITIONER_KEY="preconditioner"
453    
454    
455       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
456         """
457         initializes a new linear PDE
458    
459         @param domain: domain of the PDE
460         @type domain: L{Domain<escript.Domain>}
461         @param numEquations: number of equations. If numEquations==None the number of equations
462                              is exracted from the PDE coefficients.
463         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
464                              is exracted from the PDE coefficients.
465         @param debug: if True debug informations are printed.
466    
467         """
468         super(LinearPDE, self).__init__()
469         #
470         #   the coefficients of the general PDE:
471         #
472         self.__COEFFICIENTS_OF_GENEARL_PDE={
473           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
474           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
475           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
476           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
477           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
478           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
479           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
480           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
481           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
482           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
483           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
484           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
485    
486         # COEFFICIENTS can be overwritten by subclasses:
487         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
488         self.__altered_coefficients=False
489       # initialize attributes       # initialize attributes
490       self.__debug=None       self.__debug=debug
491       self.__domain=domain       self.__domain=domain
492       self.__numEquations=numEquations       self.__numEquations=numEquations
493       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
494       self.cleanCoefficients()       self.__resetSystem()
   
      self.__operator=escript.Operator()  
      self.__operator_isValid=False  
      self.__righthandside=escript.Data()  
      self.__righthandside_isValid=False  
      self.__solution=escript.Data()  
      self.__solution_isValid=False  
495    
496       # set some default values:       # set some default values:
497       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
498       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
499       self.__tolerance=1.e-8       self.__tolerance=1.e-8
500       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
501       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
502         self.__preconditioner=self.DEFAULT
503         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
504       self.__sym=False       self.__sym=False
      self.__lumping=False  
505    
506     def getCoefficient(self,name):       self.resetCoefficients()
507         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
508       # =============================================================================
509       #    general stuff:
510       # =============================================================================
511       def __str__(self):
512         """
513         returns string representation of the PDE
514    
515         @return: a simple representation of the PDE
516         @rtype: C{str}
517         """
518         return "<LinearPDE %d>"%id(self)
519       # =============================================================================
520       #    debug :
521       # =============================================================================
522       def setDebugOn(self):
523         """
524         switches on debugging
525       """       """
526       @brief return the value of the coefficient name       self.__debug=not None
527    
528       @param name     def setDebugOff(self):
529         """
530         switches off debugging
531       """       """
532       return self.__coefficient[name]       self.__debug=None
533    
534     def setValue(self,**coefficients):     def trace(self,text):
535        """       """
536        @brief sets new values to coefficients       print the text message if debugging is swiched on.
537         @param text: message
538         @type text: C{string}
539         """
540         if self.__debug: print "%s: %s"%(str(self),text)
541    
542        @param coefficients     # =============================================================================
543        """     # some service functions:
544        self._setValue(**coefficients)     # =============================================================================
545             def getDomain(self):
546         """
547         returns the domain of the PDE
548    
549     def _setValue(self,**coefficients):       @return: the domain of the PDE
550        """       @rtype: L{Domain<escript.Domain>}
551        @brief sets new values to coefficients       """
552         return self.__domain
553    
554        @param coefficients     def getDim(self):
555        """       """
556               returns the spatial dimension of the PDE
       # get the dictionary of the coefficinets been altered:  
       alteredCoefficients={}  
       for i,d in coefficients.iteritems():  
          if self.hasCoefficient(i):  
             if d == None:  
                 alteredCoefficients[i]=escript.Data()  
             elif isinstance(d,escript.Data):  
                 if d.isEmpty():  
                   alteredCoefficients[i]=escript.Data()  
                 else:  
                   alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
             else:  
                 alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
          else:  
             raise ValueError,"Attempt to set undefined coefficient %s"%i  
       # if numEquations and numSolutions is undefined we try identify their values based on the coefficients:  
       if self.__numEquations<1 or self.__numSolutions<1:  
             numEquations,numSolutions=identifyNumEquationsAndSolutions(self.getDomain().getDim(),alteredCoefficients)  
             if self.__numEquations<1 and numEquations>0: self.__numEquations=numEquations  
             if self.__numSolutions<1 and numSolutions>0: self.__numSolutions=numSolutions  
             if self.debug() and self.__numEquations>0: print "PDE Debug: identified number of equations is ",self.__numEquations  
             if self.debug() and self.__numSolutions>0: print "PDE Debug: identified number of solutions is ",self.__numSolutions  
557    
558        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
559        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
560           for i in self.__coefficient.iterkeys():       """
561               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()  
562    
563     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
564       """       """
565       @brief return the shape of the coefficient name       returns the number of equations
566    
567       @param name       @return: the number of equations
568         @rtype: C{int}
569         @raise UndefinedPDEError: if the number of equations is not be specified yet.
570       """       """
571       if self.hasCoefficient(name):       if self.__numEquations==None:
572          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
573       else:       else:
574          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
575    
576     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
577       """       """
578       @brief return the atoms of the coefficient name       returns the number of unknowns
579    
580       @param name       @return: the number of unknowns
581         @rtype: C{int}
582         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
583       """       """
584       if self.hasCoefficient(name):       if self.__numSolutions==None:
585          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
586       else:       else:
587          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
588    
589     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
590       """       """
591       @brief annonced that coefficient name has been changed       return status for order reduction for equation
592    
593       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
594         @rtype: L{bool}
595       """       """
596       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  
597    
598     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
599        """       """
600        @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  
601    
602        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
603        """       @rtype: L{bool}
604        return self.__coefficient.has_key(name)       """
605         return self.__reduce_solution_order
606    
607     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
608       """       """
609       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
610    
611         @return: representation space of equation
612         @rtype: L{FunctionSpace<escript.FunctionSpace>}
613       """       """
614       return self.__row_function_space       if self.reduceEquationOrder():
615             return escript.ReducedSolution(self.getDomain())
616         else:
617             return escript.Solution(self.getDomain())
618    
619     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
620       """       """
621       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
622    
623         @return: representation space of solution
624         @rtype: L{FunctionSpace<escript.FunctionSpace>}
625       """       """
626       return self.__column_function_space       if self.reduceSolutionOrder():
627             return escript.ReducedSolution(self.getDomain())
628         else:
629             return escript.Solution(self.getDomain())
630    
631     # ===== debug ==============================================================  
632     def setDebugOn(self):     def getOperator(self):
633         """
634         provides access to the operator of the PDE
635    
636         @return: the operator of the PDE
637         @rtype: L{Operator<escript.Operator>}
638         """
639         m=self.getSystem()[0]
640         if self.isUsingLumping():
641             return self.copyConstraint(1./m)
642         else:
643             return m
644    
645       def getRightHandSide(self):
646         """
647         provides access to the right hand side of the PDE
648         @return: the right hand side of the PDE
649         @rtype: L{Data<escript.Data>}
650         """
651         r=self.getSystem()[1]
652         if self.isUsingLumping():
653             return self.copyConstraint(r)
654         else:
655             return r
656    
657       def applyOperator(self,u=None):
658         """
659         applies the operator of the PDE to a given u or the solution of PDE if u is not present.
660    
661         @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
662                   the current solution is used.
663         @type u: L{Data<escript.Data>} or None
664         @return: image of u
665         @rtype: L{Data<escript.Data>}
666         """
667         if u==None:
668              return self.getOperator()*self.getSolution()
669         else:
670            self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
671    
672       def getResidual(self,u=None):
673         """
674         return the residual of u or the current solution if u is not present.
675    
676         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
677                   the current solution is used.
678         @type u: L{Data<escript.Data>} or None
679         @return: residual of u
680         @rtype: L{Data<escript.Data>}
681         """
682         return self.applyOperator(u)-self.getRightHandSide()
683    
684       def checkSymmetry(self,verbose=True):
685          """
686          test the PDE for symmetry.
687    
688          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
689          @type verbose: C{bool}
690          @return:  True if the PDE is symmetric.
691          @rtype: L{Data<escript.Data>}
692          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
693          """
694          verbose=verbose or self.__debug
695          out=True
696          if self.getNumSolutions()!=self.getNumEquations():
697             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
698             out=False
699          else:
700             A=self.getCoefficientOfGeneralPDE("A")
701             if not A.isEmpty():
702                tol=util.Lsup(A)*self.__TOL
703                if self.getNumSolutions()>1:
704                   for i in range(self.getNumEquations()):
705                      for j in range(self.getDim()):
706                         for k in range(self.getNumSolutions()):
707                            for l in range(self.getDim()):
708                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
709                                   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)
710                                   out=False
711                else:
712                   for j in range(self.getDim()):
713                      for l in range(self.getDim()):
714                         if util.Lsup(A[j,l]-A[l,j])>tol:
715                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
716                            out=False
717             B=self.getCoefficientOfGeneralPDE("B")
718             C=self.getCoefficientOfGeneralPDE("C")
719             if B.isEmpty() and not C.isEmpty():
720                if verbose: print "non-symmetric PDE because B is not present but C is"
721                out=False
722             elif not B.isEmpty() and C.isEmpty():
723                if verbose: print "non-symmetric PDE because C is not present but B is"
724                out=False
725             elif not B.isEmpty() and not C.isEmpty():
726                tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.
727                if self.getNumSolutions()>1:
728                   for i in range(self.getNumEquations()):
729                       for j in range(self.getDim()):
730                          for k in range(self.getNumSolutions()):
731                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
732                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
733                                  out=False
734                else:
735                   for j in range(self.getDim()):
736                      if util.Lsup(B[j]-C[j])>tol:
737                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
738                         out=False
739             if self.getNumSolutions()>1:
740               D=self.getCoefficientOfGeneralPDE("D")
741               if not D.isEmpty():
742                 tol=util.Lsup(D)*self.__TOL
743                 for i in range(self.getNumEquations()):
744                    for k in range(self.getNumSolutions()):
745                      if util.Lsup(D[i,k]-D[k,i])>tol:
746                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
747                          out=False
748               d=self.getCoefficientOfGeneralPDE("d")
749               if not d.isEmpty():
750                 tol=util.Lsup(d)*self.__TOL
751                 for i in range(self.getNumEquations()):
752                    for k in range(self.getNumSolutions()):
753                      if util.Lsup(d[i,k]-d[k,i])>tol:
754                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
755                          out=False
756               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
757               if not d_contact.isEmpty():
758                 tol=util.Lsup(d_contact)*self.__TOL
759                 for i in range(self.getNumEquations()):
760                    for k in range(self.getNumSolutions()):
761                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
762                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
763                          out=False
764          return out
765    
766       def getSolution(self,**options):
767         """         """
768         @brief         returns the solution of the PDE. If the solution is not valid the PDE is solved.
769    
770           @return: the solution
771           @rtype: L{Data<escript.Data>}
772           @param options: solver options
773           @keyword verbose: True to get some information during PDE solution
774           @type verbose: C{bool}
775           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
776                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
777           @keyword iter_max: maximum number of iteration steps allowed.
778           @keyword drop_tolerance: threshold for drupping in L{ILUT}
779           @keyword drop_storage: maximum of allowed memory in L{ILUT}
780           @keyword truncation: maximum number of residuals in L{GMRES}
781           @keyword restart: restart cycle length in L{GMRES}
782         """         """
783         self.__debug=not None         if not self.__solution_isValid:
784              mat,f=self.getSystem()
785              if self.isUsingLumping():
786                 self.__solution=self.copyConstraint(f*mat)
787              else:
788                 options[self.__TOLERANCE_KEY]=self.getTolerance()
789                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
790                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
791                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
792                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
793                 self.trace("PDE is resolved.")
794                 self.trace("solver options: %s"%str(options))
795                 self.__solution=mat.solve(f,options)
796              self.__solution_isValid=True
797           return self.__solution
798    
799     def setDebugOff(self):     def getFlux(self,u=None):
800         """
801         returns the flux M{J} for a given M{u}
802    
803         M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
804    
805         or
806    
807         M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
808    
809         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
810         @type u: L{Data<escript.Data>} or None
811         @return: flux
812         @rtype: L{Data<escript.Data>}
813         """
814         if u==None: u=self.getSolution()
815         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
816       # =============================================================================
817       #   solver settings:
818       # =============================================================================
819       def setSolverMethod(self,solver=None,preconditioner=None):
820         """         """
821         @brief         sets a new solver
822    
823           @param solver: sets a new solver method.
824           @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}.
825           @param preconditioner: sets a new solver method.
826           @type solver: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}
827         """         """
828         self.__debug=None         if solver==None: solve=self.DEFAULT
829           if preconditioner==None: preconditioner=self.DEFAULT
830           if not (solver,preconditioner)==self.getSolverMethod():
831               self.__solver_method=solver
832               self.__preconditioner=preconditioner
833               self.__checkMatrixType()
834               self.trace("New solver is %s"%self.getSolverMethodName())
835    
836     def debug(self):     def getSolverMethodName(self):
837         """         """
838         @brief returns true if the PDE is in the debug mode         returns the name of the solver currently used
839    
840           @return: the name of the solver currently used.
841           @rtype: C{string}
842         """         """
        return self.__debug  
843    
844     #===== Lumping ===========================         m=self.getSolverMethod()
845     def setLumpingOn(self):         p=self.getSolverPackage()
846        """         method=""
847        @brief indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
848        """         elif m[0]==self.DIRECT: method= "DIRECT"
849        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
850           raise SystemError,"Lumping is not working yet! Talk to the experts"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
851           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.PCG: method= "PCG"
852           self.__rebuildOperator()         elif m[0]==self.CR: method= "CR"
853           self.__lumping=True         elif m[0]==self.CGS: method= "CGS"
854           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
855           elif m[0]==self.SSOR: method= "SSOR"
856           elif m[0]==self.GMRES: method= "GMRES"
857           elif m[0]==self.PRES20: method= "PRES20"
858           elif m[0]==self.LUMPING: method= "LUMPING"
859           if m[1]==self.DEFAULT: method+="+DEFAULT"
860           elif m[1]==self.JACOBI: method+= "+JACOBI"
861           elif m[1]==self.ILU0: method+= "+ILU0"
862           elif m[1]==self.ILUT: method+= "+ILUT"
863           elif m[1]==self.SSOR: method+= "+SSOR"
864           if p==self.DEFAULT: package="DEFAULT"
865           elif p==self.PASO: package= "PASO"
866           elif p==self.MKL: package= "MKL"
867           elif p==self.SCSL: package= "SCSL"
868           elif p==self.UMFPACK: package= "UMFPACK"
869           else : method="unknown"
870           return "%s solver of %s package"%(method,package)
871    
    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  
872    
873     def setLumping(self,flag=False):     def getSolverMethod(self):
874        """         """
875        @brief set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
876    
877     def isUsingLumping(self):         @return: the solver method currently be used.
878        """         @rtype: C{int}
879        @brief         """
880        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
881    
882     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
883         """         """
884         @brief sets a new solver         sets a new solver package
885    
886           @param solver: sets a new solver method.
887           @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
888         """         """
889         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
890           if not package==self.getSolverPackage():
891             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
892             self.__checkMatrixType()             self.__checkMatrixType()
893               self.trace("New solver is %s"%self.getSolverMethodName())
894    
895     def getSolverMethod(self):     def getSolverPackage(self):
896         """         """
897         @brief returns the solver method         returns the package of the solver
898    
899           @return: the solver package currently being used.
900           @rtype: C{int}
901         """         """
902         return self.__solver_method         return self.__solver_package
903    
904       def isUsingLumping(self):
905          """
906          checks if matrix lumping is used a solver method
907    
908          @return: True is lumping is currently used a solver method.
909          @rtype: C{bool}
910          """
911          return self.getSolverMethod()[0]==self.LUMPING
912    
    #============ tolerance business =========================================================  
913     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
914         """         """
915         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
916    
917           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
918    
919           defines the stopping criterion.
920    
921           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
922                       the system will be resolved.
923           @type tol: positive C{float}
924           @raise ValueException: if tolerance is not positive.
925         """         """
926         if not tol>0:         if not tol>0:
927             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
928         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
929         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
930         self.__tolerance=tol         self.__tolerance=tol
931         return         return
932    
933     def getTolerance(self):     def getTolerance(self):
934         """         """
935         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
936    
937           @return: tolerance currently used.
938           @rtype: C{float}
939         """         """
940         return self.__tolerance         return self.__tolerance
941    
942     #===== symmetry  flag ==========================     # =============================================================================
943       #    symmetry  flag:
944       # =============================================================================
945     def isSymmetric(self):     def isSymmetric(self):
946        """        """
947        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
948    
949          @return: True is a symmetric PDE is indicated, otherwise False is returned
950          @rtype: C{bool}
951        """        """
952        return self.__sym        return self.__sym
953    
954     def setSymmetryOn(self):     def setSymmetryOn(self):
955        """        """
956        @brief sets the symmetry flag to true        sets the symmetry flag.
957        """        """
958        if not self.isSymmetric():        if not self.isSymmetric():
959           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
960           self.__sym=True           self.__sym=True
961           self.__checkMatrixType()           self.__checkMatrixType()
962    
963     def setSymmetryOff(self):     def setSymmetryOff(self):
964        """        """
965        @brief sets the symmetry flag to false        removes the symmetry flag.
966        """        """
967        if self.isSymmetric():        if self.isSymmetric():
968           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
969           self.__sym=False           self.__sym=False
970           self.__checkMatrixType()           self.__checkMatrixType()
971    
972     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
973       """        """
974       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
975    
976       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
977       """        @type flag: C{bool}
978       if flag:        """
979          self.setSymmetryOn()        if flag:
980       else:           self.setSymmetryOn()
981          self.setSymmetryOff()        else:
982             self.setSymmetryOff()
983    
984     #===== order reduction ==========================     # =============================================================================
985       # function space handling for the equation as well as the solution
986       # =============================================================================
987     def setReducedOrderOn(self):     def setReducedOrderOn(self):
988       """       """
989       @brief switches to on reduced order       switches on reduced order for solution and equation representation
990    
991         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
992       """       """
993       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
994       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
995    
996     def setReducedOrderOff(self):     def setReducedOrderOff(self):
997       """       """
998       @brief switches to full order       switches off reduced order for solution and equation representation
999    
1000         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1001       """       """
1002       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1003       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1004    
1005     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1006       """       """
1007       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1008         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1009       @param flag                    if flag is not present order reduction is switched off
1010         @type flag: C{bool}
1011         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1012       """       """
1013       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1014       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1015    
1016     #===== order reduction solution ==========================  
1017     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1018       """       """
1019       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1020    
1021         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1022       """       """
1023       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1024       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1025           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1026           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1027           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1028             self.__resetSystem()
1029    
1030     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1031       """       """
1032       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1033    
1034         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1035       """       """
1036       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1037       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1038           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1039           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1040           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1041             self.__resetSystem()
1042    
1043     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1044       """       """
1045       @brief sets order for test functions according to flag       sets order for test functions according to flag
1046    
1047       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1048                      if flag is not present order reduction is switched off
1049         @type flag: C{bool}
1050         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1051       """       """
1052       if flag:       if flag:
1053          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1054       else:       else:
1055          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1056                                                                                                                                                              
    #===== order reduction equation ==========================  
1057     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1058       """       """
1059       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1060    
1061         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1062       """       """
1063       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1064       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1065           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1066           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1067           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1068             self.__resetSystem()
1069    
1070     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1071       """       """
1072       @brief switches to full order for test functions       switches off reduced order for equation representation
1073    
1074         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1075       """       """
1076       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1077       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1078           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1079           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1080           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1081             self.__resetSystem()
1082    
1083     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1084       """       """
1085       @brief sets order for test functions according to flag       sets order for test functions according to flag
1086    
1087       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1088                      if flag is not present order reduction is switched off
1089         @type flag: C{bool}
1090         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1091       """       """
1092       if flag:       if flag:
1093          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1094       else:       else:
1095          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1096    
1097     # ==== initialization =====================================================================     # =============================================================================
1098     def __makeNewOperator(self):     # private method:
1099       # =============================================================================
1100       def __checkMatrixType(self):
1101         """
1102         reassess the matrix type and, if a new matrix is needed, resets the system.
1103         """
1104         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1105         if not new_matrix_type==self.__matrix_type:
1106             self.trace("Matrix type is now %d."%new_matrix_type)
1107             self.__matrix_type=new_matrix_type
1108             self.__resetSystem()
1109       #
1110       #   rebuild switches :
1111       #
1112       def __invalidateSolution(self):
1113           """
1114           indicates the PDE has to be resolved if the solution is requested
1115           """
1116           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1117           self.__solution_isValid=False
1118    
1119       def __invalidateOperator(self):
1120           """
1121           indicates the operator has to be rebuilt next time it is used
1122           """
1123           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1124           self.__invalidateSolution()
1125           self.__operator_is_Valid=False
1126    
1127       def __invalidateRightHandSide(self):
1128           """
1129           indicates the right hand side has to be rebuild next time it is used
1130         """         """
1131         @brief         if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1132           self.__invalidateSolution()
1133           self.__righthandside_isValid=False
1134    
1135       def __invalidateSystem(self):
1136         """         """
1137           annonced that everthing has to be rebuild:
1138           """
1139           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1140           self.__invalidateSolution()
1141           self.__invalidateOperator()
1142           self.__invalidateRightHandSide()
1143    
1144       def __resetSystem(self):
1145           """
1146           annonced that everthing has to be rebuild:
1147           """
1148           self.trace("New System is built from scratch.")
1149           self.__operator=escript.Operator()
1150           self.__operator_is_Valid=False
1151           self.__righthandside=escript.Data()
1152           self.__righthandside_isValid=False
1153           self.__solution=escript.Data()
1154           self.__solution_isValid=False
1155       #
1156       #    system initialization:
1157       #
1158       def __getNewOperator(self):
1159           """
1160           returns an instance of a new operator
1161           """
1162           self.trace("New operator is allocated.")
1163         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1164                             self.getNumEquations(), \                             self.getNumEquations(), \
1165                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 617  class LinearPDE: Line 1167  class LinearPDE:
1167                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1168                             self.__matrix_type)                             self.__matrix_type)
1169    
1170     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1171         """         """
1172         @brief         returns an instance of a new right hand side
1173         """         """
1174         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1175           if self.getNumEquations()>1:
1176               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1177           else:
1178               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1179    
1180     def __makeNewSolution(self):     def __getNewSolution(self):
1181         """         """
1182         @brief         returns an instance of a new solution
1183         """         """
1184         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1185           if self.getNumSolutions()>1:
1186               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1187           else:
1188               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1189    
1190     def __getFreshOperator(self):     def __makeFreshSolution(self):
1191         """         """
1192         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1193         """         """
1194         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1195             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1196         else:         else:
1197             self.__operator.setValue(0.)             self.__solution*=0
1198             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1199         return self.__operator         return self.__solution
1200    
1201     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1202         """         """
1203         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1204         """         """
1205         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1206             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1207         else:         else:
1208             print "fix self.__righthandside*=0"             self.__righthandside*=0
1209             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1210             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1211    
1212     # ==== rebuild switches =====================================================================     def __makeFreshOperator(self):
    def __rebuildSolution(self,deep=False):  
1213         """         """
1214         @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
1215         """         """
1216         if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."         if self.__operator.isEmpty():
1217         self.__solution_isValid=False             self.__operator=self.__getNewOperator()
1218         if deep: self.__solution=escript.Data(deep)         else:
1219               self.__operator.resetValues()
1220               self.trace("Operator reset to zero")
1221           return self.__operator
1222    
1223     def __rebuildOperator(self,deep=False):     def __applyConstraint(self):
1224         """         """
1225         @brief indicates the operator has to be rebuilt next time it is used         applies the constraints defined by q and r to the system
1226         """         """
1227         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if not self.isUsingLumping():
1228         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1229         self.__operator_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1230         if deep: self.__operator=escript.Operator()            if not q.isEmpty() and not self.__operator.isEmpty():
1231                 # q is the row and column mask to indicate where constraints are set:
1232                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1233                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1234                 u=self.__getNewSolution()
1235                 if r.isEmpty():
1236                    r_s=self.__getNewSolution()
1237                 else:
1238                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1239                 u.copyWithMask(r_s,col_q)
1240                 if not self.__righthandside.isEmpty():
1241                    self.__righthandside-=self.__operator*u
1242                    self.__righthandside=self.copyConstraint(self.__righthandside)
1243                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1244       # =============================================================================
1245       # function giving access to coefficients of the general PDE:
1246       # =============================================================================
1247       def getCoefficientOfGeneralPDE(self,name):
1248         """
1249         return the value of the coefficient name of the general PDE.
1250    
1251         @note: This method is called by the assembling routine it can be overwritten
1252               to map coefficients of a particular PDE to the general PDE.
1253         @param name: name of the coefficient requested.
1254         @type name: C{string}
1255         @return: the value of the coefficient  name
1256         @rtype: L{Data<escript.Data>}
1257         @raise IllegalCoefficient: if name is not one of coefficients
1258                      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}.
1259         """
1260         if self.hasCoefficientOfGeneralPDE(name):
1261            return self.getCoefficient(name)
1262         else:
1263            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1264    
1265     def __rebuildRightHandSide(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
1266         """       """
1267         @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()  
1268    
1269     def __rebuildSystem(self,deep=False):       @param name: name of the coefficient enquired.
1270         """       @type name: C{string}
1271         @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.
1272         """       @rtype: C{bool}
1273         self.__rebuildSolution(deep)  
1274         self.__rebuildOperator(deep)       """
1275         self.__rebuildRightHandSide(deep)       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1276      
1277     def __checkMatrixType(self):     def createCoefficientOfGeneralPDE(self,name):
1278       """       """
1279       @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
1280    
1281         @param name: name of the coefficient requested.
1282         @type name: C{string}
1283         @return: a coefficient name initialized to 0.
1284         @rtype: L{Data<escript.Data>}
1285         @raise IllegalCoefficient: if name is not one of coefficients
1286                      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}.
1287       """       """
1288       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       if self.hasCoefficientOfGeneralPDE(name):
1289       if not new_matrix_type==self.__matrix_type:          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1290           if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type       else:
1291           self.__matrix_type=new_matrix_type          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1292           self.__rebuildOperator(deep=True)  
1293       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1294         """
1295         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1296    
1297         @param name: name of the coefficient enquired.
1298         @type name: C{string}
1299         @return: the function space to be used for coefficient name
1300         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1301         @raise IllegalCoefficient: if name is not one of coefficients
1302                      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}.
1303         """
1304         if self.hasCoefficientOfGeneralPDE(name):
1305            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1306         else:
1307            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1308    
1309       def getShapeOfCoefficientOfGeneralPDE(self,name):
1310         """
1311         return the shape of the coefficient name of the general PDE
1312    
1313     #============ assembling =======================================================       @param name: name of the coefficient enquired.
1314     def __copyConstraint(self,u):       @type name: C{string}
1315         @return: the shape of the coefficient name
1316         @rtype: C{tuple} of C{int}
1317         @raise IllegalCoefficient: if name is not one of coefficients
1318                      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}.
1319         """
1320         if self.hasCoefficientOfGeneralPDE(name):
1321            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1322         else:
1323            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1324    
1325       # =============================================================================
1326       # functions giving access to coefficients of a particular PDE implementation:
1327       # =============================================================================
1328       def getCoefficient(self,name):
1329         """
1330         returns the value of the coefficient name
1331    
1332         @param name: name of the coefficient requested.
1333         @type name: C{string}
1334         @return: the value of the coefficient name
1335         @rtype: L{Data<escript.Data>}
1336         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1337         """
1338         if self.hasCoefficient(name):
1339             return self.COEFFICIENTS[name].getValue()
1340         else:
1341            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1342    
1343       def hasCoefficient(self,name):
1344         """
1345         return True if name is the name of a coefficient
1346    
1347         @param name: name of the coefficient enquired.
1348         @type name: C{string}
1349         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1350         @rtype: C{bool}
1351         """
1352         return self.COEFFICIENTS.has_key(name)
1353    
1354       def createCoefficient(self, name):
1355         """
1356         create a L{Data<escript.Data>} object corresponding to coefficient name
1357    
1358         @return: a coefficient name initialized to 0.
1359         @rtype: L{Data<escript.Data>}
1360         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1361         """
1362         if self.hasCoefficient(name):
1363            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1364         else:
1365            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1366    
1367       def getFunctionSpaceForCoefficient(self,name):
1368         """
1369         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1370    
1371         @param name: name of the coefficient enquired.
1372         @type name: C{string}
1373         @return: the function space to be used for coefficient name
1374         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1375         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1376         """
1377         if self.hasCoefficient(name):
1378            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1379         else:
1380            raise ValueError,"unknown coefficient %s requested"%name
1381       def getShapeOfCoefficient(self,name):
1382         """
1383         return the shape of the coefficient name
1384    
1385         @param name: name of the coefficient enquired.
1386         @type name: C{string}
1387         @return: the shape of the coefficient name
1388         @rtype: C{tuple} of C{int}
1389         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1390         """
1391         if self.hasCoefficient(name):
1392            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1393         else:
1394            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1395    
1396       def resetCoefficients(self):
1397         """
1398         resets all coefficients to there default values.
1399         """
1400         for i in self.COEFFICIENTS.iterkeys():
1401             self.COEFFICIENTS[i].resetValue()
1402    
1403       def alteredCoefficient(self,name):
1404         """
1405         announce that coefficient name has been changed
1406    
1407         @param name: name of the coefficient enquired.
1408         @type name: C{string}
1409         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1410         @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.
1411         """
1412         if self.hasCoefficient(name):
1413            self.trace("Coefficient %s has been altered."%name)
1414            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1415               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1416               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1417         else:
1418            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1419    
1420       def copyConstraint(self,u):
1421        """        """
1422        @brief copies the constrint condition into u        copies the constraint into u and returns u.
1423    
1424          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1425          @type u: L{Data<escript.Data>}
1426          @return: the input u modified by the constraints.
1427          @rtype: L{Data<escript.Data>}
1428          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1429        """        """
1430        q=self.getCoefficient("q")        q=self.getCoefficientOfGeneralPDE("q")
1431        r=self.getCoefficient("r")        r=self.getCoefficientOfGeneralPDE("r")
1432        if not q.isEmpty():        if not q.isEmpty():
1433            if r.isEmpty():           if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1434               r2=escript.Data(0,u.getShape(),u.getFunctionSpace())           if r.isEmpty():
1435            else:               r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1436               r2=escript.Data(r,u.getFunctionSpace())           else:
1437            u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))               r=escript.Data(r,u.getFunctionSpace())
1438             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1439     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  
1440    
1441     def getRightHandSide(self,ignoreConstraint=False):     def setValue(self,**coefficients):
1442         """        """
1443         @brief returns the right hand side of the PDE        sets new values to coefficients
1444    
1445         @param ignoreConstraint        @param coefficients: new values assigned to coefficients
1446         """        @keyword A: value for coefficient A.
1447         if not self.__righthandside_isValid:        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1448             if self.debug() : print "PDE Debug: New right hand side is built."        @keyword B: value for coefficient B
1449             self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1450                           self.getCoefficient("X"), \        @keyword C: value for coefficient C
1451                           self.getCoefficient("Y"),\        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1452                           self.getCoefficient("y"),\        @keyword D: value for coefficient D
1453                           self.getCoefficient("y_contact"))        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1454             self.__righthandside_isValid=True        @keyword X: value for coefficient X
1455             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>}.
1456         return self.__righthandside        @keyword Y: value for coefficient Y
1457          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1458          @keyword d: value for coefficient d
1459          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1460          @keyword y: value for coefficient y
1461          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1462          @keyword d_contact: value for coefficient d_contact
1463          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1464                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1465          @keyword y_contact: value for coefficient y_contact
1466          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1467                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1468          @keyword r: values prescribed to the solution at the locations of constraints
1469          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1470                   depending of reduced order is used for the solution.
1471          @keyword q: mask for location of constraints
1472          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1473                   depending of reduced order is used for the representation of the equation.
1474          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1475          """
1476          # check if the coefficients are  legal:
1477          for i in coefficients.iterkeys():
1478             if not self.hasCoefficient(i):
1479                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1480          # if the number of unknowns or equations is still unknown we try to estimate them:
1481          if self.__numEquations==None or self.__numSolutions==None:
1482             for i,d in coefficients.iteritems():
1483                if hasattr(d,"shape"):
1484                    s=d.shape
1485                elif hasattr(d,"getShape"):
1486                    s=d.getShape()
1487                else:
1488                    s=numarray.array(d).shape
1489                if s!=None:
1490                    # get number of equations and number of unknowns:
1491                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1492                    if res==None:
1493                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1494                    else:
1495                        if self.__numEquations==None: self.__numEquations=res[0]
1496                        if self.__numSolutions==None: self.__numSolutions=res[1]
1497          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1498          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1499          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1500          for i,d in coefficients.iteritems():
1501            try:
1502               self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1503            except IllegalCoefficientValue,m:
1504               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1505            self.alteredCoefficient(i)
1506    
1507          self.__altered_coefficients=True
1508          # check if the systrem is inhomogeneous:
1509          if len(coefficients)>0 and not self.isUsingLumping():
1510             q=self.getCoefficientOfGeneralPDE("q")
1511             r=self.getCoefficientOfGeneralPDE("r")
1512             homogeneous_constraint=True
1513             if not q.isEmpty() and not r.isEmpty():
1514                 if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1515                   self.trace("Inhomogeneous constraint detected.")
1516                   self.__invalidateSystem()
1517    
1518     def getSystem(self):     def getSystem(self):
1519         """         """
1520         @brief         return the operator and right hand side of the PDE
1521    
1522           @return: the discrete version of the PDE
1523           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1524         """         """
1525         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."  
1526            if self.isUsingLumping():            if self.isUsingLumping():
1527                self.getRightHandSide(ignoreConstraint=True)                if not self.__operator_is_Valid:
1528                self.getOperator()                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1529                     if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Using coefficient A in lumped matrix can produce wrong results"
1530                     if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"
1531                     if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Using coefficient C in lumped matrix can produce wrong results"
1532                     mat=self.__getNewOperator()
1533                     self.getDomain().addPDEToSystem(mat,escript.Data(), \
1534                               self.getCoefficientOfGeneralPDE("A"), \
1535                               self.getCoefficientOfGeneralPDE("B"), \
1536                               self.getCoefficientOfGeneralPDE("C"), \
1537                               self.getCoefficientOfGeneralPDE("D"), \
1538                               escript.Data(), \
1539                               escript.Data(), \
1540                               self.getCoefficientOfGeneralPDE("d"), \
1541                               escript.Data(),\
1542                               self.getCoefficientOfGeneralPDE("d_contact"), \
1543                               escript.Data())
1544                     self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))
1545                     del mat
1546                     self.trace("New lumped operator has been built.")
1547                     self.__operator_is_Valid=True
1548                  if not self.__righthandside_isValid:
1549                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1550                                   self.getCoefficientOfGeneralPDE("X"), \
1551                                   self.getCoefficientOfGeneralPDE("Y"),\
1552                                   self.getCoefficientOfGeneralPDE("y"),\
1553                                   self.getCoefficientOfGeneralPDE("y_contact"))
1554                     self.trace("New right hand side as been built.")
1555                     self.__righthandside_isValid=True
1556            else:            else:
1557                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1558                              self.getCoefficient("A"), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1559                              self.getCoefficient("B"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1560                              self.getCoefficient("C"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1561                              self.getCoefficient("D"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1562                              self.getCoefficient("X"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1563                              self.getCoefficient("Y"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1564                              self.getCoefficient("d"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1565                              self.getCoefficient("y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1566                              self.getCoefficient("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1567                              self.getCoefficient("y_contact"))                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1568            self.__operator_isValid=True                                 self.getCoefficientOfGeneralPDE("y_contact"))
1569            self.__righthandside_isValid=True                   self.__applyConstraint()
1570            self.__applyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1571            self.__copyConstraint(self.__righthandside)                   self.trace("New system has been built.")
1572         elif not self.__operator_isValid:                   self.__operator_is_Valid=True
1573            self.getOperator()                   self.__righthandside_isValid=True
1574         elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1575            self.getRightHandSide()                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1576                                   self.getCoefficientOfGeneralPDE("X"), \
1577                                   self.getCoefficientOfGeneralPDE("Y"),\
1578                                   self.getCoefficientOfGeneralPDE("y"),\
1579                                   self.getCoefficientOfGeneralPDE("y_contact"))
1580                     self.__righthandside=self.copyConstraint(self.__righthandside)
1581                     self.trace("New right hand side has been built.")
1582                     self.__righthandside_isValid=True
1583                 elif not self.__operator_is_Valid:
1584                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1585                                self.getCoefficientOfGeneralPDE("A"), \
1586                                self.getCoefficientOfGeneralPDE("B"), \
1587                                self.getCoefficientOfGeneralPDE("C"), \
1588                                self.getCoefficientOfGeneralPDE("D"), \
1589                                escript.Data(), \
1590                                escript.Data(), \
1591                                self.getCoefficientOfGeneralPDE("d"), \
1592                                escript.Data(),\
1593                                self.getCoefficientOfGeneralPDE("d_contact"), \
1594                                escript.Data())
1595                     self.__applyConstraint()
1596                     self.trace("New operator has been built.")
1597                     self.__operator_is_Valid=True
1598         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1599    
    def solve(self,**options):  
       """  
       @brief solve the PDE  
1600    
1601        @param options  class Poisson(LinearPDE):
1602        """     """
1603        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  
1604    
1605     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief returns the solution of the PDE  
1606    
1607         @param options     with natural boundary conditons
1608         """  
1609         if not self.__solution_isValid:     M{n[j]*grad(u)[j] = 0 }
1610             if self.debug() : print "PDE Debug: PDE is resolved."  
1611             self.__solution=self.solve(**options)     and constraints:
1612             self.__solution_isValid=True  
1613         return self.__solution     M{u=0} where M{q>0}
1614     #============ some serivice functions  =====================================================  
1615     def getDomain(self):     """
1616       """  
1617       @brief returns the domain of the PDE     def __init__(self,domain,debug=False):
1618       """       """
1619       return self.__domain       initializes a new Poisson equation
1620    
1621         @param domain: domain of the PDE
1622         @type domain: L{Domain<escript.Domain>}
1623         @param debug: if True debug informations are printed.
1624    
    def getDim(self):  
1625       """       """
1626       @brief returns the spatial dimension of the PDE       super(Poisson, self).__init__(domain,1,1,debug)
1627         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1628                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1629         self.setSymmetryOn()
1630    
1631       def setValue(self,**coefficients):
1632       """       """
1633       return self.getDomain().getDim()       sets new values to coefficients
1634    
1635     def getNumEquations(self):       @param coefficients: new values assigned to coefficients
1636         @keyword f: value for right hand side M{f}
1637         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1638         @keyword q: mask for location of constraints
1639         @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>}
1640                   depending of reduced order is used for the representation of the equation.
1641         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1642         """
1643         super(Poisson, self).setValue(**coefficients)
1644    
1645       def getCoefficientOfGeneralPDE(self,name):
1646         """
1647         return the value of the coefficient name of the general PDE
1648         @param name: name of the coefficient requested.
1649         @type name: C{string}
1650         @return: the value of the coefficient  name
1651         @rtype: L{Data<escript.Data>}
1652         @raise IllegalCoefficient: if name is not one of coefficients
1653                      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}.
1654         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1655         """
1656         if name == "A" :
1657             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1658         elif name == "B" :
1659             return escript.Data()
1660         elif name == "C" :
1661             return escript.Data()
1662         elif name == "D" :
1663             return escript.Data()
1664         elif name == "X" :
1665             return escript.Data()
1666         elif name == "Y" :
1667             return self.getCoefficient("f")
1668         elif name == "d" :
1669             return escript.Data()
1670         elif name == "y" :
1671             return escript.Data()
1672         elif name == "d_contact" :
1673             return escript.Data()
1674         elif name == "y_contact" :
1675             return escript.Data()
1676         elif name == "r" :
1677             return escript.Data()
1678         elif name == "q" :
1679             return self.getCoefficient("q")
1680         else:
1681            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1682    
1683    class Helmholtz(LinearPDE):
1684       """
1685       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1686    
1687       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1688    
1689       with natural boundary conditons
1690    
1691       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1692    
1693       and constraints:
1694    
1695       M{u=r} where M{q>0}
1696    
1697       """
1698    
1699       def __init__(self,domain,debug=False):
1700       """       """
1701       @brief returns the number of equations       initializes a new Poisson equation
1702    
1703         @param domain: domain of the PDE
1704         @type domain: L{Domain<escript.Domain>}
1705         @param debug: if True debug informations are printed.
1706    
1707         """
1708         super(Helmholtz, self).__init__(domain,1,1,debug)
1709         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1710                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1711                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1712                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1713                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1714                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1715                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1716         self.setSymmetryOn()
1717    
1718       def setValue(self,**coefficients):
1719       """       """
1720       if self.__numEquations>0:       sets new values to coefficients
1721           return self.__numEquations  
1722         @param coefficients: new values assigned to coefficients
1723         @keyword omega: value for coefficient M{S{omega}}
1724         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1725         @keyword k: value for coefficeint M{k}
1726         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1727         @keyword f: value for right hand side M{f}
1728         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1729         @keyword alpha: value for right hand side M{S{alpha}}
1730         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1731         @keyword g: value for right hand side M{g}
1732         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1733         @keyword r: prescribed values M{r} for the solution in constraints.
1734         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1735                   depending of reduced order is used for the representation of the equation.
1736         @keyword q: mask for location of constraints
1737         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1738                   depending of reduced order is used for the representation of the equation.
1739         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1740         """
1741         super(Helmholtz, self).setValue(**coefficients)
1742    
1743       def getCoefficientOfGeneralPDE(self,name):
1744         """
1745         return the value of the coefficient name of the general PDE
1746    
1747         @param name: name of the coefficient requested.
1748         @type name: C{string}
1749         @return: the value of the coefficient  name
1750         @rtype: L{Data<escript.Data>}
1751         @raise IllegalCoefficient: if name is not one of coefficients
1752                      "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}.
1753         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1754         """
1755         if name == "A" :
1756             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1757         elif name == "B" :
1758             return escript.Data()
1759         elif name == "C" :
1760             return escript.Data()
1761         elif name == "D" :
1762             return self.getCoefficient("omega")
1763         elif name == "X" :
1764             return escript.Data()
1765         elif name == "Y" :
1766             return self.getCoefficient("f")
1767         elif name == "d" :
1768             return self.getCoefficient("alpha")
1769         elif name == "y" :
1770             return self.getCoefficient("g")
1771         elif name == "d_contact" :
1772             return escript.Data()
1773         elif name == "y_contact" :
1774             return escript.Data()
1775         elif name == "r" :
1776             return self.getCoefficient("r")
1777         elif name == "q" :
1778             return self.getCoefficient("q")
1779       else:       else:
1780           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1781    
1782     def getNumSolutions(self):  class LameEquation(LinearPDE):
1783       """     """
1784       @brief returns the number of unknowns     Class to define a Lame equation problem:
1785    
1786       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] }
1787    
1788       with natural boundary conditons:
1789    
1790       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] }
1791    
1792       and constraints:
1793    
1794       M{u[i]=r[i]} where M{q[i]>0}
1795    
1796       """
1797    
1798       def __init__(self,domain,debug=False):
1799          super(LameEquation, self).__init__(domain,\
1800                                             domain.getDim(),domain.getDim(),debug)
1801          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1802                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1803                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1804                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1805                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1806                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1807                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1808          self.setSymmetryOn()
1809    
1810       def setValue(self,**coefficients):
1811       """       """
1812       if self.__numSolutions>0:       sets new values to coefficients
1813          return self.__numSolutions  
1814         @param coefficients: new values assigned to coefficients
1815         @keyword lame_mu: value for coefficient M{S{mu}}
1816         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1817         @keyword lame_lambda: value for coefficient M{S{lambda}}
1818         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1819         @keyword F: value for internal force M{F}
1820         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1821         @keyword sigma: value for initial stress M{S{sigma}}
1822         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1823         @keyword f: value for extrenal force M{f}
1824         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1825         @keyword r: prescribed values M{r} for the solution in constraints.
1826         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1827                   depending of reduced order is used for the representation of the equation.
1828         @keyword q: mask for location of constraints
1829         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1830                   depending of reduced order is used for the representation of the equation.
1831         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1832         """
1833         super(LameEquation, self).setValue(**coefficients)
1834    
1835       def getCoefficientOfGeneralPDE(self,name):
1836         """
1837         return the value of the coefficient name of the general PDE
1838    
1839         @param name: name of the coefficient requested.
1840         @type name: C{string}
1841         @return: the value of the coefficient  name
1842         @rtype: L{Data<escript.Data>}
1843         @raise IllegalCoefficient: if name is not one of coefficients
1844                      "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}.
1845         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1846         """
1847         if name == "A" :
1848             out =self.createCoefficientOfGeneralPDE("A")
1849             for i in range(self.getDim()):
1850               for j in range(self.getDim()):
1851                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1852                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1853                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1854             return out
1855         elif name == "B" :
1856             return escript.Data()
1857         elif name == "C" :
1858             return escript.Data()
1859         elif name == "D" :
1860             return escript.Data()
1861         elif name == "X" :
1862             return self.getCoefficient("sigma")
1863         elif name == "Y" :
1864             return self.getCoefficient("F")
1865         elif name == "d" :
1866             return escript.Data()
1867         elif name == "y" :
1868             return self.getCoefficient("f")
1869         elif name == "d_contact" :
1870             return escript.Data()
1871         elif name == "y_contact" :
1872             return escript.Data()
1873         elif name == "r" :
1874             return self.getCoefficient("r")
1875         elif name == "q" :
1876             return self.getCoefficient("q")
1877       else:       else:
1878          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1879    
1880    class AdvectivePDE(LinearPDE):
1881       """
1882       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1883       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1884    
1885       In the following we set
1886    
1887       M{Z[j]=C[j]-B[j]}
1888    
1889       or
1890    
1891       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1892    
1893       To measure the dominance of the advective terms over the diffusive term M{A} the
1894       X{Pelclet number} M{P} is used. It is defined as
1895    
1896       M{P=h|Z|/(2|A|)}
1897    
1898     def checkSymmetry(self):     where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1899       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1900    
1901       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1902    
1903       M{S{Xi}=S{xi}(P) h/|Z|}
1904    
1905       where M{S{xi}} is a suitable function of the Peclet number.
1906    
1907       In the case of a single PDE the coefficient are up-dated in the following way:
1908             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1909             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1910             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1911             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1912    
1913       Similar for the case of a systems of PDEs:
1914             - 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]}
1915             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1916             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1917             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1918    
1919       where M{S{delta}} is L{kronecker}.
1920       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1921       but with the intension to stabilize the solution.
1922    
1923       """
1924       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1925        """        """
1926        @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>}
1927    
1928          @param domain: domain of the PDE
1929          @type domain: L{Domain<escript.Domain>}
1930          @param numEquations: number of equations. If numEquations==None the number of equations
1931                               is exracted from the PDE coefficients.
1932          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1933                               is exracted from the PDE coefficients.
1934          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1935                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1936          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1937          @param debug: if True debug informations are printed.
1938          """
1939          super(AdvectivePDE, self).__init__(domain,\
1940                                             numEquations,numSolutions,debug)
1941          if xi==None:
1942             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1943          else:
1944             self.__xi=xi
1945          self.__Xi=escript.Data()
1946    
1947       def setValue(**coefficients):
1948        """        """
1949        raise SystemError,"checkSymmetry is not implemented yet"        sets new values to coefficients
1950    
1951        return None        @param coefficients: new values assigned to coefficients
1952          @keyword A: value for coefficient A.
1953          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1954          @keyword B: value for coefficient B
1955          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1956          @keyword C: value for coefficient C
1957          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1958          @keyword D: value for coefficient D
1959          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1960          @keyword X: value for coefficient X
1961          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1962          @keyword Y: value for coefficient Y
1963          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1964          @keyword d: value for coefficient d
1965          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1966          @keyword y: value for coefficient y
1967          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1968          @keyword d_contact: value for coefficient d_contact
1969          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1970                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1971          @keyword y_contact: value for coefficient y_contact
1972          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1973                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1974          @keyword r: values prescribed to the solution at the locations of constraints
1975          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1976                   depending of reduced order is used for the solution.
1977          @keyword q: mask for location of constraints
1978          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1979                   depending of reduced order is used for the representation of the equation.
1980          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1981    
1982          """
1983          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
1984          super(AdvectivePDE, self).setValue(**coefficients)
1985    
1986       def ELMAN_RAMAGE(self,P):
1987         """
1988         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
1989         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
1990              - M{S{xi}(P)=0} for M{P<1}
1991              - M{S{xi}(P)=(1-1/P)/2} otherwise
1992    
1993         @param P: Preclet number
1994         @type P: L{Scalar<escript.Scalar>}
1995         @return: up-wind weightimg factor
1996         @rtype: L{Scalar<escript.Scalar>}
1997         """
1998         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
1999    
2000       def SIMPLIFIED_BROOK_HUGHES(self,P):
2001         """
2002         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2003         The original methods is
2004    
2005         M{S{xi}(P)=coth(P)-1/P}
2006    
2007         As the evaluation of M{coth} is expensive we are using the approximation:
2008    
2009             - M{S{xi}(P)=P/3} where M{P<3}
2010             - M{S{xi}(P)=1/2} otherwise
2011    
2012         @param P: Preclet number
2013         @type P: L{Scalar<escript.Scalar>}
2014         @return: up-wind weightimg factor
2015         @rtype: L{Scalar<escript.Scalar>}
2016         """
2017         c=util.whereNegative(P-3.)
2018         return P/6.*c+1./2.*(1.-c)
2019    
2020       def HALF(self,P):
2021         """
2022         Predefined function to set value M{1/2} for M{S{xi}}
2023    
2024         @param P: Preclet number
2025         @type P: L{Scalar<escript.Scalar>}
2026         @return: up-wind weightimg factor
2027         @rtype: L{Scalar<escript.Scalar>}
2028         """
2029         return escript.Scalar(0.5,P.getFunctionSpace())
2030    
2031       def __calculateXi(self,peclet_factor,flux,h):
2032           flux=util.Lsup(flux)
2033           if flux_max>0.:
2034              return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2035           else:
2036              return 0.
2037    
2038     def getFlux(self,u):     def __getXi(self):
2039         """        if self.__Xi.isEmpty():
2040         @brief returns the flux J_ij for a given u           B=self.getCoefficient("B")
2041             C=self.getCoefficient("C")
2042             A=self.getCoefficient("A")
2043             h=self.getDomain().getSize()
2044             self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2045             if not C.isEmpty() or not B.isEmpty():
2046                if not C.isEmpty() and not B.isEmpty():
2047                    flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2048                    if self.getNumEquations()>1:
2049                       if self.getNumSolutions()>1:
2050                          for i in range(self.getNumEquations()):
2051                             for k in range(self.getNumSolutions()):
2052                                for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2053                          # flux=C-util.reorderComponents(B,[0,2,1])
2054                       else:
2055                          for i in range(self.getNumEquations()):
2056                             for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2057                          # flux=C-B
2058                    else:
2059                       if self.getNumSolutions()>1:
2060                          for k in range(self.getNumSolutions()):
2061                             for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2062                          # flux=C-util.reorderComponents(B,[1,0])
2063                       else:
2064                          for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2065                          #flux=C-B
2066                    length_of_flux=util.sqrt(flux2)
2067                elif C.isEmpty():
2068                  length_of_flux=util.length(B)
2069                  #flux=B
2070                else:
2071                  length_of_flux=util.length(C)
2072                  #flux=C
2073    
2074              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}              #length_of_flux=util.length(flux)
2075                flux_max=util.Lsup(length_of_flux)
2076                if flux_max>0.:
2077                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2078                   length_of_A=util.length(A)
2079                   A_max=util.Lsup(length_of_A)
2080                   if A_max>0:
2081                        inv_A=1./(length_of_A+A_max*self.__TOL)
2082                   else:
2083                        inv_A=1./self.__TOL
2084                   peclet_number=length_of_flux*h/2*inv_A
2085                   xi=self.__xi(peclet_number)
2086                   self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2087                   self.trace("preclet number = %e"%util.Lsup(peclet_number))
2088          return self.__Xi
2089    
2090    
2091       def getCoefficientOfGeneralPDE(self,name):
2092         """
2093         return the value of the coefficient name of the general PDE
2094    
2095         @param name: name of the coefficient requested.
2096         @type name: C{string}
2097         @return: the value of the coefficient name
2098         @rtype: L{Data<escript.Data>}
2099         @raise IllegalCoefficient: if name is not one of coefficients
2100                      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}.
2101         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2102         """
2103         if not self.getNumEquations() == self.getNumSolutions():
2104              raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
2105    
2106         if name == "A" :
2107             A=self.getCoefficient("A")
2108             B=self.getCoefficient("B")
2109             C=self.getCoefficient("C")
2110             if B.isEmpty() and C.isEmpty():
2111                Aout=A
2112             else:
2113                if A.isEmpty():
2114                   Aout=self.createNewCoefficient("A")
2115                else:
2116                   Aout=A[:]
2117                Xi=self.__getXi()
2118                if self.getNumEquations()>1:
2119                    for i in range(self.getNumEquations()):
2120                       for j in range(self.getDim()):
2121                          for k in range(self.getNumSolutions()):
2122                             for l in range(self.getDim()):
2123                                if not C.isEmpty() and not B.isEmpty():
2124                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2125                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2126                                   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])
2127                                elif C.isEmpty():
2128                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2129                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2130                                else:
2131                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2132                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2133                else:
2134                    for j in range(self.getDim()):
2135                       for l in range(self.getDim()):
2136                          if not C.isEmpty() and not B.isEmpty():
2137                              Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])
2138                          elif C.isEmpty():
2139                              Aout[j,l]+=Xi*B[j]*B[l]
2140                          else:
2141                              Aout[j,l]+=Xi*C[j]*C[l]
2142                     # if not C.isEmpty() and not B.isEmpty():
2143                     #    tmp=C-B
2144                     #    Aout=Aout+Xi*util.outer(tmp,tmp)
2145                     # elif C.isEmpty():
2146                     #    Aout=Aout+Xi*util.outer(B,B)
2147                     # else:
2148                     # Aout=Aout+Xi*util.outer(C,C)
2149             return Aout
2150         elif name == "B" :
2151             B=self.getCoefficient("B")
2152             C=self.getCoefficient("C")
2153             D=self.getCoefficient("D")
2154             if C.isEmpty() or D.isEmpty():
2155                Bout=B
2156             else:
2157                Xi=self.__getXi()
2158                if B.isEmpty():
2159                    Bout=self.createNewCoefficient("B")
2160                else:
2161                    Bout=B[:]
2162                if self.getNumEquations()>1:
2163                   for k in range(self.getNumSolutions()):
2164                      for p in range(self.getNumEquations()):
2165                         tmp=Xi*D[p,k]
2166                         for i in range(self.getNumEquations()):
2167                            for j in range(self.getDim()):
2168                               Bout[i,j,k]+=tmp*C[p,i,j]
2169                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2170                else:
2171                   tmp=Xi*D
2172                   for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2173                   # Bout=Bout+Xi*D*C
2174             return Bout
2175         elif name == "C" :
2176             B=self.getCoefficient("B")
2177             C=self.getCoefficient("C")
2178             D=self.getCoefficient("D")
2179             if B.isEmpty() or D.isEmpty():
2180                Cout=C
2181             else:
2182                Xi=self.__getXi()
2183                if C.isEmpty():
2184                    Cout=self.createNewCoefficient("C")
2185                else:
2186                    Cout=C[:]
2187                if self.getNumEquations()>1:
2188                   for k in range(self.getNumSolutions()):
2189                       for p in range(self.getNumEquations()):
2190                          tmp=Xi*D[p,k]
2191                          for i in range(self.getNumEquations()):
2192                            for l in range(self.getDim()):
2193                                     Cout[i,k,l]+=tmp*B[p,l,i]
2194                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2195                else:
2196                   tmp=Xi*D
2197                   for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2198                   # Cout=Cout+tmp*D*B
2199             return Cout
2200         elif name == "D" :
2201             return self.getCoefficient("D")
2202         elif name == "X" :
2203             X=self.getCoefficient("X")
2204             Y=self.getCoefficient("Y")
2205             B=self.getCoefficient("B")
2206             C=self.getCoefficient("C")
2207             if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):
2208                Xout=X
2209             else:
2210                if X.isEmpty():
2211                    Xout=self.createNewCoefficient("X")
2212                else:
2213                    Xout=X[:]
2214                Xi=self.__getXi()
2215                if self.getNumEquations()>1:
2216                     for p in range(self.getNumEquations()):
2217                        tmp=Xi*Y[p]
2218                        for i in range(self.getNumEquations()):
2219                           for j in range(self.getDim()):
2220                              if not C.isEmpty() and not B.isEmpty():
2221                                 Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2222                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2223                              elif C.isEmpty():
2224                                 Xout[i,j]-=tmp*B[p,j,i]
2225                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2226                              else:
2227                                 Xout[i,j]+=tmp*C[p,i,j]
2228                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2229                else:
2230                     tmp=Xi*Y
2231                     for j in range(self.getDim()):
2232                        if not C.isEmpty() and not B.isEmpty():
2233                           Xout[j]+=tmp*(C[j]-B[j])
2234                           # Xout=Xout+Xi*Y*(C-B)
2235                        elif C.isEmpty():
2236                           Xout[j]-=tmp*B[j]
2237                           # Xout=Xout-Xi*Y*B
2238                        else:
2239                           Xout[j]+=tmp*C[j]
2240                           # Xout=Xout+Xi*Y*C
2241             return Xout
2242         elif name == "Y" :
2243             return self.getCoefficient("Y")
2244         elif name == "d" :
2245             return self.getCoefficient("d")
2246         elif name == "y" :
2247             return self.getCoefficient("y")
2248         elif name == "d_contact" :
2249             return self.getCoefficient("d_contact")
2250         elif name == "y_contact" :
2251             return self.getCoefficient("y_contact")
2252         elif name == "r" :
2253             return self.getCoefficient("r")
2254         elif name == "q" :
2255             return self.getCoefficient("q")
2256         else:
2257            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2258    
2259         @param u argument of the operator  class AdvectionDiffusion(LinearPDE):
2260       """
2261       Class to define PDE equation of the unisotropic advection-diffusion problem, which is genear L{LinearPDE} of the form
2262    
2263         """     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  
2264    
2265     def applyOperator(self,u):     with natural boundary conditons
        """  
        @brief applies the operator of the PDE to a given solution u in weak from  
2266    
2267         @param u argument of the operator     M{n[j]*matrixmult(k,grad(u))[j] = g- S{alpha}u }
2268    
2269         """     and constraints:
        return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())  
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        @brief return the residual of u in the weak from  
2270    
2271         @param u     M{u=r} where M{q>0}
2272         """  
2273         return self.applyOperator(u)-self.getRightHandSide()     and
2274    
2275       M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}
2276    
 class Poisson(LinearPDE):  
2277     """     """
2278     @brief Class to define a Poisson equstion problem:  
2279                                                                                                                                                                   def __init__(self,domain,debug=False):
2280     class to define a linear PDE of the form       """
2281                                                                                                                                                                     initializes a new Poisson equation
2282          -u_{,jj} = f  
2283                                                                                                                                                                     @param domain: domain of the PDE
2284       with boundary conditons:       @type domain: L{Domain<escript.Domain>}
2285                                                                                                                                                                     @param debug: if True debug informations are printed.
2286          n_j*u_{,j} = 0  
2287                                                                                                                                                                     """
2288      and constraints:       super(AdvectionDiffusion, self).__init__(domain,1,1,debug)
2289                                                                                                                                                                     self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2290           u=0 where q>0                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
2291                                                                                                                                                                                        "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2292     """                          "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2293                            "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2294     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2295         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2296         self._setValue(A=numarray.identity(self.getDomain().getDim()))                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2297         self.setSymmetryOn()                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2298         self.setValue(f,q)  
2299       def setValue(self,**coefficients):
2300     def setValue(self,f=escript.Data(),q=escript.Data()):       """
2301         self._setValue(Y=f,q=q)       sets new values to coefficients
2302    
2303                                                                                                                                                                   @param coefficients: new values assigned to coefficients
2304         @keyword omega: value for coefficient M{S{omega}}
2305         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2306         @keyword k: value for coefficient M{k}
2307         @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.
2308         @keyword v: value for coefficient M{v}
2309         @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2310         @keyword upwind: value for upwind term M{upwind}
2311         @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2312         @keyword f: value for right hand side M{f}
2313         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2314         @keyword alpha: value for right hand side M{S{alpha}}
2315         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2316         @keyword g: value for right hand side M{g}
2317         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2318         @keyword r: prescribed values M{r} for the solution in constraints.
2319         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2320                   depending of reduced order is used for the representation of the equation.
2321         @keyword q: mask for location of constraints
2322         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2323                   depending of reduced order is used for the representation of the equation.
2324         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2325         """
2326         super(AdvectionDiffusion, self).setValue(**coefficients)
2327    
2328       def getCoefficientOfGeneralPDE(self,name):
2329         """
2330         return the value of the coefficient name of the general PDE
2331    
2332         @param name: name of the coefficient requested.
2333         @type name: C{string}
2334         @return: the value of the coefficient  name
2335         @rtype: L{Data<escript.Data>}
2336         @raise IllegalCoefficient: if name is not one of coefficients
2337                      "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}.
2338         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2339         """
2340         if name == "A" :
2341             return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))
2342         elif name == "B" :
2343             return escript.Data()
2344         elif name == "C" :
2345             return self.getCoefficient("v")
2346         elif name == "D" :
2347             return self.getCoefficient("omega")
2348         elif name == "X" :
2349             return escript.Data()
2350         elif name == "Y" :
2351             return self.getCoefficient("f")
2352         elif name == "d" :
2353             return self.getCoefficient("alpha")
2354         elif name == "y" :
2355             return self.getCoefficient("g")
2356         elif name == "d_contact" :
2357             return escript.Data()
2358         elif name == "y_contact" :
2359             return escript.Data()
2360         elif name == "r" :
2361             return self.getCoefficient("r")
2362         elif name == "q" :
2363             return self.getCoefficient("q")
2364         else:
2365            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2366    
2367    
2368  # $Log$  # $Log$
2369  # Revision 1.3  2004/12/17 07:43:10  jgs  # Revision 1.14  2005/09/22 01:54:57  jgs
2370  # *** empty log message ***  # Merge of development branch dev-02 back to main trunk on 2005-09-22
2371    #
2372    # Revision 1.13  2005/09/15 03:44:19  jgs
2373    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2374    #
2375    # Revision 1.12  2005/09/01 03:31:28  jgs
2376    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2377    #
2378    # Revision 1.11  2005/08/23 01:24:28  jgs
2379    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2380    #
2381    # Revision 1.10  2005/08/12 01:45:36  jgs
2382    # erge of development branch dev-02 back to main trunk on 2005-08-12
2383    #
2384    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2385    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2386    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2387    # modified to instead use portable/cooperative "super" calls to extend base
2388    # class methods.
2389    #
2390    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2391    # Removed redundant if-loop.
2392    #
2393    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2394    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2395    #
2396    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2397    # the solver from finley are put into the standalone package paso now
2398    #
2399    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2400    # in the case of lumping no new system is allocated if the constraint is changed.
2401    #
2402    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2403    # test for Lumping added
2404    #
2405    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2406    # bug in format fixed.
2407    #
2408    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2409    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2410    #
2411    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2412    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2413    #
2414    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2415    # gneric unit testing for linearPDE
2416    #
2417    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2418    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2419    #
2420    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2421    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2422    #
2423    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2424    # epydoc mark up partially fixed
2425    #
2426    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2427    # some problems with LinearPDEs fixed.
2428    #
2429    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2430    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2431    #
2432    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2433    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2434    #
2435    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2436    # new functions in util and a new pde type in linearPDEs
2437    #
2438    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2439    # Lame equation: (linear elastic, isotropic) added
2440    #
2441    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2442    # some extensions to modellib and linearPDEs
2443    #
2444    # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2445    # Fixed up some docstrings.  Moved module-level functions to top of file so
2446    # that epydoc and doxygen can pick them up properly.
2447    #
2448    # Revision 1.1.2.22  2005/05/12 11:41:30  gross
2449    # some basic Models have been added
2450    #
2451    # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane
2452    # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of
2453    # file so that the AdvectivePDE class is picked up by doxygen.  Some
2454    # reformatting of docstrings.  Addition of code to make equations come out
2455    # as proper LaTeX.
2456    #
2457    # Revision 1.1.2.20  2005/04/15 07:09:08  gross
2458    # some problems with functionspace and linearPDEs fixed.
2459    #
2460    # Revision 1.1.2.19  2005/03/04 05:27:07  gross
2461    # bug in SystemPattern fixed.
2462    #
2463    # Revision 1.1.2.18  2005/02/08 06:16:45  gross
2464    # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed
2465    #
2466    # Revision 1.1.2.17  2005/02/08 05:56:19  gross
2467    # Reference Number handling added
2468    #
2469    # Revision 1.1.2.16  2005/02/07 04:41:28  gross
2470    # some function exposed to python to make mesh merging running
2471    #
2472    # Revision 1.1.2.15  2005/02/03 00:14:44  gross
2473    # timeseries add and ESySParameter.py renames esysXML.py for consistence
2474    #
2475    # Revision 1.1.2.14  2005/02/01 06:44:10  gross
2476    # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working
2477    #
2478    # Revision 1.1.2.13  2005/01/25 00:47:07  gross
2479    # updates in the documentation
2480    #
2481    # Revision 1.1.2.12  2005/01/12 01:28:04  matt
2482    # Added createCoefficient method for linearPDEs.
2483    #
2484    # Revision 1.1.2.11  2005/01/11 01:55:34  gross
2485    # a problem in linearPDE class fixed
2486    #
2487    # Revision 1.1.2.10  2005/01/07 01:13:29  gross
2488    # some bugs in linearPDE fixed
2489    #
2490    # Revision 1.1.2.9  2005/01/06 06:24:58  gross
2491    # some bugs in slicing fixed
2492    #
2493    # Revision 1.1.2.8  2005/01/05 04:21:40  gross
2494    # FunctionSpace checking/matchig in slicing added
2495    #
2496    # Revision 1.1.2.7  2004/12/29 10:03:41  gross
2497    # bug in setValue fixed
2498    #
2499    # Revision 1.1.2.6  2004/12/29 05:29:59  gross
2500    # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()
2501    #
2502    # Revision 1.1.2.5  2004/12/29 00:18:41  gross
2503    # AdvectivePDE added
2504    #
2505    # Revision 1.1.2.4  2004/12/24 06:05:41  gross
2506    # some changes in linearPDEs to add AdevectivePDE
2507  #  #
2508  # Revision 1.1.2.3  2004/12/16 00:12:34  gross  # Revision 1.1.2.3  2004/12/16 00:12:34  gross
2509  # __init__ of LinearPDE does not accept any coefficients anymore  # __init__ of LinearPDE does not accept any coefficient anymore
2510  #  #
2511  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs
2512  # *** empty log message ***  # *** empty log message ***
# Line 998  class Poisson(LinearPDE): Line 2550  class Poisson(LinearPDE):
2550  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2551  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2552  #  #
 #  

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