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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 531 by gross, Wed Feb 15 08:11:10 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       @cvar AMG: algebraic multi grid
423       @cvar RILU: recursive ILU
424    
425       """
426       DEFAULT= 0
427       DIRECT= 1
428       CHOLEVSKY= 2
429       PCG= 3
430       CR= 4
431       CGS= 5
432       BICGSTAB= 6
433       SSOR= 7
434       ILU0= 8
435       ILUT= 9
436       JACOBI= 10
437       GMRES= 11
438       PRES20= 12
439       LUMPING= 13
440       NO_REORDERING= 17
441       MINIMUM_FILL_IN= 18
442       NESTED_DISSECTION= 19
443       SCSL= 14
444       MKL= 15
445       UMFPACK= 16
446       ITERATIVE= 20
447       PASO= 21
448       AMG= 22
449       RILU = 23
450    
451       __TOL=1.e-13
452       __PACKAGE_KEY="package"
453       __METHOD_KEY="method"
454       __SYMMETRY_KEY="symmetric"
455       __TOLERANCE_KEY="tolerance"
456       __PRECONDITIONER_KEY="preconditioner"
457    
458    
459       def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
460         """
461         initializes a new linear PDE
462    
463         @param domain: domain of the PDE
464         @type domain: L{Domain<escript.Domain>}
465         @param numEquations: number of equations. If numEquations==None the number of equations
466                              is exracted from the PDE coefficients.
467         @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
468                              is exracted from the PDE coefficients.
469         @param debug: if True debug informations are printed.
470    
471         """
472         super(LinearPDE, self).__init__()
473         #
474         #   the coefficients of the general PDE:
475         #
476         self.__COEFFICIENTS_OF_GENEARL_PDE={
477           "A"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
478           "B"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
479           "C"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
480           "D"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
481           "X"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
482           "Y"         : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
483           "d"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
484           "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
485           "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
486           "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
487           "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
488           "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
489    
490         # COEFFICIENTS can be overwritten by subclasses:
491         self.COEFFICIENTS=self.__COEFFICIENTS_OF_GENEARL_PDE
492         self.__altered_coefficients=False
493       # initialize attributes       # initialize attributes
494       self.__debug=None       self.__debug=debug
495       self.__domain=domain       self.__domain=domain
496       self.__numEquations=numEquations       self.__numEquations=numEquations
497       self.__numSolutions=numSolutions       self.__numSolutions=numSolutions
498       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  
499    
500       # set some default values:       # set some default values:
501       self.__homogeneous_constraint=True       self.__reduce_equation_order=False
502       self.__row_function_space=escript.Solution(self.__domain)       self.__reduce_solution_order=False
      self.__column_function_space=escript.Solution(self.__domain)  
503       self.__tolerance=1.e-8       self.__tolerance=1.e-8
504       self.__solver_method=util.DEFAULT_METHOD       self.__solver_method=self.DEFAULT
505       self.__matrix_type=self.__domain.getSystemMatrixTypeId(util.DEFAULT_METHOD,False)       self.__solver_package=self.DEFAULT
506         self.__preconditioner=self.DEFAULT
507         self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
508       self.__sym=False       self.__sym=False
      self.__lumping=False  
509    
510     def getCoefficient(self,name):       self.resetCoefficients()
511         self.trace("PDE Coeffients are %s"%str(self.COEFFICIENTS.keys()))
512       # =============================================================================
513       #    general stuff:
514       # =============================================================================
515       def __str__(self):
516         """
517         returns string representation of the PDE
518    
519         @return: a simple representation of the PDE
520         @rtype: C{str}
521         """
522         return "<LinearPDE %d>"%id(self)
523       # =============================================================================
524       #    debug :
525       # =============================================================================
526       def setDebugOn(self):
527         """
528         switches on debugging
529       """       """
530       @brief return the value of the coefficient name       self.__debug=not None
531    
532       @param name     def setDebugOff(self):
533         """
534         switches off debugging
535       """       """
536       return self.__coefficient[name]       self.__debug=None
537    
538     def setValue(self,**coefficients):     def trace(self,text):
539        """       """
540        @brief sets new values to coefficients       print the text message if debugging is swiched on.
541         @param text: message
542         @type text: C{string}
543         """
544         if self.__debug: print "%s: %s"%(str(self),text)
545    
546        @param coefficients     # =============================================================================
547        """     # some service functions:
548        self._setValue(**coefficients)     # =============================================================================
549             def getDomain(self):
550         """
551         returns the domain of the PDE
552    
553     def _setValue(self,**coefficients):       @return: the domain of the PDE
554        """       @rtype: L{Domain<escript.Domain>}
555        @brief sets new values to coefficients       """
556         return self.__domain
557    
558        @param coefficients     def getDim(self):
559        """       """
560               returns the spatial dimension of the PDE
       # get the dictionary of the coefficinets been altered:  
       alteredCoefficients={}  
       for i,d in coefficients.iteritems():  
          if self.hasCoefficient(i):  
             if d == None:  
                 alteredCoefficients[i]=escript.Data()  
             elif isinstance(d,escript.Data):  
                 if d.isEmpty():  
                   alteredCoefficients[i]=escript.Data()  
                 else:  
                   alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
             else:  
                 alteredCoefficients[i]=escript.Data(d,self.getFunctionSpaceOfCoefficient(i))  
          else:  
             raise ValueError,"Attempt to set undefined coefficient %s"%i  
       # if numEquations and numSolutions is undefined we try identify their values based on the coefficients:  
       if self.__numEquations<1 or self.__numSolutions<1:  
             numEquations,numSolutions=identifyNumEquationsAndSolutions(self.getDomain().getDim(),alteredCoefficients)  
             if self.__numEquations<1 and numEquations>0: self.__numEquations=numEquations  
             if self.__numSolutions<1 and numSolutions>0: self.__numSolutions=numSolutions  
             if self.debug() and self.__numEquations>0: print "PDE Debug: identified number of equations is ",self.__numEquations  
             if self.debug() and self.__numSolutions>0: print "PDE Debug: identified number of solutions is ",self.__numSolutions  
561    
562        # now we check the shape of the coefficient if numEquations and numSolutions are set:       @return: the spatial dimension of the PDE domain
563        if  self.__numEquations>0 and  self.__numSolutions>0:       @rtype: C{int}
564           for i in self.__coefficient.iterkeys():       """
565               if alteredCoefficients.has_key(i) and not alteredCoefficients[i].isEmpty():       return self.getDomain().getDim()
                  if not self.getShapeOfCoefficient(i)==alteredCoefficients[i].getShape():  
                     raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),alteredCoefficients[i].getShape())  
              else:  
                  if not self.__coefficient[i].isEmpty():  
                     if not self.getShapeOfCoefficient(i)==self.__coefficient[i].getShape():  
                        raise ValueError,"Expected shape for coefficient %s is %s but actual shape is %s."%(i,self.getShapeOfCoefficient(i),self.__coefficient[i].getShape())  
       # overwrite new values:  
       for i,d in alteredCoefficients.iteritems():  
          if self.debug(): print "PDE Debug: Coefficient %s has been altered."%i  
          self.__coefficient[i]=d  
          self.alteredCoefficient(i)  
   
       # reset the HomogeneousConstraintFlag:  
       self.__setHomogeneousConstraintFlag()  
       if not "q" in alteredCoefficients and not self.__homogeneous_constraint: self.__rebuildSystem()  
   
    def cleanCoefficients(self):  
      """  
      @brief resets all coefficients to default values.  
      """  
      self.__coefficient={}  
      for i in _PDECoefficientTypes.iterkeys():  
          self.__coefficient[i]=escript.Data()  
566    
567     def getShapeOfCoefficient(self,name):     def getNumEquations(self):
568       """       """
569       @brief return the shape of the coefficient name       returns the number of equations
570    
571       @param name       @return: the number of equations
572         @rtype: C{int}
573         @raise UndefinedPDEError: if the number of equations is not be specified yet.
574       """       """
575       if self.hasCoefficient(name):       if self.__numEquations==None:
576          return _PDECoefficientTypes[name].buildShape(self.getNumEquations(),self.getNumSolutions(),self.getDomain().getDim())           raise UndefinedPDEError,"Number of equations is undefined. Please specify argument numEquations."
577       else:       else:
578          raise ValueError,"Solution coefficient %s requested"%name           return self.__numEquations
579    
580     def getFunctionSpaceOfCoefficient(self,name):     def getNumSolutions(self):
581       """       """
582       @brief return the atoms of the coefficient name       returns the number of unknowns
583    
584       @param name       @return: the number of unknowns
585         @rtype: C{int}
586         @raise UndefinedPDEError: if the number of unknowns is not be specified yet.
587       """       """
588       if self.hasCoefficient(name):       if self.__numSolutions==None:
589          return _PDECoefficientTypes[name].getFunctionSpace(self.getDomain())          raise UndefinedPDEError,"Number of solution is undefined. Please specify argument numSolutions."
590       else:       else:
591          raise ValueError,"Solution coefficient %s requested"%name          return self.__numSolutions
592    
593     def alteredCoefficient(self,name):     def reduceEquationOrder(self):
594       """       """
595       @brief annonced that coefficient name has been changed       return status for order reduction for equation
596    
597       @param name       @return: return True is reduced interpolation order is used for the represenation of the equation
598         @rtype: L{bool}
599       """       """
600       if self.hasCoefficient(name):       return self.__reduce_equation_order
         if _PDECoefficientTypes[name].isAlteringOperator(): self.__rebuildOperator()  
         if _PDECoefficientTypes[name].isAlteringRightHandSide(): self.__rebuildRightHandSide()  
      else:  
         raise ValueError,"Solution coefficient %s requested"%name  
601    
602     def __setHomogeneousConstraintFlag(self):     def reduceSolutionOrder(self):
603        """       """
604        @brief checks if the constraints are homogeneous and sets self.__homogeneous_constraint accordingly.       return status for order reduction for the solution
       """  
       self.__homogeneous_constraint=True  
       q=self.getCoefficient("q")  
       r=self.getCoefficient("r")  
       if not q.isEmpty() and not r.isEmpty():  
          print (q*r).Lsup(), 1.e-13*r.Lsup()  
          if (q*r).Lsup()>=1.e-13*r.Lsup(): self.__homogeneous_constraint=False  
       if self.debug():  
            if self.__homogeneous_constraint:  
                print "PDE Debug: Constraints are homogeneous."  
            else:  
                print "PDE Debug: Constraints are inhomogeneous."  
   
   
    def hasCoefficient(self,name):  
       """  
       @brief return true if name is the name of a coefficient  
605    
606        @param name       @return: return True is reduced interpolation order is used for the represenation of the solution
607        """       @rtype: L{bool}
608        return self.__coefficient.has_key(name)       """
609         return self.__reduce_solution_order
610    
611     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
612       """       """
613       @brief return true if the test functions should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
614    
615         @return: representation space of equation
616         @rtype: L{FunctionSpace<escript.FunctionSpace>}
617       """       """
618       return self.__row_function_space       if self.reduceEquationOrder():
619             return escript.ReducedSolution(self.getDomain())
620         else:
621             return escript.Solution(self.getDomain())
622    
623     def getFunctionSpaceForSolution(self):     def getFunctionSpaceForSolution(self):
624       """       """
625       @brief return true if the interpolation of the solution should use reduced order       returns the L{FunctionSpace<escript.FunctionSpace>} used to represent the solution
626    
627         @return: representation space of solution
628         @rtype: L{FunctionSpace<escript.FunctionSpace>}
629       """       """
630       return self.__column_function_space       if self.reduceSolutionOrder():
631             return escript.ReducedSolution(self.getDomain())
632         else:
633             return escript.Solution(self.getDomain())
634    
635     # ===== debug ==============================================================  
636     def setDebugOn(self):     def getOperator(self):
637         """
638         provides access to the operator of the PDE
639    
640         @return: the operator of the PDE
641         @rtype: L{Operator<escript.Operator>}
642         """
643         m=self.getSystem()[0]
644         if self.isUsingLumping():
645             return self.copyConstraint(1./m)
646         else:
647             return m
648    
649       def getRightHandSide(self):
650         """
651         provides access to the right hand side of the PDE
652         @return: the right hand side of the PDE
653         @rtype: L{Data<escript.Data>}
654         """
655         r=self.getSystem()[1]
656         if self.isUsingLumping():
657             return self.copyConstraint(r)
658         else:
659             return r
660    
661       def applyOperator(self,u=None):
662         """
663         applies the operator of the PDE to a given u or the solution of PDE if u is not present.
664    
665         @param u: argument of the operator. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
666                   the current solution is used.
667         @type u: L{Data<escript.Data>} or None
668         @return: image of u
669         @rtype: L{Data<escript.Data>}
670         """
671         if u==None:
672              return self.getOperator()*self.getSolution()
673         else:
674            self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
675    
676       def getResidual(self,u=None):
677         """
678         return the residual of u or the current solution if u is not present.
679    
680         @param u: argument in the residual calculation. It must be representable in C{elf.getFunctionSpaceForSolution()}. If u is not present or equals L{None}
681                   the current solution is used.
682         @type u: L{Data<escript.Data>} or None
683         @return: residual of u
684         @rtype: L{Data<escript.Data>}
685         """
686         return self.applyOperator(u)-self.getRightHandSide()
687    
688       def checkSymmetry(self,verbose=True):
689          """
690          test the PDE for symmetry.
691    
692          @param verbose: if equal to True or not present a report on coefficients which are breaking the symmetry is printed.
693          @type verbose: C{bool}
694          @return:  True if the PDE is symmetric.
695          @rtype: L{Data<escript.Data>}
696          @note: This is a very expensive operation. It should be used for degugging only! The symmetry flag is not altered.
697          """
698          verbose=verbose or self.__debug
699          out=True
700          if self.getNumSolutions()!=self.getNumEquations():
701             if verbose: print "non-symmetric PDE because of different number of equations and solutions"
702             out=False
703          else:
704             A=self.getCoefficientOfGeneralPDE("A")
705             if not A.isEmpty():
706                tol=util.Lsup(A)*self.__TOL
707                if self.getNumSolutions()>1:
708                   for i in range(self.getNumEquations()):
709                      for j in range(self.getDim()):
710                         for k in range(self.getNumSolutions()):
711                            for l in range(self.getDim()):
712                                if util.Lsup(A[i,j,k,l]-A[k,l,i,j])>tol:
713                                   if verbose: print "non-symmetric PDE because A[%d,%d,%d,%d]!=A[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
714                                   out=False
715                else:
716                   for j in range(self.getDim()):
717                      for l in range(self.getDim()):
718                         if util.Lsup(A[j,l]-A[l,j])>tol:
719                            if verbose: print "non-symmetric PDE because A[%d,%d]!=A[%d,%d]"%(j,l,l,j)
720                            out=False
721             B=self.getCoefficientOfGeneralPDE("B")
722             C=self.getCoefficientOfGeneralPDE("C")
723             if B.isEmpty() and not C.isEmpty():
724                if verbose: print "non-symmetric PDE because B is not present but C is"
725                out=False
726             elif not B.isEmpty() and C.isEmpty():
727                if verbose: print "non-symmetric PDE because C is not present but B is"
728                out=False
729             elif not B.isEmpty() and not C.isEmpty():
730                tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.
731                if self.getNumSolutions()>1:
732                   for i in range(self.getNumEquations()):
733                       for j in range(self.getDim()):
734                          for k in range(self.getNumSolutions()):
735                             if util.Lsup(B[i,j,k]-C[k,i,j])>tol:
736                                  if verbose: print "non-symmetric PDE because B[%d,%d,%d]!=C[%d,%d,%d]"%(i,j,k,k,i,j)
737                                  out=False
738                else:
739                   for j in range(self.getDim()):
740                      if util.Lsup(B[j]-C[j])>tol:
741                         if verbose: print "non-symmetric PDE because B[%d]!=C[%d]"%(j,j)
742                         out=False
743             if self.getNumSolutions()>1:
744               D=self.getCoefficientOfGeneralPDE("D")
745               if not D.isEmpty():
746                 tol=util.Lsup(D)*self.__TOL
747                 for i in range(self.getNumEquations()):
748                    for k in range(self.getNumSolutions()):
749                      if util.Lsup(D[i,k]-D[k,i])>tol:
750                          if verbose: print "non-symmetric PDE because D[%d,%d]!=D[%d,%d]"%(i,k,k,i)
751                          out=False
752               d=self.getCoefficientOfGeneralPDE("d")
753               if not d.isEmpty():
754                 tol=util.Lsup(d)*self.__TOL
755                 for i in range(self.getNumEquations()):
756                    for k in range(self.getNumSolutions()):
757                      if util.Lsup(d[i,k]-d[k,i])>tol:
758                          if verbose: print "non-symmetric PDE because d[%d,%d]!=d[%d,%d]"%(i,k,k,i)
759                          out=False
760               d_contact=self.getCoefficientOfGeneralPDE("d_contact")
761               if not d_contact.isEmpty():
762                 tol=util.Lsup(d_contact)*self.__TOL
763                 for i in range(self.getNumEquations()):
764                    for k in range(self.getNumSolutions()):
765                      if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
766                          if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
767                          out=False
768          return out
769    
770       def getSolution(self,**options):
771         """         """
772         @brief         returns the solution of the PDE. If the solution is not valid the PDE is solved.
773    
774           @return: the solution
775           @rtype: L{Data<escript.Data>}
776           @param options: solver options
777           @keyword verbose: True to get some information during PDE solution
778           @type verbose: C{bool}
779           @keyword reordering: reordering scheme to be used during elimination. Allowed values are
780                                L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
781           @keyword iter_max: maximum number of iteration steps allowed.
782           @keyword drop_tolerance: threshold for drupping in L{ILUT}
783           @keyword drop_storage: maximum of allowed memory in L{ILUT}
784           @keyword truncation: maximum number of residuals in L{GMRES}
785           @keyword restart: restart cycle length in L{GMRES}
786         """         """
787         self.__debug=not None         if not self.__solution_isValid:
788              mat,f=self.getSystem()
789              if self.isUsingLumping():
790                 self.__solution=self.copyConstraint(f*mat)
791              else:
792                 options[self.__TOLERANCE_KEY]=self.getTolerance()
793                 options[self.__METHOD_KEY]=self.getSolverMethod()[0]
794                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
795                 options[self.__PACKAGE_KEY]=self.getSolverPackage()
796                 options[self.__SYMMETRY_KEY]=self.isSymmetric()
797                 self.trace("PDE is resolved.")
798                 self.trace("solver options: %s"%str(options))
799                 self.__solution=mat.solve(f,options)
800              self.__solution_isValid=True
801           return self.__solution
802    
803     def setDebugOff(self):     def getFlux(self,u=None):
804         """
805         returns the flux M{J} for a given M{u}
806    
807         M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
808    
809         or
810    
811         M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
812    
813         @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
814         @type u: L{Data<escript.Data>} or None
815         @return: flux
816         @rtype: L{Data<escript.Data>}
817         """
818         if u==None: u=self.getSolution()
819         return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")
820       # =============================================================================
821       #   solver settings:
822       # =============================================================================
823       def setSolverMethod(self,solver=None,preconditioner=None):
824         """         """
825         @brief         sets a new solver
826    
827           @param solver: sets a new solver method.
828           @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, L{AMG}
829           @param preconditioner: sets a new solver method.
830           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
831         """         """
832         self.__debug=None         if solver==None: solve=self.DEFAULT
833           if preconditioner==None: preconditioner=self.DEFAULT
834           if not (solver,preconditioner)==self.getSolverMethod():
835               self.__solver_method=solver
836               self.__preconditioner=preconditioner
837               self.__checkMatrixType()
838               self.trace("New solver is %s"%self.getSolverMethodName())
839    
840     def debug(self):     def getSolverMethodName(self):
841         """         """
842         @brief returns true if the PDE is in the debug mode         returns the name of the solver currently used
843    
844           @return: the name of the solver currently used.
845           @rtype: C{string}
846         """         """
        return self.__debug  
847    
848     #===== Lumping ===========================         m=self.getSolverMethod()
849     def setLumpingOn(self):         p=self.getSolverPackage()
850        """         method=""
851        @brief indicates to use matrix lumping         if m[0]==self.DEFAULT: method="DEFAULT"
852        """         elif m[0]==self.DIRECT: method= "DIRECT"
853        if not self.isUsingLumping():         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
854           raise SystemError,"Lumping is not working yet! Talk to the experts"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
855           if self.debug() : print "PDE Debug: lumping is set on"         elif m[0]==self.PCG: method= "PCG"
856           self.__rebuildOperator()         elif m[0]==self.CR: method= "CR"
857           self.__lumping=True         elif m[0]==self.CGS: method= "CGS"
858           elif m[0]==self.BICGSTAB: method= "BICGSTAB"
859           elif m[0]==self.SSOR: method= "SSOR"
860           elif m[0]==self.GMRES: method= "GMRES"
861           elif m[0]==self.PRES20: method= "PRES20"
862           elif m[0]==self.LUMPING: method= "LUMPING"
863           elif m[0]==self.AMG: method= "AMG"
864           if m[1]==self.DEFAULT: method+="+DEFAULT"
865           elif m[1]==self.JACOBI: method+= "+JACOBI"
866           elif m[1]==self.ILU0: method+= "+ILU0"
867           elif m[1]==self.ILUT: method+= "+ILUT"
868           elif m[1]==self.SSOR: method+= "+SSOR"
869           elif m[1]==self.AMG: method+= "+AMG"
870           elif m[1]==self.RILU: method+= "+RILU"
871           if p==self.DEFAULT: package="DEFAULT"
872           elif p==self.PASO: package= "PASO"
873           elif p==self.MKL: package= "MKL"
874           elif p==self.SCSL: package= "SCSL"
875           elif p==self.UMFPACK: package= "UMFPACK"
876           else : method="unknown"
877           return "%s solver of %s package"%(method,package)
878    
    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  
879    
880     def setLumping(self,flag=False):     def getSolverMethod(self):
881        """         """
882        @brief set the matrix lumping flag to flag         returns the solver method
       """  
       if flag:  
          self.setLumpingOn()  
       else:  
          self.setLumpingOff()  
883    
884     def isUsingLumping(self):         @return: the solver method currently be used.
885        """         @rtype: C{int}
886        @brief         """
887        """         return self.__solver_method,self.__preconditioner
       return self.__lumping  
888    
889     #============ method business =========================================================     def setSolverPackage(self,package=None):
    def setSolverMethod(self,solver=util.DEFAULT_METHOD):  
890         """         """
891         @brief sets a new solver         sets a new solver package
892    
893           @param solver: sets a new solver method.
894           @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}
895         """         """
896         if not solver==self.getSolverMethod():         if package==None: package=self.DEFAULT
897           if not package==self.getSolverPackage():
898             self.__solver_method=solver             self.__solver_method=solver
            if self.debug() : print "PDE Debug: New solver is %s"%solver  
899             self.__checkMatrixType()             self.__checkMatrixType()
900               self.trace("New solver is %s"%self.getSolverMethodName())
901    
902     def getSolverMethod(self):     def getSolverPackage(self):
903         """         """
904         @brief returns the solver method         returns the package of the solver
905    
906           @return: the solver package currently being used.
907           @rtype: C{int}
908         """         """
909         return self.__solver_method         return self.__solver_package
910    
911       def isUsingLumping(self):
912          """
913          checks if matrix lumping is used a solver method
914    
915          @return: True is lumping is currently used a solver method.
916          @rtype: C{bool}
917          """
918          return self.getSolverMethod()[0]==self.LUMPING
919    
    #============ tolerance business =========================================================  
920     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
921         """         """
922         @brief resets the tolerance to tol.         resets the tolerance for the solver method to tol where for an appropriate norm M{|.|}
923    
924           M{|L{getResidual}()|<tol*|L{getRightHandSide}()|}
925    
926           defines the stopping criterion.
927    
928           @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
929                       the system will be resolved.
930           @type tol: positive C{float}
931           @raise ValueException: if tolerance is not positive.
932         """         """
933         if not tol>0:         if not tol>0:
934             raise ValueException,"Tolerance as to be positive"             raise ValueException,"Tolerance as to be positive"
935         if tol<self.getTolerance(): self.__rebuildSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
936         if self.debug() : print "PDE Debug: New tolerance %e",tol         self.trace("New tolerance %e"%tol)
937         self.__tolerance=tol         self.__tolerance=tol
938         return         return
939    
940     def getTolerance(self):     def getTolerance(self):
941         """         """
942         @brief returns the tolerance set for the solution         returns the tolerance set for the solution
943    
944           @return: tolerance currently used.
945           @rtype: C{float}
946         """         """
947         return self.__tolerance         return self.__tolerance
948    
949     #===== symmetry  flag ==========================     # =============================================================================
950       #    symmetry  flag:
951       # =============================================================================
952     def isSymmetric(self):     def isSymmetric(self):
953        """        """
954        @brief returns true is the operator is considered to be symmetric        checks if symmetry is indicated.
955    
956          @return: True is a symmetric PDE is indicated, otherwise False is returned
957          @rtype: C{bool}
958        """        """
959        return self.__sym        return self.__sym
960    
961     def setSymmetryOn(self):     def setSymmetryOn(self):
962        """        """
963        @brief sets the symmetry flag to true        sets the symmetry flag.
964        """        """
965        if not self.isSymmetric():        if not self.isSymmetric():
966           if self.debug() : print "PDE Debug: Operator is set to be symmetric"           self.trace("PDE is set to be symmetric")
967           self.__sym=True           self.__sym=True
968           self.__checkMatrixType()           self.__checkMatrixType()
969    
970     def setSymmetryOff(self):     def setSymmetryOff(self):
971        """        """
972        @brief sets the symmetry flag to false        removes the symmetry flag.
973        """        """
974        if self.isSymmetric():        if self.isSymmetric():
975           if self.debug() : print "PDE Debug: Operator is set to be unsymmetric"           self.trace("PDE is set to be unsymmetric")
976           self.__sym=False           self.__sym=False
977           self.__checkMatrixType()           self.__checkMatrixType()
978    
979     def setSymmetryTo(self,flag=False):     def setSymmetryTo(self,flag=False):
980       """        """
981       @brief sets the symmetry flag to flag        sets the symmetry flag to flag
982    
983       @param flag        @param flag: If flag, the symmetry flag is set otherwise the symmetry flag is released.
984       """        @type flag: C{bool}
985       if flag:        """
986          self.setSymmetryOn()        if flag:
987       else:           self.setSymmetryOn()
988          self.setSymmetryOff()        else:
989             self.setSymmetryOff()
990    
991     #===== order reduction ==========================     # =============================================================================
992       # function space handling for the equation as well as the solution
993       # =============================================================================
994     def setReducedOrderOn(self):     def setReducedOrderOn(self):
995       """       """
996       @brief switches to on reduced order       switches on reduced order for solution and equation representation
997    
998         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
999       """       """
1000       self.setReducedOrderForSolutionOn()       self.setReducedOrderForSolutionOn()
1001       self.setReducedOrderForEquationOn()       self.setReducedOrderForEquationOn()
1002    
1003     def setReducedOrderOff(self):     def setReducedOrderOff(self):
1004       """       """
1005       @brief switches to full order       switches off reduced order for solution and equation representation
1006    
1007         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1008       """       """
1009       self.setReducedOrderForSolutionOff()       self.setReducedOrderForSolutionOff()
1010       self.setReducedOrderForEquationOff()       self.setReducedOrderForEquationOff()
1011    
1012     def setReducedOrderTo(self,flag=False):     def setReducedOrderTo(self,flag=False):
1013       """       """
1014       @brief sets order according to flag       sets order reduction for both solution and equation representation according to flag.
1015         @param flag: if flag is True, the order reduction is switched on for both  solution and equation representation, otherwise or
1016       @param flag                    if flag is not present order reduction is switched off
1017         @type flag: C{bool}
1018         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1019       """       """
1020       self.setReducedOrderForSolutionTo(flag)       self.setReducedOrderForSolutionTo(flag)
1021       self.setReducedOrderForEquationTo(flag)       self.setReducedOrderForEquationTo(flag)
                                                                                                                                                             
1022    
1023     #===== order reduction solution ==========================  
1024     def setReducedOrderForSolutionOn(self):     def setReducedOrderForSolutionOn(self):
1025       """       """
1026       @brief switches to reduced order to interpolate solution       switches on reduced order for solution representation
1027    
1028         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1029       """       """
1030       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_solution_order:
1031       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1032           if self.debug() : print "PDE Debug: Reduced order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1033           self.__column_function_space=new_fs           self.trace("Reduced order is used to solution representation.")
1034           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=True
1035             self.__resetSystem()
1036    
1037     def setReducedOrderForSolutionOff(self):     def setReducedOrderForSolutionOff(self):
1038       """       """
1039       @brief switches to full order to interpolate solution       switches off reduced order for solution representation
1040    
1041         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1042       """       """
1043       new_fs=escript.Solution(self.getDomain())       if self.__reduce_solution_order:
1044       if self.getFunctionSpaceForSolution()!=new_fs:           if self.__altered_coefficients:
1045           if self.debug() : print "PDE Debug: Full order is used to interpolate solution."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1046           self.__column_function_space=new_fs           self.trace("Full order is used to interpolate solution.")
1047           self.__rebuildSystem(deep=True)           self.__reduce_solution_order=False
1048             self.__resetSystem()
1049    
1050     def setReducedOrderForSolutionTo(self,flag=False):     def setReducedOrderForSolutionTo(self,flag=False):
1051       """       """
1052       @brief sets order for test functions according to flag       sets order for test functions according to flag
1053    
1054       @param flag       @param flag: if flag is True, the order reduction is switched on for solution representation, otherwise or
1055                      if flag is not present order reduction is switched off
1056         @type flag: C{bool}
1057         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1058       """       """
1059       if flag:       if flag:
1060          self.setReducedOrderForSolutionOn()          self.setReducedOrderForSolutionOn()
1061       else:       else:
1062          self.setReducedOrderForSolutionOff()          self.setReducedOrderForSolutionOff()
1063                                                                                                                                                              
    #===== order reduction equation ==========================  
1064     def setReducedOrderForEquationOn(self):     def setReducedOrderForEquationOn(self):
1065       """       """
1066       @brief switches to reduced order for test functions       switches on reduced order for equation representation
1067    
1068         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1069       """       """
1070       new_fs=escript.ReducedSolution(self.getDomain())       if not self.__reduce_equation_order:
1071       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1072           if self.debug() : print "PDE Debug: Reduced order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1073           self.__row_function_space=new_fs           self.trace("Reduced order is used for test functions.")
1074           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=True
1075             self.__resetSystem()
1076    
1077     def setReducedOrderForEquationOff(self):     def setReducedOrderForEquationOff(self):
1078       """       """
1079       @brief switches to full order for test functions       switches off reduced order for equation representation
1080    
1081         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1082       """       """
1083       new_fs=escript.Solution(self.getDomain())       if self.__reduce_equation_order:
1084       if self.getFunctionSpaceForEquation()!=new_fs:           if self.__altered_coefficients:
1085           if self.debug() : print "PDE Debug: Full order is used for test functions."                raise RuntimeError,"order cannot be altered after coefficients have been defined."
1086           self.__row_function_space=new_fs           self.trace("Full order is used for test functions.")
1087           self.__rebuildSystem(deep=True)           self.__reduce_equation_order=False
1088             self.__resetSystem()
1089    
1090     def setReducedOrderForEquationTo(self,flag=False):     def setReducedOrderForEquationTo(self,flag=False):
1091       """       """
1092       @brief sets order for test functions according to flag       sets order for test functions according to flag
1093    
1094       @param flag       @param flag: if flag is True, the order reduction is switched on for equation representation, otherwise or
1095                      if flag is not present order reduction is switched off
1096         @type flag: C{bool}
1097         @raise RuntimeError: if order reduction is altered after a coefficient has been set.
1098       """       """
1099       if flag:       if flag:
1100          self.setReducedOrderForEquationOn()          self.setReducedOrderForEquationOn()
1101       else:       else:
1102          self.setReducedOrderForEquationOff()          self.setReducedOrderForEquationOff()
                                                                                                                                                             
1103    
1104     # ==== initialization =====================================================================     # =============================================================================
1105     def __makeNewOperator(self):     # private method:
1106       # =============================================================================
1107       def __checkMatrixType(self):
1108         """
1109         reassess the matrix type and, if a new matrix is needed, resets the system.
1110         """
1111         new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1112         if not new_matrix_type==self.__matrix_type:
1113             self.trace("Matrix type is now %d."%new_matrix_type)
1114             self.__matrix_type=new_matrix_type
1115             self.__resetSystem()
1116       #
1117       #   rebuild switches :
1118       #
1119       def __invalidateSolution(self):
1120           """
1121           indicates the PDE has to be resolved if the solution is requested
1122           """
1123           if self.__solution_isValid: self.trace("PDE has to be resolved.")
1124           self.__solution_isValid=False
1125    
1126       def __invalidateOperator(self):
1127           """
1128           indicates the operator has to be rebuilt next time it is used
1129           """
1130           if self.__operator_is_Valid: self.trace("Operator has to be rebuilt.")
1131           self.__invalidateSolution()
1132           self.__operator_is_Valid=False
1133    
1134       def __invalidateRightHandSide(self):
1135           """
1136           indicates the right hand side has to be rebuild next time it is used
1137         """         """
1138         @brief         if self.__righthandside_isValid: self.trace("Right hand side has to be rebuilt.")
1139           self.__invalidateSolution()
1140           self.__righthandside_isValid=False
1141    
1142       def __invalidateSystem(self):
1143         """         """
1144           annonced that everthing has to be rebuild:
1145           """
1146           if self.__righthandside_isValid: self.trace("System has to be rebuilt.")
1147           self.__invalidateSolution()
1148           self.__invalidateOperator()
1149           self.__invalidateRightHandSide()
1150    
1151       def __resetSystem(self):
1152           """
1153           annonced that everthing has to be rebuild:
1154           """
1155           self.trace("New System is built from scratch.")
1156           self.__operator=escript.Operator()
1157           self.__operator_is_Valid=False
1158           self.__righthandside=escript.Data()
1159           self.__righthandside_isValid=False
1160           self.__solution=escript.Data()
1161           self.__solution_isValid=False
1162       #
1163       #    system initialization:
1164       #
1165       def __getNewOperator(self):
1166           """
1167           returns an instance of a new operator
1168           """
1169           self.trace("New operator is allocated.")
1170         return self.getDomain().newOperator( \         return self.getDomain().newOperator( \
1171                             self.getNumEquations(), \                             self.getNumEquations(), \
1172                             self.getFunctionSpaceForEquation(), \                             self.getFunctionSpaceForEquation(), \
# Line 617  class LinearPDE: Line 1174  class LinearPDE:
1174                             self.getFunctionSpaceForSolution(), \                             self.getFunctionSpaceForSolution(), \
1175                             self.__matrix_type)                             self.__matrix_type)
1176    
1177     def __makeNewRightHandSide(self):     def __getNewRightHandSide(self):
1178         """         """
1179         @brief         returns an instance of a new right hand side
1180         """         """
1181         return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)         self.trace("New right hand side is allocated.")
1182           if self.getNumEquations()>1:
1183               return escript.Data(0.,(self.getNumEquations(),),self.getFunctionSpaceForEquation(),True)
1184           else:
1185               return escript.Data(0.,(),self.getFunctionSpaceForEquation(),True)
1186    
1187     def __makeNewSolution(self):     def __getNewSolution(self):
1188         """         """
1189         @brief         returns an instance of a new solution
1190         """         """
1191         return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)         self.trace("New solution is allocated.")
1192           if self.getNumSolutions()>1:
1193               return escript.Data(0.,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True)
1194           else:
1195               return escript.Data(0.,(),self.getFunctionSpaceForSolution(),True)
1196    
1197     def __getFreshOperator(self):     def __makeFreshSolution(self):
1198         """         """
1199         @brief         makes sure that the solution is instantiated and returns it initialized by zeros
1200         """         """
1201         if self.__operator.isEmpty():         if self.__solution.isEmpty():
1202             self.__operator=self.__makeNewOperator()             self.__solution=self.__getNewSolution()
            if self.debug() : print "PDE Debug: New operator allocated"  
1203         else:         else:
1204             self.__operator.setValue(0.)             self.__solution*=0
1205             if self.debug() : print "PDE Debug: Operator reset to zero"             self.trace("Solution is reset to zero.")
1206         return self.__operator         return self.__solution
1207    
1208     def __getFreshRightHandSide(self):     def __makeFreshRightHandSide(self):
1209         """         """
1210         @brief         makes sure that the right hand side is instantiated and returns it initialized by zeros
1211         """         """
1212         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1213             self.__righthandside=self.__makeNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
            if self.debug() : print "PDE Debug: New right hand side allocated"  
1214         else:         else:
1215             print "fix self.__righthandside*=0"             self.__righthandside*=0
1216             self.__righthandside*=0.             self.trace("Right hand side is reset to zero.")
1217             if self.debug() : print "PDE Debug: Right hand side reset to zero"         return self.__righthandside
        return  self.__righthandside  
1218    
1219     # ==== rebuild switches =====================================================================     def __makeFreshOperator(self):
    def __rebuildSolution(self,deep=False):  
1220         """         """
1221         @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
1222         """         """
1223         if self.__solution_isValid and self.debug() : print "PDE Debug: PDE has to be resolved."         if self.__operator.isEmpty():
1224         self.__solution_isValid=False             self.__operator=self.__getNewOperator()
1225         if deep: self.__solution=escript.Data(deep)         else:
1226               self.__operator.resetValues()
1227               self.trace("Operator reset to zero")
1228           return self.__operator
1229    
1230     def __rebuildOperator(self,deep=False):     def __applyConstraint(self):
1231         """         """
1232         @brief indicates the operator has to be rebuilt next time it is used         applies the constraints defined by q and r to the system
1233         """         """
1234         if self.__operator_isValid and self.debug() : print "PDE Debug: Operator has to be rebuilt."         if not self.isUsingLumping():
1235         self.__rebuildSolution(deep)            q=self.getCoefficientOfGeneralPDE("q")
1236         self.__operator_isValid=False            r=self.getCoefficientOfGeneralPDE("r")
1237         if deep: self.__operator=escript.Operator()            if not q.isEmpty() and not self.__operator.isEmpty():
1238                 # q is the row and column mask to indicate where constraints are set:
1239                 row_q=escript.Data(q,self.getFunctionSpaceForEquation())
1240                 col_q=escript.Data(q,self.getFunctionSpaceForSolution())
1241                 u=self.__getNewSolution()
1242                 if r.isEmpty():
1243                    r_s=self.__getNewSolution()
1244                 else:
1245                    r_s=escript.Data(r,self.getFunctionSpaceForSolution())
1246                 u.copyWithMask(r_s,col_q)
1247                 if not self.__righthandside.isEmpty():
1248                    self.__righthandside-=self.__operator*u
1249                    self.__righthandside=self.copyConstraint(self.__righthandside)
1250                 self.__operator.nullifyRowsAndCols(row_q,col_q,1.)
1251       # =============================================================================
1252       # function giving access to coefficients of the general PDE:
1253       # =============================================================================
1254       def getCoefficientOfGeneralPDE(self,name):
1255         """
1256         return the value of the coefficient name of the general PDE.
1257    
1258         @note: This method is called by the assembling routine it can be overwritten
1259               to map coefficients of a particular PDE to the general PDE.
1260         @param name: name of the coefficient requested.
1261         @type name: C{string}
1262         @return: the value of the coefficient  name
1263         @rtype: L{Data<escript.Data>}
1264         @raise IllegalCoefficient: if name is not one of coefficients
1265                      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}.
1266         """
1267         if self.hasCoefficientOfGeneralPDE(name):
1268            return self.getCoefficient(name)
1269         else:
1270            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1271    
1272     def __rebuildRightHandSide(self,deep=False):     def hasCoefficientOfGeneralPDE(self,name):
1273         """       """
1274         @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()  
1275    
1276     def __rebuildSystem(self,deep=False):       @param name: name of the coefficient enquired.
1277         """       @type name: C{string}
1278         @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.
1279         """       @rtype: C{bool}
1280         self.__rebuildSolution(deep)  
1281         self.__rebuildOperator(deep)       """
1282         self.__rebuildRightHandSide(deep)       return self.__COEFFICIENTS_OF_GENEARL_PDE.has_key(name)
1283      
1284     def __checkMatrixType(self):     def createCoefficientOfGeneralPDE(self,name):
1285       """       """
1286       @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
1287    
1288         @param name: name of the coefficient requested.
1289         @type name: C{string}
1290         @return: a coefficient name initialized to 0.
1291         @rtype: L{Data<escript.Data>}
1292         @raise IllegalCoefficient: if name is not one of coefficients
1293                      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}.
1294       """       """
1295       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.isSymmetric())       if self.hasCoefficientOfGeneralPDE(name):
1296       if not new_matrix_type==self.__matrix_type:          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
1297           if self.debug() : print "PDE Debug: Matrix type is now %d."%new_matrix_type       else:
1298           self.__matrix_type=new_matrix_type          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1299           self.__rebuildOperator(deep=True)  
1300       def getFunctionSpaceForCoefficientOfGeneralPDE(self,name):
1301         """
1302         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name of the general PDE
1303    
1304         @param name: name of the coefficient enquired.
1305         @type name: C{string}
1306         @return: the function space to be used for coefficient name
1307         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1308         @raise IllegalCoefficient: if name is not one of coefficients
1309                      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}.
1310         """
1311         if self.hasCoefficientOfGeneralPDE(name):
1312            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
1313         else:
1314            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1315    
1316       def getShapeOfCoefficientOfGeneralPDE(self,name):
1317         """
1318         return the shape of the coefficient name of the general PDE
1319    
1320     #============ assembling =======================================================       @param name: name of the coefficient enquired.
1321     def __copyConstraint(self,u):       @type name: C{string}
1322         @return: the shape of the coefficient name
1323         @rtype: C{tuple} of C{int}
1324         @raise IllegalCoefficient: if name is not one of coefficients
1325                      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}.
1326         """
1327         if self.hasCoefficientOfGeneralPDE(name):
1328            return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1329         else:
1330            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1331    
1332       # =============================================================================
1333       # functions giving access to coefficients of a particular PDE implementation:
1334       # =============================================================================
1335       def getCoefficient(self,name):
1336         """
1337         returns the value of the coefficient name
1338    
1339         @param name: name of the coefficient requested.
1340         @type name: C{string}
1341         @return: the value of the coefficient name
1342         @rtype: L{Data<escript.Data>}
1343         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1344         """
1345         if self.hasCoefficient(name):
1346             return self.COEFFICIENTS[name].getValue()
1347         else:
1348            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1349    
1350       def hasCoefficient(self,name):
1351         """
1352         return True if name is the name of a coefficient
1353    
1354         @param name: name of the coefficient enquired.
1355         @type name: C{string}
1356         @return: True if name is the name of a coefficient of the general PDE. Otherwise False.
1357         @rtype: C{bool}
1358         """
1359         return self.COEFFICIENTS.has_key(name)
1360    
1361       def createCoefficient(self, name):
1362         """
1363         create a L{Data<escript.Data>} object corresponding to coefficient name
1364    
1365         @return: a coefficient name initialized to 0.
1366         @rtype: L{Data<escript.Data>}
1367         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1368         """
1369         if self.hasCoefficient(name):
1370            return escript.Data(0.,self.getShapeOfCoefficient(name),self.getFunctionSpaceForCoefficient(name))
1371         else:
1372            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1373    
1374       def getFunctionSpaceForCoefficient(self,name):
1375         """
1376         return the L{FunctionSpace<escript.FunctionSpace>} to be used for coefficient name
1377    
1378         @param name: name of the coefficient enquired.
1379         @type name: C{string}
1380         @return: the function space to be used for coefficient name
1381         @rtype: L{FunctionSpace<escript.FunctionSpace>}
1382         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1383         """
1384         if self.hasCoefficient(name):
1385            return self.COEFFICIENTS[name].getFunctionSpace(self.getDomain())
1386         else:
1387            raise ValueError,"unknown coefficient %s requested"%name
1388       def getShapeOfCoefficient(self,name):
1389         """
1390         return the shape of the coefficient name
1391    
1392         @param name: name of the coefficient enquired.
1393         @type name: C{string}
1394         @return: the shape of the coefficient name
1395         @rtype: C{tuple} of C{int}
1396         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1397         """
1398         if self.hasCoefficient(name):
1399            return self.COEFFICIENTS[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
1400         else:
1401            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1402    
1403       def resetCoefficients(self):
1404         """
1405         resets all coefficients to there default values.
1406         """
1407         for i in self.COEFFICIENTS.iterkeys():
1408             self.COEFFICIENTS[i].resetValue()
1409    
1410       def alteredCoefficient(self,name):
1411         """
1412         announce that coefficient name has been changed
1413    
1414         @param name: name of the coefficient enquired.
1415         @type name: C{string}
1416         @raise IllegalCoefficient: if name is not a coefficient of the PDE.
1417         @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.
1418         """
1419         if self.hasCoefficient(name):
1420            self.trace("Coefficient %s has been altered."%name)
1421            if not ((name=="q" or name=="r") and self.isUsingLumping()):
1422               if self.COEFFICIENTS[name].isAlteringOperator(): self.__invalidateOperator()
1423               if self.COEFFICIENTS[name].isAlteringRightHandSide(): self.__invalidateRightHandSide()
1424         else:
1425            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1426    
1427       def copyConstraint(self,u):
1428        """        """
1429        @brief copies the constrint condition into u        copies the constraint into u and returns u.
1430    
1431          @param u: a function of rank 0 is a single PDE is solved and of shape (numSolution,) for a system of PDEs
1432          @type u: L{Data<escript.Data>}
1433          @return: the input u modified by the constraints.
1434          @rtype: L{Data<escript.Data>}
1435          @warning: u is altered if it has the appropriate L{FunctionSpace<escript.FunctionSpace>}
1436        """        """
1437        q=self.getCoefficient("q")        q=self.getCoefficientOfGeneralPDE("q")
1438        r=self.getCoefficient("r")        r=self.getCoefficientOfGeneralPDE("r")
1439        if not q.isEmpty():        if not q.isEmpty():
1440            if r.isEmpty():           if u.isEmpty(): u=escript.Data(0.,q.getShape(),q.getFunctionSpace())
1441               r2=escript.Data(0,u.getShape(),u.getFunctionSpace())           if r.isEmpty():
1442            else:               r=escript.Data(0,u.getShape(),u.getFunctionSpace())
1443               r2=escript.Data(r,u.getFunctionSpace())           else:
1444            u.copyWithMask(r2,escript.Data(q,u.getFunctionSpace()))               r=escript.Data(r,u.getFunctionSpace())
1445             u.copyWithMask(r,escript.Data(q,u.getFunctionSpace()))
1446     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  
1447    
1448     def getRightHandSide(self,ignoreConstraint=False):     def setValue(self,**coefficients):
1449         """        """
1450         @brief returns the right hand side of the PDE        sets new values to coefficients
1451    
1452         @param ignoreConstraint        @param coefficients: new values assigned to coefficients
1453         """        @keyword A: value for coefficient A.
1454         if not self.__righthandside_isValid:        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1455             if self.debug() : print "PDE Debug: New right hand side is built."        @keyword B: value for coefficient B
1456             self.getDomain().addPDEToRHS(self.__getFreshRightHandSide(), \        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1457                           self.getCoefficient("X"), \        @keyword C: value for coefficient C
1458                           self.getCoefficient("Y"),\        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1459                           self.getCoefficient("y"),\        @keyword D: value for coefficient D
1460                           self.getCoefficient("y_contact"))        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1461             self.__righthandside_isValid=True        @keyword X: value for coefficient X
1462             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>}.
1463         return self.__righthandside        @keyword Y: value for coefficient Y
1464          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1465          @keyword d: value for coefficient d
1466          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1467          @keyword y: value for coefficient y
1468          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1469          @keyword d_contact: value for coefficient d_contact
1470          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1471                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1472          @keyword y_contact: value for coefficient y_contact
1473          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1474                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1475          @keyword r: values prescribed to the solution at the locations of constraints
1476          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1477                   depending of reduced order is used for the solution.
1478          @keyword q: mask for location of constraints
1479          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1480                   depending of reduced order is used for the representation of the equation.
1481          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1482          """
1483          # check if the coefficients are  legal:
1484          for i in coefficients.iterkeys():
1485             if not self.hasCoefficient(i):
1486                raise IllegalCoefficient,"Attempt to set unknown coefficient %s"%i
1487          # if the number of unknowns or equations is still unknown we try to estimate them:
1488          if self.__numEquations==None or self.__numSolutions==None:
1489             for i,d in coefficients.iteritems():
1490                if hasattr(d,"shape"):
1491                    s=d.shape
1492                elif hasattr(d,"getShape"):
1493                    s=d.getShape()
1494                else:
1495                    s=numarray.array(d).shape
1496                if s!=None:
1497                    # get number of equations and number of unknowns:
1498                    res=self.COEFFICIENTS[i].estimateNumEquationsAndNumSolutions(self.getDomain(),s)
1499                    if res==None:
1500                        raise IllegalCoefficientValue,"Illegal shape %s of coefficient %s"%(s,i)
1501                    else:
1502                        if self.__numEquations==None: self.__numEquations=res[0]
1503                        if self.__numSolutions==None: self.__numSolutions=res[1]
1504          if self.__numEquations==None: raise UndefinedPDEError,"unidententified number of equations"
1505          if self.__numSolutions==None: raise UndefinedPDEError,"unidententified number of solutions"
1506          # now we check the shape of the coefficient if numEquations and numSolutions are set:
1507          for i,d in coefficients.iteritems():
1508            try:
1509               self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1510            except IllegalCoefficientValue,m:
1511               raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1512            self.alteredCoefficient(i)
1513    
1514          self.__altered_coefficients=True
1515          # check if the systrem is inhomogeneous:
1516          if len(coefficients)>0 and not self.isUsingLumping():
1517             q=self.getCoefficientOfGeneralPDE("q")
1518             r=self.getCoefficientOfGeneralPDE("r")
1519             homogeneous_constraint=True
1520             if not q.isEmpty() and not r.isEmpty():
1521                 if util.Lsup(q*r)>=1.e-13*util.Lsup(r):
1522                   self.trace("Inhomogeneous constraint detected.")
1523                   self.__invalidateSystem()
1524    
1525     def getSystem(self):     def getSystem(self):
1526         """         """
1527         @brief         return the operator and right hand side of the PDE
1528    
1529           @return: the discrete version of the PDE
1530           @rtype: C{tuple} of L{Operator,<escript.Operator>} and L{Data<escript.Data>}.
1531         """         """
1532         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."  
1533            if self.isUsingLumping():            if self.isUsingLumping():
1534                self.getRightHandSide(ignoreConstraint=True)                if not self.__operator_is_Valid:
1535                self.getOperator()                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1536                          raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1537                     if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1538                          raise ValueError,"coefficient A in lumped matrix may not be present."
1539                     if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1540                          raise ValueError,"coefficient A in lumped matrix may not be present."
1541                     if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1542                          raise ValueError,"coefficient A in lumped matrix may not be present."
1543                     D=self.getCoefficientOfGeneralPDE("D")
1544                     if not D.isEmpty():
1545                         if self.getNumSolutions()>1:
1546                            D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))
1547                         else:
1548                            D_times_e=D
1549                     else:
1550                        D_times_e=escript.Data()
1551                     d=self.getCoefficientOfGeneralPDE("d")
1552                     if not d.isEmpty():
1553                         if self.getNumSolutions()>1:
1554                            d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))
1555                         else:
1556                            d_times_e=d
1557                     else:
1558                        d_times_e=escript.Data()
1559                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1560                     if not d_contact.isEmpty():
1561                         if self.getNumSolutions()>1:
1562                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1563                         else:
1564                            d_contact_times_e=d_contact
1565                     else:
1566                        d_contact_times_e=escript.Data()
1567        
1568                     self.__operator=self.__getNewRightHandSide()
1569                     self.getDomain().addPDEToRHS(self.__operator, \
1570                                                  escript.Data(), \
1571                                                  D_times_e, \
1572                                                  d_times_e,\
1573                                                  d_contact_times_e)
1574                     self.__operator=1./self.__operator
1575                     self.trace("New lumped operator has been built.")
1576                     self.__operator_is_Valid=True
1577                  if not self.__righthandside_isValid:
1578                     self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1579                                   self.getCoefficientOfGeneralPDE("X"), \
1580                                   self.getCoefficientOfGeneralPDE("Y"),\
1581                                   self.getCoefficientOfGeneralPDE("y"),\
1582                                   self.getCoefficientOfGeneralPDE("y_contact"))
1583                     self.trace("New right hand side as been built.")
1584                     self.__righthandside_isValid=True
1585            else:            else:
1586                self.getDomain().addPDEToSystem(self.__getFreshOperator(),self.__getFreshRightHandSide(), \               if not self.__operator_is_Valid and not self.__righthandside_isValid:
1587                              self.getCoefficient("A"), \                   self.getDomain().addPDEToSystem(self.__makeFreshOperator(),self.__makeFreshRightHandSide(), \
1588                              self.getCoefficient("B"), \                                 self.getCoefficientOfGeneralPDE("A"), \
1589                              self.getCoefficient("C"), \                                 self.getCoefficientOfGeneralPDE("B"), \
1590                              self.getCoefficient("D"), \                                 self.getCoefficientOfGeneralPDE("C"), \
1591                              self.getCoefficient("X"), \                                 self.getCoefficientOfGeneralPDE("D"), \
1592                              self.getCoefficient("Y"), \                                 self.getCoefficientOfGeneralPDE("X"), \
1593                              self.getCoefficient("d"), \                                 self.getCoefficientOfGeneralPDE("Y"), \
1594                              self.getCoefficient("y"), \                                 self.getCoefficientOfGeneralPDE("d"), \
1595                              self.getCoefficient("d_contact"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1596                              self.getCoefficient("y_contact"))                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1597            self.__operator_isValid=True                                 self.getCoefficientOfGeneralPDE("y_contact"))
1598            self.__righthandside_isValid=True                   self.__applyConstraint()
1599            self.__applyConstraint()                   self.__righthandside=self.copyConstraint(self.__righthandside)
1600            self.__copyConstraint(self.__righthandside)                   self.trace("New system has been built.")
1601         elif not self.__operator_isValid:                   self.__operator_is_Valid=True
1602            self.getOperator()                   self.__righthandside_isValid=True
1603         elif not self.__righthandside_isValid:               elif not self.__righthandside_isValid:
1604            self.getRightHandSide()                   self.getDomain().addPDEToRHS(self.__makeFreshRightHandSide(), \
1605                                   self.getCoefficientOfGeneralPDE("X"), \
1606                                   self.getCoefficientOfGeneralPDE("Y"),\
1607                                   self.getCoefficientOfGeneralPDE("y"),\
1608                                   self.getCoefficientOfGeneralPDE("y_contact"))
1609                     self.__righthandside=self.copyConstraint(self.__righthandside)
1610                     self.trace("New right hand side has been built.")
1611                     self.__righthandside_isValid=True
1612                 elif not self.__operator_is_Valid:
1613                     self.getDomain().addPDEToSystem(self.__makeFreshOperator(),escript.Data(), \
1614                                self.getCoefficientOfGeneralPDE("A"), \
1615                                self.getCoefficientOfGeneralPDE("B"), \
1616                                self.getCoefficientOfGeneralPDE("C"), \
1617                                self.getCoefficientOfGeneralPDE("D"), \
1618                                escript.Data(), \
1619                                escript.Data(), \
1620                                self.getCoefficientOfGeneralPDE("d"), \
1621                                escript.Data(),\
1622                                self.getCoefficientOfGeneralPDE("d_contact"), \
1623                                escript.Data())
1624                     self.__applyConstraint()
1625                     self.trace("New operator has been built.")
1626                     self.__operator_is_Valid=True
1627         return (self.__operator,self.__righthandside)         return (self.__operator,self.__righthandside)
1628    
    def solve(self,**options):  
       """  
       @brief solve the PDE  
1629    
1630        @param options  class Poisson(LinearPDE):
1631        """     """
1632        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  
1633    
1634     def getSolution(self,**options):     M{-grad(grad(u)[j])[j] = f}
        """  
        @brief returns the solution of the PDE  
1635    
1636         @param options     with natural boundary conditons
1637         """  
1638         if not self.__solution_isValid:     M{n[j]*grad(u)[j] = 0 }
1639             if self.debug() : print "PDE Debug: PDE is resolved."  
1640             self.__solution=self.solve(**options)     and constraints:
1641             self.__solution_isValid=True  
1642         return self.__solution     M{u=0} where M{q>0}
1643     #============ some serivice functions  =====================================================  
1644     def getDomain(self):     """
1645       """  
1646       @brief returns the domain of the PDE     def __init__(self,domain,debug=False):
1647       """       """
1648       return self.__domain       initializes a new Poisson equation
1649    
1650         @param domain: domain of the PDE
1651         @type domain: L{Domain<escript.Domain>}
1652         @param debug: if True debug informations are printed.
1653    
    def getDim(self):  
1654       """       """
1655       @brief returns the spatial dimension of the PDE       super(Poisson, self).__init__(domain,1,1,debug)
1656         self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1657                              "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1658         self.setSymmetryOn()
1659    
1660       def setValue(self,**coefficients):
1661       """       """
1662       return self.getDomain().getDim()       sets new values to coefficients
1663    
1664     def getNumEquations(self):       @param coefficients: new values assigned to coefficients
1665         @keyword f: value for right hand side M{f}
1666         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1667         @keyword q: mask for location of constraints
1668         @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>}
1669                   depending of reduced order is used for the representation of the equation.
1670         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1671         """
1672         super(Poisson, self).setValue(**coefficients)
1673    
1674       def getCoefficientOfGeneralPDE(self,name):
1675         """
1676         return the value of the coefficient name of the general PDE
1677         @param name: name of the coefficient requested.
1678         @type name: C{string}
1679         @return: the value of the coefficient  name
1680         @rtype: L{Data<escript.Data>}
1681         @raise IllegalCoefficient: if name is not one of coefficients
1682                      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}.
1683         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1684         """
1685         if name == "A" :
1686             return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1687         elif name == "B" :
1688             return escript.Data()
1689         elif name == "C" :
1690             return escript.Data()
1691         elif name == "D" :
1692             return escript.Data()
1693         elif name == "X" :
1694             return escript.Data()
1695         elif name == "Y" :
1696             return self.getCoefficient("f")
1697         elif name == "d" :
1698             return escript.Data()
1699         elif name == "y" :
1700             return escript.Data()
1701         elif name == "d_contact" :
1702             return escript.Data()
1703         elif name == "y_contact" :
1704             return escript.Data()
1705         elif name == "r" :
1706             return escript.Data()
1707         elif name == "q" :
1708             return self.getCoefficient("q")
1709         else:
1710            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1711    
1712    class Helmholtz(LinearPDE):
1713       """
1714       Class to define a Helmhotz equation problem, which is genear L{LinearPDE} of the form
1715    
1716       M{S{omega}*u - grad(k*grad(u)[j])[j] = f}
1717    
1718       with natural boundary conditons
1719    
1720       M{k*n[j]*grad(u)[j] = g- S{alpha}u }
1721    
1722       and constraints:
1723    
1724       M{u=r} where M{q>0}
1725    
1726       """
1727    
1728       def __init__(self,domain,debug=False):
1729       """       """
1730       @brief returns the number of equations       initializes a new Poisson equation
1731    
1732         @param domain: domain of the PDE
1733         @type domain: L{Domain<escript.Domain>}
1734         @param debug: if True debug informations are printed.
1735    
1736         """
1737         super(Helmholtz, self).__init__(domain,1,1,debug)
1738         self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1739                            "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1740                            "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1741                            "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1742                            "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1743                            "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1744                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1745         self.setSymmetryOn()
1746    
1747       def setValue(self,**coefficients):
1748       """       """
1749       if self.__numEquations>0:       sets new values to coefficients
1750           return self.__numEquations  
1751         @param coefficients: new values assigned to coefficients
1752         @keyword omega: value for coefficient M{S{omega}}
1753         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1754         @keyword k: value for coefficeint M{k}
1755         @type k: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1756         @keyword f: value for right hand side M{f}
1757         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1758         @keyword alpha: value for right hand side M{S{alpha}}
1759         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1760         @keyword g: value for right hand side M{g}
1761         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1762         @keyword r: prescribed values M{r} for the solution in constraints.
1763         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1764                   depending of reduced order is used for the representation of the equation.
1765         @keyword q: mask for location of constraints
1766         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1767                   depending of reduced order is used for the representation of the equation.
1768         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1769         """
1770         super(Helmholtz, self).setValue(**coefficients)
1771    
1772       def getCoefficientOfGeneralPDE(self,name):
1773         """
1774         return the value of the coefficient name of the general PDE
1775    
1776         @param name: name of the coefficient requested.
1777         @type name: C{string}
1778         @return: the value of the coefficient  name
1779         @rtype: L{Data<escript.Data>}
1780         @raise IllegalCoefficient: if name is not one of coefficients
1781                      "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}.
1782         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1783         """
1784         if name == "A" :
1785             return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))*self.getCoefficient("k")
1786         elif name == "B" :
1787             return escript.Data()
1788         elif name == "C" :
1789             return escript.Data()
1790         elif name == "D" :
1791             return self.getCoefficient("omega")
1792         elif name == "X" :
1793             return escript.Data()
1794         elif name == "Y" :
1795             return self.getCoefficient("f")
1796         elif name == "d" :
1797             return self.getCoefficient("alpha")
1798         elif name == "y" :
1799             return self.getCoefficient("g")
1800         elif name == "d_contact" :
1801             return escript.Data()
1802         elif name == "y_contact" :
1803             return escript.Data()
1804         elif name == "r" :
1805             return self.getCoefficient("r")
1806         elif name == "q" :
1807             return self.getCoefficient("q")
1808       else:       else:
1809           raise ValueError,"Number of equations is undefined. Please specify argument numEquations."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1810    
1811     def getNumSolutions(self):  class LameEquation(LinearPDE):
1812       """     """
1813       @brief returns the number of unknowns     Class to define a Lame equation problem:
1814    
1815       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] }
1816    
1817       with natural boundary conditons:
1818    
1819       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] }
1820    
1821       and constraints:
1822    
1823       M{u[i]=r[i]} where M{q[i]>0}
1824    
1825       """
1826    
1827       def __init__(self,domain,debug=False):
1828          super(LameEquation, self).__init__(domain,\
1829                                             domain.getDim(),domain.getDim(),debug)
1830          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1831                              "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1832                              "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1833                              "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1834                              "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1835                              "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1836                              "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1837          self.setSymmetryOn()
1838    
1839       def setValue(self,**coefficients):
1840       """       """
1841       if self.__numSolutions>0:       sets new values to coefficients
1842          return self.__numSolutions  
1843         @param coefficients: new values assigned to coefficients
1844         @keyword lame_mu: value for coefficient M{S{mu}}
1845         @type lame_mu: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1846         @keyword lame_lambda: value for coefficient M{S{lambda}}
1847         @type lame_lambda: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
1848         @keyword F: value for internal force M{F}
1849         @type F: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}
1850         @keyword sigma: value for initial stress M{S{sigma}}
1851         @type sigma: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}
1852         @keyword f: value for extrenal force M{f}
1853         @type f: any type that can be casted to L{Vector<escript.Vector>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}
1854         @keyword r: prescribed values M{r} for the solution in constraints.
1855         @type r: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1856                   depending of reduced order is used for the representation of the equation.
1857         @keyword q: mask for location of constraints
1858         @type q: any type that can be casted to L{Vector<escript.Vector>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1859                   depending of reduced order is used for the representation of the equation.
1860         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1861         """
1862         super(LameEquation, self).setValue(**coefficients)
1863    
1864       def getCoefficientOfGeneralPDE(self,name):
1865         """
1866         return the value of the coefficient name of the general PDE
1867    
1868         @param name: name of the coefficient requested.
1869         @type name: C{string}
1870         @return: the value of the coefficient  name
1871         @rtype: L{Data<escript.Data>}
1872         @raise IllegalCoefficient: if name is not one of coefficients
1873                      "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}.
1874         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1875         """
1876         if name == "A" :
1877             out =self.createCoefficientOfGeneralPDE("A")
1878             for i in range(self.getDim()):
1879               for j in range(self.getDim()):
1880                 out[i,i,j,j] += self.getCoefficient("lame_lambda")
1881                 out[i,j,j,i] += self.getCoefficient("lame_mu")
1882                 out[i,j,i,j] += self.getCoefficient("lame_mu")
1883             return out
1884         elif name == "B" :
1885             return escript.Data()
1886         elif name == "C" :
1887             return escript.Data()
1888         elif name == "D" :
1889             return escript.Data()
1890         elif name == "X" :
1891             return self.getCoefficient("sigma")
1892         elif name == "Y" :
1893             return self.getCoefficient("F")
1894         elif name == "d" :
1895             return escript.Data()
1896         elif name == "y" :
1897             return self.getCoefficient("f")
1898         elif name == "d_contact" :
1899             return escript.Data()
1900         elif name == "y_contact" :
1901             return escript.Data()
1902         elif name == "r" :
1903             return self.getCoefficient("r")
1904         elif name == "q" :
1905             return self.getCoefficient("q")
1906       else:       else:
1907          raise ValueError,"Number of solution is undefined. Please specify argument numSolutions."          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
1908    
1909    class AdvectivePDE(LinearPDE):
1910       """
1911       In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}
1912       up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.
1913    
1914       In the following we set
1915    
1916       M{Z[j]=C[j]-B[j]}
1917    
1918       or
1919    
1920       M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1921    
1922       To measure the dominance of the advective terms over the diffusive term M{A} the
1923       X{Pelclet number} M{P} is used. It is defined as
1924    
1925       M{P=h|Z|/(2|A|)}
1926    
1927     def checkSymmetry(self):     where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1928       from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1929    
1930       From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
1931    
1932       M{S{Xi}=S{xi}(P) h/|Z|}
1933    
1934       where M{S{xi}} is a suitable function of the Peclet number.
1935    
1936       In the case of a single PDE the coefficient are up-dated in the following way:
1937             - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}
1938             - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}
1939             - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}
1940             - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}
1941    
1942       Similar for the case of a systems of PDEs:
1943             - 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]}
1944             - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}
1945             - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}
1946             - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}
1947    
1948       where M{S{delta}} is L{kronecker}.
1949       Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}
1950       but with the intension to stabilize the solution.
1951    
1952       """
1953       def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1954        """        """
1955        @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>}
1956    
1957          @param domain: domain of the PDE
1958          @type domain: L{Domain<escript.Domain>}
1959          @param numEquations: number of equations. If numEquations==None the number of equations
1960                               is exracted from the PDE coefficients.
1961          @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1962                               is exracted from the PDE coefficients.
1963          @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1964                     M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1965          @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1966          @param debug: if True debug informations are printed.
1967          """
1968          super(AdvectivePDE, self).__init__(domain,\
1969                                             numEquations,numSolutions,debug)
1970          if xi==None:
1971             self.__xi=AdvectivePDE.ELMAN_RAMAGE
1972          else:
1973             self.__xi=xi
1974          self.__Xi=escript.Data()
1975    
1976       def setValue(**coefficients):
1977        """        """
1978        raise SystemError,"checkSymmetry is not implemented yet"        sets new values to coefficients
1979    
1980        return None        @param coefficients: new values assigned to coefficients
1981          @keyword A: value for coefficient A.
1982          @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1983          @keyword B: value for coefficient B
1984          @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1985          @keyword C: value for coefficient C
1986          @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1987          @keyword D: value for coefficient D
1988          @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1989          @keyword X: value for coefficient X
1990          @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1991          @keyword Y: value for coefficient Y
1992          @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1993          @keyword d: value for coefficient d
1994          @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1995          @keyword y: value for coefficient y
1996          @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1997          @keyword d_contact: value for coefficient d_contact
1998          @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
1999                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
2000          @keyword y_contact: value for coefficient y_contact
2001          @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
2002                           or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
2003          @keyword r: values prescribed to the solution at the locations of constraints
2004          @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2005                   depending of reduced order is used for the solution.
2006          @keyword q: mask for location of constraints
2007          @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2008                   depending of reduced order is used for the representation of the equation.
2009          @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2010    
2011          """
2012          if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
2013          super(AdvectivePDE, self).setValue(**coefficients)
2014    
2015       def ELMAN_RAMAGE(self,P):
2016         """
2017         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2018         This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
2019              - M{S{xi}(P)=0} for M{P<1}
2020              - M{S{xi}(P)=(1-1/P)/2} otherwise
2021    
2022         @param P: Preclet number
2023         @type P: L{Scalar<escript.Scalar>}
2024         @return: up-wind weightimg factor
2025         @rtype: L{Scalar<escript.Scalar>}
2026         """
2027         return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2028    
2029       def SIMPLIFIED_BROOK_HUGHES(self,P):
2030         """
2031         Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2032         The original methods is
2033    
2034         M{S{xi}(P)=coth(P)-1/P}
2035    
2036         As the evaluation of M{coth} is expensive we are using the approximation:
2037    
2038             - M{S{xi}(P)=P/3} where M{P<3}
2039             - M{S{xi}(P)=1/2} otherwise
2040    
2041         @param P: Preclet number
2042         @type P: L{Scalar<escript.Scalar>}
2043         @return: up-wind weightimg factor
2044         @rtype: L{Scalar<escript.Scalar>}
2045         """
2046         c=util.whereNegative(P-3.)
2047         return P/6.*c+1./2.*(1.-c)
2048    
2049       def HALF(self,P):
2050         """
2051         Predefined function to set value M{1/2} for M{S{xi}}
2052    
2053         @param P: Preclet number
2054         @type P: L{Scalar<escript.Scalar>}
2055         @return: up-wind weightimg factor
2056         @rtype: L{Scalar<escript.Scalar>}
2057         """
2058         return escript.Scalar(0.5,P.getFunctionSpace())
2059    
2060       def __calculateXi(self,peclet_factor,flux,h):
2061           flux=util.Lsup(flux)
2062           if flux_max>0.:
2063              return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)
2064           else:
2065              return 0.
2066    
2067     def getFlux(self,u):     def __getXi(self):
2068         """        if self.__Xi.isEmpty():
2069         @brief returns the flux J_ij for a given u           B=self.getCoefficient("B")
2070             C=self.getCoefficient("C")
2071             A=self.getCoefficient("A")
2072             h=self.getDomain().getSize()
2073             self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2074             if not C.isEmpty() or not B.isEmpty():
2075                if not C.isEmpty() and not B.isEmpty():
2076                    flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2077                    if self.getNumEquations()>1:
2078                       if self.getNumSolutions()>1:
2079                          for i in range(self.getNumEquations()):
2080                             for k in range(self.getNumSolutions()):
2081                                for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2082                          # flux=C-util.reorderComponents(B,[0,2,1])
2083                       else:
2084                          for i in range(self.getNumEquations()):
2085                             for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2086                          # flux=C-B
2087                    else:
2088                       if self.getNumSolutions()>1:
2089                          for k in range(self.getNumSolutions()):
2090                             for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2091                          # flux=C-util.reorderComponents(B,[1,0])
2092                       else:
2093                          for l in range(self.getDim()): flux2+=(C[l]-B[l])**2
2094                          #flux=C-B
2095                    length_of_flux=util.sqrt(flux2)
2096                elif C.isEmpty():
2097                  length_of_flux=util.length(B)
2098                  #flux=B
2099                else:
2100                  length_of_flux=util.length(C)
2101                  #flux=C
2102    
2103              J_ij=A_{ijkl}u_{k,l}+B_{ijk}u_k-X_{ij}              #length_of_flux=util.length(flux)
2104                flux_max=util.Lsup(length_of_flux)
2105                if flux_max>0.:
2106                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2107                   length_of_A=util.length(A)
2108                   A_max=util.Lsup(length_of_A)
2109                   if A_max>0:
2110                        inv_A=1./(length_of_A+A_max*self.__TOL)
2111                   else:
2112                        inv_A=1./self.__TOL
2113                   peclet_number=length_of_flux*h/2*inv_A
2114                   xi=self.__xi(peclet_number)
2115                   self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)
2116                   self.trace("preclet number = %e"%util.Lsup(peclet_number))
2117          return self.__Xi
2118    
2119    
2120       def getCoefficientOfGeneralPDE(self,name):
2121         """
2122         return the value of the coefficient name of the general PDE
2123    
2124         @param name: name of the coefficient requested.
2125         @type name: C{string}
2126         @return: the value of the coefficient name
2127         @rtype: L{Data<escript.Data>}
2128         @raise IllegalCoefficient: if name is not one of coefficients
2129                      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}.
2130         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2131         """
2132         if not self.getNumEquations() == self.getNumSolutions():
2133              raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."
2134    
2135         if name == "A" :
2136             A=self.getCoefficient("A")
2137             B=self.getCoefficient("B")
2138             C=self.getCoefficient("C")
2139             if B.isEmpty() and C.isEmpty():
2140                Aout=A
2141             else:
2142                if A.isEmpty():
2143                   Aout=self.createNewCoefficient("A")
2144                else:
2145                   Aout=A[:]
2146                Xi=self.__getXi()
2147                if self.getNumEquations()>1:
2148                    for i in range(self.getNumEquations()):
2149                       for j in range(self.getDim()):
2150                          for k in range(self.getNumSolutions()):
2151                             for l in range(self.getDim()):
2152                                if not C.isEmpty() and not B.isEmpty():
2153                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2154                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2155                                   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])
2156                                elif C.isEmpty():
2157                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2158                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2159                                else:
2160                                   for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2161                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2162                else:
2163                    for j in range(self.getDim()):
2164                       for l in range(self.getDim()):
2165                          if not C.isEmpty() and not B.isEmpty():
2166                              Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])
2167                          elif C.isEmpty():
2168                              Aout[j,l]+=Xi*B[j]*B[l]
2169                          else:
2170                              Aout[j,l]+=Xi*C[j]*C[l]
2171                     # if not C.isEmpty() and not B.isEmpty():
2172                     #    tmp=C-B
2173                     #    Aout=Aout+Xi*util.outer(tmp,tmp)
2174                     # elif C.isEmpty():
2175                     #    Aout=Aout+Xi*util.outer(B,B)
2176                     # else:
2177                     # Aout=Aout+Xi*util.outer(C,C)
2178             return Aout
2179         elif name == "B" :
2180             B=self.getCoefficient("B")
2181             C=self.getCoefficient("C")
2182             D=self.getCoefficient("D")
2183             if C.isEmpty() or D.isEmpty():
2184                Bout=B
2185             else:
2186                Xi=self.__getXi()
2187                if B.isEmpty():
2188                    Bout=self.createNewCoefficient("B")
2189                else:
2190                    Bout=B[:]
2191                if self.getNumEquations()>1:
2192                   for k in range(self.getNumSolutions()):
2193                      for p in range(self.getNumEquations()):
2194                         tmp=Xi*D[p,k]
2195                         for i in range(self.getNumEquations()):
2196                            for j in range(self.getDim()):
2197                               Bout[i,j,k]+=tmp*C[p,i,j]
2198                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2199                else:
2200                   tmp=Xi*D
2201                   for j in range(self.getDim()): Bout[j]+=tmp*C[j]
2202                   # Bout=Bout+Xi*D*C
2203             return Bout
2204         elif name == "C" :
2205             B=self.getCoefficient("B")
2206             C=self.getCoefficient("C")
2207             D=self.getCoefficient("D")
2208             if B.isEmpty() or D.isEmpty():
2209                Cout=C
2210             else:
2211                Xi=self.__getXi()
2212                if C.isEmpty():
2213                    Cout=self.createNewCoefficient("C")
2214                else:
2215                    Cout=C[:]
2216                if self.getNumEquations()>1:
2217                   for k in range(self.getNumSolutions()):
2218                       for p in range(self.getNumEquations()):
2219                          tmp=Xi*D[p,k]
2220                          for i in range(self.getNumEquations()):
2221                            for l in range(self.getDim()):
2222                                     Cout[i,k,l]+=tmp*B[p,l,i]
2223                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2224                else:
2225                   tmp=Xi*D
2226                   for j in range(self.getDim()): Cout[j]+=tmp*B[j]
2227                   # Cout=Cout+tmp*D*B
2228             return Cout
2229         elif name == "D" :
2230             return self.getCoefficient("D")
2231         elif name == "X" :
2232             X=self.getCoefficient("X")
2233             Y=self.getCoefficient("Y")
2234             B=self.getCoefficient("B")
2235             C=self.getCoefficient("C")
2236             if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):
2237                Xout=X
2238             else:
2239                if X.isEmpty():
2240                    Xout=self.createNewCoefficient("X")
2241                else:
2242                    Xout=X[:]
2243                Xi=self.__getXi()
2244                if self.getNumEquations()>1:
2245                     for p in range(self.getNumEquations()):
2246                        tmp=Xi*Y[p]
2247                        for i in range(self.getNumEquations()):
2248                           for j in range(self.getDim()):
2249                              if not C.isEmpty() and not B.isEmpty():
2250                                 Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2251                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2252                              elif C.isEmpty():
2253                                 Xout[i,j]-=tmp*B[p,j,i]
2254                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2255                              else:
2256                                 Xout[i,j]+=tmp*C[p,i,j]
2257                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2258                else:
2259                     tmp=Xi*Y
2260                     for j in range(self.getDim()):
2261                        if not C.isEmpty() and not B.isEmpty():
2262                           Xout[j]+=tmp*(C[j]-B[j])
2263                           # Xout=Xout+Xi*Y*(C-B)
2264                        elif C.isEmpty():
2265                           Xout[j]-=tmp*B[j]
2266                           # Xout=Xout-Xi*Y*B
2267                        else:
2268                           Xout[j]+=tmp*C[j]
2269                           # Xout=Xout+Xi*Y*C
2270             return Xout
2271         elif name == "Y" :
2272             return self.getCoefficient("Y")
2273         elif name == "d" :
2274             return self.getCoefficient("d")
2275         elif name == "y" :
2276             return self.getCoefficient("y")
2277         elif name == "d_contact" :
2278             return self.getCoefficient("d_contact")
2279         elif name == "y_contact" :
2280             return self.getCoefficient("y_contact")
2281         elif name == "r" :
2282             return self.getCoefficient("r")
2283         elif name == "q" :
2284             return self.getCoefficient("q")
2285         else:
2286            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2287    
2288         @param u argument of the operator  class AdvectionDiffusion(LinearPDE):
2289       """
2290       Class to define PDE equation of the unisotropic advection-diffusion problem, which is genear L{LinearPDE} of the form
2291    
2292         """     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  
2293    
2294     def applyOperator(self,u):     with natural boundary conditons
        """  
        @brief applies the operator of the PDE to a given solution u in weak from  
2295    
2296         @param u argument of the operator     M{n[j]*matrixmult(k,grad(u))[j] = g- S{alpha}u }
2297    
2298         """     and constraints:
        return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())  
                                                                                                                                                             
    def getResidual(self,u):  
        """  
        @brief return the residual of u in the weak from  
2299    
2300         @param u     M{u=r} where M{q>0}
2301         """  
2302         return self.applyOperator(u)-self.getRightHandSide()     and
2303    
2304       M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}
2305    
 class Poisson(LinearPDE):  
2306     """     """
2307     @brief Class to define a Poisson equstion problem:  
2308                                                                                                                                                                   def __init__(self,domain,debug=False):
2309     class to define a linear PDE of the form       """
2310                                                                                                                                                                     initializes a new Poisson equation
2311          -u_{,jj} = f  
2312                                                                                                                                                                     @param domain: domain of the PDE
2313       with boundary conditons:       @type domain: L{Domain<escript.Domain>}
2314                                                                                                                                                                     @param debug: if True debug informations are printed.
2315          n_j*u_{,j} = 0  
2316                                                                                                                                                                     """
2317      and constraints:       super(AdvectionDiffusion, self).__init__(domain,1,1,debug)
2318                                                                                                                                                                     self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2319           u=0 where q>0                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
2320                                                                                                                                                                                        "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2321     """                          "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2322                            "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),
2323     def __init__(self,domain=None,f=escript.Data(),q=escript.Data()):                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
2324         LinearPDE.__init__(self,domain=identifyDomain(domain,{"f":f, "q":q}))                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
2325         self._setValue(A=numarray.identity(self.getDomain().getDim()))                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
2326         self.setSymmetryOn()                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2327         self.setValue(f,q)  
2328       def setValue(self,**coefficients):
2329     def setValue(self,f=escript.Data(),q=escript.Data()):       """
2330         self._setValue(Y=f,q=q)       sets new values to coefficients
2331    
2332                                                                                                                                                                   @param coefficients: new values assigned to coefficients
2333         @keyword omega: value for coefficient M{S{omega}}
2334         @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2335         @keyword k: value for coefficient M{k}
2336         @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.
2337         @keyword v: value for coefficient M{v}
2338         @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2339         @keyword upwind: value for upwind term M{upwind}
2340         @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.
2341         @keyword f: value for right hand side M{f}
2342         @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.
2343         @keyword alpha: value for right hand side M{S{alpha}}
2344         @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2345         @keyword g: value for right hand side M{g}
2346         @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
2347         @keyword r: prescribed values M{r} for the solution in constraints.
2348         @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2349                   depending of reduced order is used for the representation of the equation.
2350         @keyword q: mask for location of constraints
2351         @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
2352                   depending of reduced order is used for the representation of the equation.
2353         @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2354         """
2355         super(AdvectionDiffusion, self).setValue(**coefficients)
2356    
2357       def getCoefficientOfGeneralPDE(self,name):
2358         """
2359         return the value of the coefficient name of the general PDE
2360    
2361         @param name: name of the coefficient requested.
2362         @type name: C{string}
2363         @return: the value of the coefficient  name
2364         @rtype: L{Data<escript.Data>}
2365         @raise IllegalCoefficient: if name is not one of coefficients
2366                      "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}.
2367         @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
2368         """
2369         if name == "A" :
2370             return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))
2371         elif name == "B" :
2372             return escript.Data()
2373         elif name == "C" :
2374             return self.getCoefficient("v")
2375         elif name == "D" :
2376             return self.getCoefficient("omega")
2377         elif name == "X" :
2378             return escript.Data()
2379         elif name == "Y" :
2380             return self.getCoefficient("f")
2381         elif name == "d" :
2382             return self.getCoefficient("alpha")
2383         elif name == "y" :
2384             return self.getCoefficient("g")
2385         elif name == "d_contact" :
2386             return escript.Data()
2387         elif name == "y_contact" :
2388             return escript.Data()
2389         elif name == "r" :
2390             return self.getCoefficient("r")
2391         elif name == "q" :
2392             return self.getCoefficient("q")
2393         else:
2394            raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2395    
2396    
2397  # $Log$  # $Log$
2398  # Revision 1.3  2004/12/17 07:43:10  jgs  # Revision 1.14  2005/09/22 01:54:57  jgs
2399  # *** empty log message ***  # Merge of development branch dev-02 back to main trunk on 2005-09-22
2400    #
2401    # Revision 1.13  2005/09/15 03:44:19  jgs
2402    # Merge of development branch dev-02 back to main trunk on 2005-09-15
2403    #
2404    # Revision 1.12  2005/09/01 03:31:28  jgs
2405    # Merge of development branch dev-02 back to main trunk on 2005-09-01
2406    #
2407    # Revision 1.11  2005/08/23 01:24:28  jgs
2408    # Merge of development branch dev-02 back to main trunk on 2005-08-23
2409    #
2410    # Revision 1.10  2005/08/12 01:45:36  jgs
2411    # erge of development branch dev-02 back to main trunk on 2005-08-12
2412    #
2413    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2414    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2415    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2416    # modified to instead use portable/cooperative "super" calls to extend base
2417    # class methods.
2418    #
2419    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2420    # Removed redundant if-loop.
2421    #
2422    # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2423    # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2424    #
2425    # Revision 1.9.2.14  2005/09/07 06:26:16  gross
2426    # the solver from finley are put into the standalone package paso now
2427    #
2428    # Revision 1.9.2.13  2005/08/31 08:45:03  gross
2429    # in the case of lumping no new system is allocated if the constraint is changed.
2430    #
2431    # Revision 1.9.2.12  2005/08/31 07:10:23  gross
2432    # test for Lumping added
2433    #
2434    # Revision 1.9.2.11  2005/08/30 01:53:45  gross
2435    # bug in format fixed.
2436    #
2437    # Revision 1.9.2.10  2005/08/26 07:14:17  gross
2438    # a few more bugs in linearPDE fixed. remaining problem are finley problems
2439    #
2440    # Revision 1.9.2.9  2005/08/26 06:30:45  gross
2441    # fix for reported bug  0000004. test_linearPDE passes a few more tests
2442    #
2443    # Revision 1.9.2.8  2005/08/26 04:30:13  gross
2444    # gneric unit testing for linearPDE
2445    #
2446    # Revision 1.9.2.7  2005/08/25 07:06:50  gross
2447    # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so
2448    #
2449    # Revision 1.9.2.6  2005/08/24 05:01:24  gross
2450    # problem with resetting the matrix in case of resetting its values to 0 fixed.
2451    #
2452    # Revision 1.9.2.5  2005/08/24 02:03:28  gross
2453    # epydoc mark up partially fixed
2454    #
2455    # Revision 1.9.2.4  2005/08/22 07:11:09  gross
2456    # some problems with LinearPDEs fixed.
2457    #
2458    # Revision 1.9.2.3  2005/08/18 04:48:48  gross
2459    # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)
2460    #
2461    # Revision 1.9.2.2  2005/08/18 04:39:32  gross
2462    # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now
2463    #
2464    # Revision 1.9.2.1  2005/07/29 07:10:27  gross
2465    # new functions in util and a new pde type in linearPDEs
2466    #
2467    # Revision 1.1.2.25  2005/07/28 04:21:09  gross
2468    # Lame equation: (linear elastic, isotropic) added
2469    #
2470    # Revision 1.1.2.24  2005/07/22 06:37:11  gross
2471    # some extensions to modellib and linearPDEs
2472    #
2473    # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane
2474    # Fixed up some docstrings.  Moved module-level functions to top of file so
2475    # that epydoc and doxygen can pick them up properly.
2476    #
2477    # Revision 1.1.2.22  2005/05/12 11:41:30  gross
2478    # some basic Models have been added
2479    #
2480    # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane
2481    # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of
2482    # file so that the AdvectivePDE class is picked up by doxygen.  Some
2483    # reformatting of docstrings.  Addition of code to make equations come out
2484    # as proper LaTeX.
2485    #
2486    # Revision 1.1.2.20  2005/04/15 07:09:08  gross
2487    # some problems with functionspace and linearPDEs fixed.
2488    #
2489    # Revision 1.1.2.19  2005/03/04 05:27:07  gross
2490    # bug in SystemPattern fixed.
2491    #
2492    # Revision 1.1.2.18  2005/02/08 06:16:45  gross
2493    # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed
2494    #
2495    # Revision 1.1.2.17  2005/02/08 05:56:19  gross
2496    # Reference Number handling added
2497    #
2498    # Revision 1.1.2.16  2005/02/07 04:41:28  gross
2499    # some function exposed to python to make mesh merging running
2500    #
2501    # Revision 1.1.2.15  2005/02/03 00:14:44  gross
2502    # timeseries add and ESySParameter.py renames esysXML.py for consistence
2503    #
2504    # Revision 1.1.2.14  2005/02/01 06:44:10  gross
2505    # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working
2506    #
2507    # Revision 1.1.2.13  2005/01/25 00:47:07  gross
2508    # updates in the documentation
2509    #
2510    # Revision 1.1.2.12  2005/01/12 01:28:04  matt
2511    # Added createCoefficient method for linearPDEs.
2512    #
2513    # Revision 1.1.2.11  2005/01/11 01:55:34  gross
2514    # a problem in linearPDE class fixed
2515    #
2516    # Revision 1.1.2.10  2005/01/07 01:13:29  gross
2517    # some bugs in linearPDE fixed
2518    #
2519    # Revision 1.1.2.9  2005/01/06 06:24:58  gross
2520    # some bugs in slicing fixed
2521    #
2522    # Revision 1.1.2.8  2005/01/05 04:21:40  gross
2523    # FunctionSpace checking/matchig in slicing added
2524    #
2525    # Revision 1.1.2.7  2004/12/29 10:03:41  gross
2526    # bug in setValue fixed
2527    #
2528    # Revision 1.1.2.6  2004/12/29 05:29:59  gross
2529    # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()
2530    #
2531    # Revision 1.1.2.5  2004/12/29 00:18:41  gross
2532    # AdvectivePDE added
2533    #
2534    # Revision 1.1.2.4  2004/12/24 06:05:41  gross
2535    # some changes in linearPDEs to add AdevectivePDE
2536  #  #
2537  # Revision 1.1.2.3  2004/12/16 00:12:34  gross  # Revision 1.1.2.3  2004/12/16 00:12:34  gross
2538  # __init__ of LinearPDE does not accept any coefficients anymore  # __init__ of LinearPDE does not accept any coefficient anymore
2539  #  #
2540  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  # Revision 1.1.2.2  2004/12/14 03:55:01  jgs
2541  # *** empty log message ***  # *** empty log message ***
# Line 998  class Poisson(LinearPDE): Line 2579  class Poisson(LinearPDE):
2579  # Revision 1.1  2004/08/28 12:58:06  gross  # Revision 1.1  2004/08/28 12:58:06  gross
2580  # SimpleSolve is not running yet: problem with == of functionsspace  # SimpleSolve is not running yet: problem with == of functionsspace
2581  #  #
 #  

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