/[escript]/trunk/escript/py_src/linearPDEs.py
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revision 969 by ksteube, Tue Feb 13 23:02:23 2007 UTC revision 1659 by gross, Fri Jul 18 02:28:13 2008 UTC
# Line 1  Line 1 
1    #
2  # $Id$  # $Id$
3    #
4    #######################################################
5    #
6    #           Copyright 2003-2007 by ACceSS MNRF
7    #       Copyright 2007 by University of Queensland
8    #
9    #                http://esscc.uq.edu.au
10    #        Primary Business: Queensland, Australia
11    #  Licensed under the Open Software License version 3.0
12    #     http://www.opensource.org/licenses/osl-3.0.php
13    #
14    #######################################################
15    #
16    
17  """  """
18  The module provides an interface to define and solve linear partial  The module provides an interface to define and solve linear partial
19  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
# Line 19  to define of solve these sepecial PDEs. Line 34  to define of solve these sepecial PDEs.
34  @var __date__: date of the version  @var __date__: date of the version
35  """  """
36    
37    import math
38  import escript  import escript
39  import util  import util
40  import numarray  import numarray
# Line 38  class IllegalCoefficient(ValueError): Line 54  class IllegalCoefficient(ValueError):
54     """     """
55     raised if an illegal coefficient of the general ar particular PDE is requested.     raised if an illegal coefficient of the general ar particular PDE is requested.
56     """     """
57       pass
58    
59  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
60     """     """
61     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
62     """     """
63       pass
64    
65    class IllegalCoefficientFunctionSpace(ValueError):
66       """
67       raised if an incorrect function space for a coefficient is used.
68       """
69    
70  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
71     """     """
72     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
73     """     """
74       pass
75    
76  class PDECoefficient(object):  class PDECoefficient(object):
77      """      """
# Line 56  class PDECoefficient(object): Line 80  class PDECoefficient(object):
80      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
81      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
82      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
83        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
84        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
85        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
86      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
87      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
88      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
# Line 77  class PDECoefficient(object): Line 104  class PDECoefficient(object):
104      OPERATOR=10      OPERATOR=10
105      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
106      BOTH=12      BOTH=12
107        INTERIOR_REDUCED=13
108        BOUNDARY_REDUCED=14
109        CONTACT_REDUCED=15
110    
111      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
112         """         """
113         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
114    
115         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
116         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
117                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
118         @param pattern: describes the shape of the coefficient and how the shape is build for a given         @param pattern: describes the shape of the coefficient and how the shape is build for a given
119                spatial dimension and numbers of equation and solution in then PDE. For instance,                spatial dimension and numbers of equation and solution in then PDE. For instance,
120                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
# Line 94  class PDECoefficient(object): Line 125  class PDECoefficient(object):
125         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
126         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
127         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
128           @param reduced: indicates if reduced
129           @type reduced: C{bool}
130         """         """
131         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
132         self.what=where         self.what=where
# Line 123  class PDECoefficient(object): Line 155  class PDECoefficient(object):
155         """         """
156         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
157              return escript.Function(domain)              return escript.Function(domain)
158           elif self.what==self.INTERIOR_REDUCED:
159                return escript.ReducedFunction(domain)
160         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
161              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
162           elif self.what==self.BOUNDARY_REDUCED:
163                return escript.ReducedFunctionOnBoundary(domain)
164         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
165              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
166           elif self.what==self.CONTACT_REDUCED:
167                return escript.ReducedFunctionOnContactZero(domain)
168         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
169              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
170                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 161  class PDECoefficient(object): Line 199  class PDECoefficient(object):
199         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
200         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
201         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
202           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
203         """         """
204         if newValue==None:         if newValue==None:
205             newValue=escript.Data()             newValue=escript.Data()
206         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
207             if not newValue.isEmpty():             if not newValue.isEmpty():
208                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
209                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
210                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
211                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
212                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
213         else:         else:
214             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
215         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 313  class LinearPDE(object): Line 353  class LinearPDE(object):
353    
354     For a single PDE with a solution with a single component the linear PDE is defined in the following form:     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
355    
356     M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
357    
358    
359     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
360     ie. summation over indexes appearing twice in a term of a sum is performed, is used.     ie. summation over indexes appearing twice in a term of a sum is performed, is used.
361     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
362     L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.     L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
363     M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.     L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
364       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
365       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
366    
367     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
368    
369     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
370    
371     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.     where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
    Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are  
    each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
372    
373    
374     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
# Line 339  class LinearPDE(object): Line 380  class LinearPDE(object):
380    
381     The PDE is symmetrical if     The PDE is symmetrical if
382    
383     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
384    
385     For a system of PDEs and a solution with several components the PDE has the form     For a system of PDEs and a solution with several components the PDE has the form
386    
387     M{-grad(A[i,j,k,l]*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] }     M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
388    
389     M{A} 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.     M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
390     The natural boundary conditions take the form:     The natural boundary conditions take the form:
391    
392     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]}     M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
393    
394    
395     The coefficient M{d} is a rank two and M{y} is a  rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form     The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
396    
397       Constraints take the form
398    
399     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
400    
# Line 361  class LinearPDE(object): Line 403  class LinearPDE(object):
403     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
404    
405          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
406            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
407          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
408            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
409          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
410            - M{D_reduced[i,k]=D_reduced[i,k]}
411          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
412            - M{d_reduced[i,k]=d_reduced[k,i]}
413    
414     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
415     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
416     defined as     defined as
417    
418     M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}     M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
419    
420     For the case of single solution component and single PDE M{J} is defined     For the case of single solution component and single PDE M{J} is defined
421    
422     M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}     M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
423    
424     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
425     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
426     the contact condition takes the form     the contact condition takes the form
427    
428     M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}     M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
429    
430     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
431     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
432     L{jump<util.jump>}.     L{jump<util.jump>}.
433     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
434       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
435     In case of a single PDE and a single component solution the contact condition takes the form     In case of a single PDE and a single component solution the contact condition takes the form
436    
437     M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}     M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
438    
439     In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar     In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
    both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
440    
441     @cvar DEFAULT: The default method used to solve the system of linear equations     @cvar DEFAULT: The default method used to solve the system of linear equations
442     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 444  class LinearPDE(object): Line 490  class LinearPDE(object):
490     AMG= 22     AMG= 22
491     RILU = 23     RILU = 23
492     TRILINOS = 24     TRILINOS = 24
493       NONLINEAR_GMRES = 25
494    
495     SMALL_TOLERANCE=1.e-13     SMALL_TOLERANCE=1.e-13
496     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
# Line 481  class LinearPDE(object): Line 528  class LinearPDE(object):
528         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
529         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
530         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
531           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
532           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
534           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
535           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
536           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
537           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
540           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
541         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
542         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
543    
# Line 762  class LinearPDE(object): Line 819  class LinearPDE(object):
819                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
820                        if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)                        if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
821                        out=False                        out=False
822             # and now the reduced coefficients
823             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
824             if not A_reduced.isEmpty():
825                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
826                if self.getNumSolutions()>1:
827                   for i in range(self.getNumEquations()):
828                      for j in range(self.getDim()):
829                         for k in range(self.getNumSolutions()):
830                            for l in range(self.getDim()):
831                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
832                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
833                                   out=False
834                else:
835                   for j in range(self.getDim()):
836                      for l in range(self.getDim()):
837                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
838                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
839                            out=False
840             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
841             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
842             if B_reduced.isEmpty() and not C_reduced.isEmpty():
843                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
844                out=False
845             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
846                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
847                out=False
848             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
849                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
850                if self.getNumSolutions()>1:
851                   for i in range(self.getNumEquations()):
852                       for j in range(self.getDim()):
853                          for k in range(self.getNumSolutions()):
854                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
855                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
856                                  out=False
857                else:
858                   for j in range(self.getDim()):
859                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
860                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
861                         out=False
862             if self.getNumSolutions()>1:
863               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
864               if not D_reduced.isEmpty():
865                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
866                 for i in range(self.getNumEquations()):
867                    for k in range(self.getNumSolutions()):
868                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
869                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
870                          out=False
871               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
872               if not d_reduced.isEmpty():
873                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
874                 for i in range(self.getNumEquations()):
875                    for k in range(self.getNumSolutions()):
876                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
877                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
878                          out=False
879               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
880               if not d_contact_reduced.isEmpty():
881                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
882                 for i in range(self.getNumEquations()):
883                    for k in range(self.getNumSolutions()):
884                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
885                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
886                          out=False
887        return out        return out
888    
889     def getSolution(self,**options):     def getSolution(self,**options):
# Line 801  class LinearPDE(object): Line 923  class LinearPDE(object):
923       """       """
924       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
925    
926       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}       M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
927    
928       or       or
929    
930       M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}       M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
931    
932       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
933       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 813  class LinearPDE(object): Line 935  class LinearPDE(object):
935       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
936       """       """
937       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
938       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
939               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
940               -util.self.getCoefficientOfGeneralPDE("X") \
941               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
942               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
943               -util.self.getCoefficientOfGeneralPDE("X_reduced")
944     # =============================================================================     # =============================================================================
945     #   solver settings:     #   solver settings:
946     # =============================================================================     # =============================================================================
# Line 826  class LinearPDE(object): Line 953  class LinearPDE(object):
953         @param preconditioner: sets a new solver method.         @param preconditioner: sets a new solver method.
954         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
955         """         """
956         if solver==None: solve=self.DEFAULT         if solver==None: solver=self.__solver_method
957           if preconditioner==None: preconditioner=self.__preconditioner
958           if solver==None: solver=self.DEFAULT
959         if preconditioner==None: preconditioner=self.DEFAULT         if preconditioner==None: preconditioner=self.DEFAULT
960         if not (solver,preconditioner)==self.getSolverMethod():         if not (solver,preconditioner)==self.getSolverMethod():
961             self.__solver_method=solver             self.__solver_method=solver
# Line 1210  class LinearPDE(object): Line 1339  class LinearPDE(object):
1339         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1340             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1341         else:         else:
1342             self.__righthandside*=0             self.__righthandside.setToZero()
1343             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1344         return self.__righthandside         return self.__righthandside
1345    
# Line 1260  class LinearPDE(object): Line 1389  class LinearPDE(object):
1389       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1390       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1391       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1392                    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}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1393                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1394       """       """
1395       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1396          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1288  class LinearPDE(object): Line 1418  class LinearPDE(object):
1418       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1419       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1420       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1421                    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}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1422                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1423       """       """
1424       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1425          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1304  class LinearPDE(object): Line 1435  class LinearPDE(object):
1435       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1436       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1437       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1438                    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}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1439                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1440       """       """
1441       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1442          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1320  class LinearPDE(object): Line 1452  class LinearPDE(object):
1452       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1453       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1454       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1455                    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}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1456                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1457       """       """
1458       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1459          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
# Line 1450  class LinearPDE(object): Line 1583  class LinearPDE(object):
1583        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1584        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1585        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1586          @keyword A_reduced: value for coefficient A_reduced.
1587          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1588        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1589        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1590          @keyword B_reduced: value for coefficient B_reduced
1591          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1592        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1593        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1594          @keyword C_reduced: value for coefficient C_reduced
1595          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1596        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1597        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1598          @keyword D_reduced: value for coefficient D_reduced
1599          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1600        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1601        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1602          @keyword X_reduced: value for coefficient X_reduced
1603          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1604        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1605        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1606          @keyword Y_reduced: value for coefficient Y_reduced
1607          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1608        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1609        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1610          @keyword d_reduced: value for coefficient d_reduced
1611          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1612        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1613        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1614        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1615        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1616                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1617          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1618        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1619        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1620                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1621          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1622        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1623        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1624                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1504  class LinearPDE(object): Line 1653  class LinearPDE(object):
1653        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1654        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1655          try:          try:
1656             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1657                                             self.getNumEquations(),self.getNumSolutions(),
1658                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1659               self.alteredCoefficient(i)
1660            except IllegalCoefficientFunctionSpace,m:
1661                # if the function space is wrong then we try the reduced version:
1662                i_red=i+"_reduced"
1663                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1664                    try:
1665                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1666                                                          self.getNumEquations(),self.getNumSolutions(),
1667                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1668                        self.alteredCoefficient(i_red)
1669                    except IllegalCoefficientValue,m:
1670                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1671                    except IllegalCoefficientFunctionSpace,m:
1672                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673                else:
1674                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1675          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1676             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1677        self.__altered_coefficients=True        self.__altered_coefficients=True
1678        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1679        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1535  class LinearPDE(object): Line 1700  class LinearPDE(object):
1700                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1701                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient A in lumped matrix may not be present."
1702                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1703                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient B in lumped matrix may not be present."
1704                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1705                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient C in lumped matrix may not be present."
1706                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1707                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1708                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1709                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1710                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1711                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1712                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1713                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1714                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1715                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1716                   D=self.getCoefficientOfGeneralPDE("D")                   D=self.getCoefficientOfGeneralPDE("D")
1717                     d=self.getCoefficientOfGeneralPDE("d")
1718                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1719                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1720                   if not D.isEmpty():                   if not D.isEmpty():
1721                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
                         #D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))  
1722                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1723                       else:                       else:
1724                          D_times_e=D                          D_times_e=D
1725                   else:                   else:
1726                      D_times_e=escript.Data()                      D_times_e=escript.Data()
                  d=self.getCoefficientOfGeneralPDE("d")  
1727                   if not d.isEmpty():                   if not d.isEmpty():
1728                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
                         #d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))  
1729                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1730                       else:                       else:
1731                          d_times_e=d                          d_times_e=d
1732                   else:                   else:
1733                      d_times_e=escript.Data()                      d_times_e=escript.Data()
1734                   d_contact=self.getCoefficientOfGeneralPDE("d_contact")        
1735                   if not d_contact.isEmpty():                   if not D_reduced.isEmpty():
1736                         if self.getNumSolutions()>1:
1737                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1738                         else:
1739                            D_reduced_times_e=D_reduced
1740                     else:
1741                        D_reduced_times_e=escript.Data()
1742                     if not d_reduced.isEmpty():
1743                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1744                          d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))                          d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1745                       else:                       else:
1746                          d_contact_times_e=d_contact                          d_reduced_times_e=d_reduced
1747                   else:                   else:
1748                      d_contact_times_e=escript.Data()                      d_reduced_times_e=escript.Data()
1749        
1750                   self.__operator=self.__getNewRightHandSide()                   self.__operator=self.__getNewRightHandSide()
1751                   self.getDomain().addPDEToRHS(self.__operator, \                   if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1752                                                escript.Data(), \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1753                                                D_times_e, \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1754                                                d_times_e,\                   else:
1755                                                d_contact_times_e)                      self.getDomain().addPDEToRHS(self.__operator, \
1756                                                     escript.Data(), \
1757                                                     D_times_e, \
1758                                                     d_times_e,\
1759                                                     escript.Data())
1760                        self.getDomain().addPDEToRHS(self.__operator, \
1761                                                     escript.Data(), \
1762                                                     D_reduced_times_e, \
1763                                                     d_reduced_times_e,\
1764                                                     escript.Data())
1765                        print "RHS:",util.inf(self.__operator),util.sup(self.__operator)
1766                   self.__operator=1./self.__operator                   self.__operator=1./self.__operator
1767                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1768                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1580  class LinearPDE(object): Line 1772  class LinearPDE(object):
1772                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1773                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1774                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1775                     self.getDomain().addPDEToRHS(self.__righthandside, \
1776                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1777                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1778                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1779                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1780                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1781                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1782            else:            else:
# Line 1595  class LinearPDE(object): Line 1792  class LinearPDE(object):
1792                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1793                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1794                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1795                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1796                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1806                   self.__applyConstraint()                   self.__applyConstraint()
1807                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1808                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1606  class LinearPDE(object): Line 1814  class LinearPDE(object):
1814                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1815                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1816                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1817                     self.getDomain().addPDEToRHS(self.__righthandside, \
1818                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1819                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1820                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1821                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1822                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1823                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1824                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1621  class LinearPDE(object): Line 1834  class LinearPDE(object):
1834                              escript.Data(),\                              escript.Data(),\
1835                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1836                              escript.Data())                              escript.Data())
1837                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1838                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1839                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1840                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1841                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1842                                escript.Data(), \
1843                                escript.Data(), \
1844                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1845                                escript.Data(),\
1846                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1847                                escript.Data())
1848                   self.__applyConstraint()                   self.__applyConstraint()
1849                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1850                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1654  class Poisson(LinearPDE): Line 1878  class Poisson(LinearPDE):
1878       """       """
1879       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1880       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1881                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1882                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1883       self.setSymmetryOn()       self.setSymmetryOn()
1884    
1885     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1702  class Poisson(LinearPDE): Line 1927  class Poisson(LinearPDE):
1927           return escript.Data()           return escript.Data()
1928       elif name == "y_contact" :       elif name == "y_contact" :
1929           return escript.Data()           return escript.Data()
1930         elif name == "A_reduced" :
1931             return escript.Data()
1932         elif name == "B_reduced" :
1933             return escript.Data()
1934         elif name == "C_reduced" :
1935             return escript.Data()
1936         elif name == "D_reduced" :
1937             return escript.Data()
1938         elif name == "X_reduced" :
1939             return escript.Data()
1940         elif name == "Y_reduced" :
1941             return self.getCoefficient("f_reduced")
1942         elif name == "d_reduced" :
1943             return escript.Data()
1944         elif name == "y_reduced" :
1945             return escript.Data()
1946         elif name == "d_contact_reduced" :
1947             return escript.Data()
1948         elif name == "y_contact_reduced" :
1949             return escript.Data()
1950       elif name == "r" :       elif name == "r" :
1951           return escript.Data()           return escript.Data()
1952       elif name == "q" :       elif name == "q" :
# Line 1738  class Helmholtz(LinearPDE): Line 1983  class Helmholtz(LinearPDE):
1983       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1984                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1985                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1988                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1990                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1991                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1992       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1801  class Helmholtz(LinearPDE): Line 2048  class Helmholtz(LinearPDE):
2048           return escript.Data()           return escript.Data()
2049       elif name == "y_contact" :       elif name == "y_contact" :
2050           return escript.Data()           return escript.Data()
2051         elif name == "A_reduced" :
2052             return escript.Data()
2053         elif name == "B_reduced" :
2054             return escript.Data()
2055         elif name == "C_reduced" :
2056             return escript.Data()
2057         elif name == "D_reduced" :
2058             return escript.Data()
2059         elif name == "X_reduced" :
2060             return escript.Data()
2061         elif name == "Y_reduced" :
2062             return self.getCoefficient("f_reduced")
2063         elif name == "d_reduced" :
2064             return escript.Data()
2065         elif name == "y_reduced" :
2066            return self.getCoefficient("g_reduced")
2067         elif name == "d_contact_reduced" :
2068             return escript.Data()
2069         elif name == "y_contact_reduced" :
2070             return escript.Data()
2071       elif name == "r" :       elif name == "r" :
2072           return self.getCoefficient("r")           return self.getCoefficient("r")
2073       elif name == "q" :       elif name == "q" :
# Line 1899  class LameEquation(LinearPDE): Line 2166  class LameEquation(LinearPDE):
2166           return escript.Data()           return escript.Data()
2167       elif name == "y_contact" :       elif name == "y_contact" :
2168           return escript.Data()           return escript.Data()
2169         elif name == "A_reduced" :
2170             return escript.Data()
2171         elif name == "B_reduced" :
2172             return escript.Data()
2173         elif name == "C_reduced" :
2174             return escript.Data()
2175         elif name == "D_reduced" :
2176             return escript.Data()
2177         elif name == "X_reduced" :
2178             return escript.Data()
2179         elif name == "Y_reduced" :
2180             return escript.Data()
2181         elif name == "d_reduced" :
2182             return escript.Data()
2183         elif name == "y_reduced" :
2184             return escript.Data()
2185         elif name == "d_contact_reduced" :
2186             return escript.Data()
2187         elif name == "y_contact_reduced" :
2188             return escript.Data()
2189       elif name == "r" :       elif name == "r" :
2190           return self.getCoefficient("r")           return self.getCoefficient("r")
2191       elif name == "q" :       elif name == "q" :
# Line 1906  class LameEquation(LinearPDE): Line 2193  class LameEquation(LinearPDE):
2193       else:       else:
2194          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2195    
2196  class AdvectivePDE(LinearPDE):  def LinearSinglePDE(domain,debug=False):
2197     """     """
2198     In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}     defines a single linear PDEs
    up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.  
   
    In the following we set  
   
    M{Z[j]=C[j]-B[j]}  
   
    or  
   
    M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}  
   
    To measure the dominance of the advective terms over the diffusive term M{A} the  
    X{Pelclet number} M{P} is used. It is defined as  
   
    M{P=h|Z|/(2|A|)}  
   
    where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size  
    from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.  
   
    From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:  
   
    M{S{Xi}=S{xi}(P) h/|Z|}  
   
    where M{S{xi}} is a suitable function of the Peclet number.  
   
    In the case of a single PDE the coefficient are up-dated in the following way:  
          - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}  
          - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}  
          - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}  
          - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}  
   
    Similar for the case of a systems of PDEs:  
          - 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]}  
          - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}  
          - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}  
          - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}  
   
    where M{S{delta}} is L{kronecker}.  
    Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}  
    but with the intension to stabilize the solution.  
2199    
2200       @param domain: domain of the PDE
2201       @type domain: L{Domain<escript.Domain>}
2202       @param debug: if True debug informations are printed.
2203       @rtype: L{LinearPDE}
2204     """     """
2205     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
       """  
       creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}  
   
       @param domain: domain of the PDE  
       @type domain: L{Domain<escript.Domain>}  
       @param numEquations: number of equations. If numEquations==None the number of equations  
                            is exracted from the PDE coefficients.  
       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components  
                            is exracted from the PDE coefficients.  
       @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the  
                  M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.  
       @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.  
       @param debug: if True debug informations are printed.  
       """  
       super(AdvectivePDE, self).__init__(domain,\  
                                          numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def setValue(self,**coefficients):  
       """  
       sets new values to coefficients  
2206    
2207        @param coefficients: new values assigned to coefficients  def LinearPDESystem(domain,debug=False):
2208        @keyword A: value for coefficient A.     """
2209        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.     defines a system of linear PDEs
       @keyword B: value for coefficient B  
       @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword C: value for coefficient C  
       @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword D: value for coefficient D  
       @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword X: value for coefficient X  
       @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword Y: value for coefficient Y  
       @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword d: value for coefficient d  
       @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
       @keyword y: value for coefficient y  
       @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
       @keyword d_contact: value for coefficient d_contact  
       @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
                        or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.  
       @keyword y_contact: value for coefficient y_contact  
       @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
                        or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.  
       @keyword r: values prescribed to the solution at the locations of constraints  
       @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}  
                depending of reduced order is used for the solution.  
       @keyword q: mask for location of constraints  
       @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}  
                depending of reduced order is used for the representation of the equation.  
       @raise IllegalCoefficient: if an unknown coefficient keyword is used.  
2210    
2211        """     @param domain: domain of the PDE
2212        if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()     @type domain: L{Domain<escript.Domain>}
2213        super(AdvectivePDE, self).setValue(**coefficients)     @param debug: if True debug informations are printed.
2214       @rtype: L{LinearPDE}
2215       """
2216       return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2217    
2218     def ELMAN_RAMAGE(self,P):  class TransportPDE(object):
2219       """       """
2220       Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.       Warning: This is still a very experimental. The class is still changing!
      This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)  
           - M{S{xi}(P)=0} for M{P<1}  
           - M{S{xi}(P)=(1-1/P)/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))  
   
    def SIMPLIFIED_BROOK_HUGHES(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      The original methods is  
   
      M{S{xi}(P)=coth(P)-1/P}  
   
      As the evaluation of M{coth} is expensive we are using the approximation:  
   
          - M{S{xi}(P)=P/3} where M{P<3}  
          - M{S{xi}(P)=1/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      c=util.whereNegative(P-3.)  
      return P/6.*c+1./2.*(1.-c)  
   
    def HALF(self,P):  
      """  
      Predefined function to set value M{1/2} for M{S{xi}}  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return escript.Scalar(0.5,P.getFunctionSpace())  
   
    def __getXi(self):  
       if self.__Xi.isEmpty():  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          A=self.getCoefficient("A")  
          h=self.getDomain().getSize()  
          self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))  
          if not C.isEmpty() or not B.isEmpty():  
             if not C.isEmpty() and not B.isEmpty():  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for i in range(self.getNumEquations()):  
                          for k in range(self.getNumSolutions()):  
                             for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2  
                       length_of_flux=util.sqrt(flux2)  
                       # flux=C-util.reorderComponents(B,[0,2,1])  
                    else:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2  
                       length_of_flux=util.sqrt(flux2)  
                       # flux=C-B  
                 else:  
                    if self.getNumSolutions()>1:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2  
                       # flux=C-util.reorderComponents(B,[1,0])  
                       length_of_flux=util.sqrt(flux2)  
                    else:  
                       length_of_flux=util.length(C-B)  
             elif C.isEmpty():  
               length_of_flux=util.length(B)  
             else:  
               length_of_flux=util.length(C)  
             flux_max=util.Lsup(length_of_flux)  
             if flux_max>0.:  
               if A.isEmpty():  
                   inv_A=1./self.SMALL_TOLERANCE  
                   peclet_number=escript.Scalar(inv_A,length_of_flux.getFunctionSpace())  
                   xi=self.__xi(self,peclet_number)  
               else:  
                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))  
                   length_of_A=util.length(A)  
                   A_max=util.Lsup(length_of_A)  
                   if A_max>0:  
                        inv_A=1./(length_of_A+A_max*self.SMALL_TOLERANCE)  
                   else:  
                        inv_A=1./self.SMALL_TOLERANCE  
                   peclet_number=length_of_flux*h/2*inv_A  
                   xi=self.__xi(self,peclet_number)  
               self.__Xi=h*xi/(length_of_flux+flux_max*self.SMALL_TOLERANCE)  
               self.trace("preclet number = %e"%util.Lsup(peclet_number))  
             else:  
               self.__Xi=escript.Scalar(0.,length_of_flux.getFunctionSpace())  
       return self.__Xi  
2221    
2222         Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2223        
2224         u=r where q>0
2225        
2226         all coefficients are constant over time.
2227    
2228         typical usage:
2229    
2230             p=TransportPDE(dom)
2231             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2232             p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2233             t=0
2234             dt=0.1
2235             while (t<1.):
2236                  u=p.solve(dt)
2237    
2238         """
2239         def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2240            self.__domain=domain
2241            self.__num_equations=num_equations
2242            self.__useSUPG=useSUPG
2243            self.__trace=trace
2244            self.__theta=theta
2245            self.__matrix_type=0
2246            self.__reduced=True
2247            self.__reassemble=True
2248            if self.__useSUPG:
2249               self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2250               self.__pde.setSymmetryOn()
2251               self.__pde.setReducedOrderOn()
2252            else:
2253               self.__transport_problem=self.__getNewTransportProblem()
2254            self.setTolerance()
2255            self.__M=escript.Data()
2256            self.__A=escript.Data()
2257            self.__B=escript.Data()
2258            self.__C=escript.Data()
2259            self.__D=escript.Data()
2260            self.__X=escript.Data()
2261            self.__Y=escript.Data()
2262            self.__d=escript.Data()
2263            self.__y=escript.Data()
2264            self.__d_contact=escript.Data()
2265            self.__y_contact=escript.Data()
2266            self.__r=escript.Data()
2267            self.__q=escript.Data()
2268    
2269         def trace(self,text):
2270                 if self.__trace: print text
2271         def getSafeTimeStepSize(self):
2272            if self.__useSUPG:
2273                if self.__reassemble:
2274                   h=self.__domain.getSize()
2275                   dt=None
2276                   if not self.__A.isEmpty():
2277                      dt2=util.inf(h**2*self.__M/util.length(self.__A))
2278                      if dt == None:
2279                         dt = dt2
2280                      else:
2281                         dt=1./(1./dt+1./dt2)
2282                   if not self.__B.isEmpty():
2283                      dt2=util.inf(h*self.__M/util.length(self.__B))
2284                      if dt == None:
2285                         dt = dt2
2286                      else:
2287                         dt=1./(1./dt+1./dt2)
2288                   if not  self.__C.isEmpty():
2289                      dt2=util.inf(h*self.__M/util.length(self.__C))
2290                      if dt == None:
2291                         dt = dt2
2292                      else:
2293                         dt=1./(1./dt+1./dt2)
2294                   if not self.__D.isEmpty():
2295                      dt2=util.inf(self.__M/util.length(self.__D))
2296                      if dt == None:
2297                         dt = dt2
2298                      else:
2299                         dt=1./(1./dt+1./dt2)
2300                   self.__dt = dt/2
2301                return self.__dt
2302            else:
2303                return self.__getTransportProblem().getSafeTimeStepSize()
2304         def getDomain(self):
2305            return self.__domain
2306         def getTheta(self):
2307            return self.__theta
2308         def getNumEquations(self):
2309            return self.__num_equations
2310         def setReducedOn(self):
2311              if not self.reduced():
2312                  if self.__useSUPG:
2313                     self.__pde.setReducedOrderOn()
2314                  else:
2315                     self.__transport_problem=self.__getNewTransportProblem()
2316              self.__reduced=True
2317         def setReducedOff(self):
2318              if self.reduced():
2319                  if self.__useSUPG:
2320                     self.__pde.setReducedOrderOff()
2321                  else:
2322                     self.__transport_problem=self.__getNewTransportProblem()
2323              self.__reduced=False
2324         def reduced(self):
2325             return self.__reduced
2326         def getFunctionSpace(self):
2327            if self.reduced():
2328               return escript.ReducedSolution(self.getDomain())
2329            else:
2330               return escript.Solution(self.getDomain())
2331    
2332     def getCoefficientOfGeneralPDE(self,name):       def setTolerance(self,tol=1.e-8):
2333       """          self.__tolerance=tol
2334       return the value of the coefficient name of the general PDE          if self.__useSUPG:
2335                  self.__pde.setTolerance(self.__tolerance)
2336    
2337       @param name: name of the coefficient requested.       def __getNewTransportProblem(self):
2338       @type name: C{string}         """
2339       @return: the value of the coefficient name         returns an instance of a new operator
2340       @rtype: L{Data<escript.Data>}         """
2341       @raise IllegalCoefficient: if name is not one of coefficients         self.trace("New Transport problem is allocated.")
2342                    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}.         return self.getDomain().newTransportProblem( \
2343       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.                                 self.getTheta(),
2344       """                                 self.getNumEquations(), \
2345       if not self.getNumEquations() == self.getNumSolutions():                                 self.getFunctionSpace(), \
2346            raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."                                 self.__matrix_type)
2347              
2348       if name == "A" :       def __getNewSolutionVector(self):
2349           A=self.getCoefficient("A")           if self.getNumEquations() ==1 :
2350           B=self.getCoefficient("B")                  out=escript.Data(0.0,(),self.getFunctionSpace())
          C=self.getCoefficient("C")  
          if B.isEmpty() and C.isEmpty():  
             Aout=A  
          else:  
             if A.isEmpty():  
                Aout=self.createCoefficientOfGeneralPDE("A")  
             else:  
                Aout=A[:]  
             Xi=self.__getXi()  
             if self.getNumEquations()>1:  
                 for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()):  
                             if not C.isEmpty() and not B.isEmpty():  
                                # tmp=C-util.reorderComponents(B,[0,2,1])  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)  
                                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])  
                             elif C.isEmpty():  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)  
                             else:  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)  
             else:  
                if not C.isEmpty() and not B.isEmpty():  
                    delta=(C-B)  
                    Aout+=util.outer(Xi*delta,delta)  
                elif not B.isEmpty():  
                    Aout+=util.outer(Xi*B,B)  
                elif not C.isEmpty():  
                    Aout+=util.outer(Xi*C,C)  
          return Aout  
      elif name == "B" :  
          # return self.getCoefficient("B")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if C.isEmpty() or D.isEmpty():  
             Bout=B  
          else:  
             Xi=self.__getXi()  
             if B.isEmpty():  
                 Bout=self.createCoefficientOfGeneralPDE("B")  
             else:  
                 Bout=B[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                   for p in range(self.getNumEquations()):  
                      tmp=Xi*D[p,k]  
                      for i in range(self.getNumEquations()):  
                         for j in range(self.getDim()):  
                            Bout[i,j,k]+=tmp*C[p,i,j]  
                            # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)  
             else:  
                Bout+=(Xi*D)*C  
          return Bout  
      elif name == "C" :  
          # return self.getCoefficient("C")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if B.isEmpty() or D.isEmpty():  
             Cout=C  
          else:  
             Xi=self.__getXi()  
             if C.isEmpty():  
                 Cout=self.createCoefficientOfGeneralPDE("C")  
             else:  
                 Cout=C[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                    for p in range(self.getNumEquations()):  
                       tmp=Xi*D[p,k]  
                       for i in range(self.getNumEquations()):  
                         for l in range(self.getDim()):  
                                  Cout[i,k,l]+=tmp*B[p,l,i]  
                                  # Cout=Cout+Xi*B[p,l,i]*D[p,k]  
             else:  
                Cout+=(Xi*D)*B  
          return Cout  
      elif name == "D" :  
          return self.getCoefficient("D")  
      elif name == "X" :  
          # return self.getCoefficient("X")  
          X=self.getCoefficient("X")  
          Y=self.getCoefficient("Y")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):  
             Xout=X  
2351           else:           else:
2352              if X.isEmpty():                  out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2353                  Xout=self.createCoefficientOfGeneralPDE("X")           return out
             else:  
                 Xout=X[:]  
             Xi=self.__getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                              # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                              # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
                              # Xout=X_out+Xi*util.inner(Y,C,offset=1)  
             else:  
               if not C.isEmpty() and not B.isEmpty():  
                 Xout+=(Xi*Y)*(C-B)  
               elif C.isEmpty():  
                 Xout-=(Xi*Y)*B  
               else:  
                 Xout+=(Xi*Y)*C  
          return Xout  
      elif name == "Y" :  
          return self.getCoefficient("Y")  
      elif name == "d" :  
          return self.getCoefficient("d")  
      elif name == "y" :  
          return self.getCoefficient("y")  
      elif name == "d_contact" :  
          return self.getCoefficient("d_contact")  
      elif name == "y_contact" :  
          return self.getCoefficient("y_contact")  
      elif name == "r" :  
          return self.getCoefficient("r")  
      elif name == "q" :  
          return self.getCoefficient("q")  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2354    
2355  # $Log$       def __getTransportProblem(self):
2356  # Revision 1.14  2005/09/22 01:54:57  jgs         if self.__reassemble:
2357  # Merge of development branch dev-02 back to main trunk on 2005-09-22               self.__source=self.__getNewSolutionVector()
2358  #               self.__transport_problem.reset()
2359  # Revision 1.13  2005/09/15 03:44:19  jgs               self.getDomain().addPDEToTransportProblem(
2360  # Merge of development branch dev-02 back to main trunk on 2005-09-15                           self.__transport_problem,
2361  #                           self.__source,
2362  # Revision 1.12  2005/09/01 03:31:28  jgs                           self.__M,
2363  # Merge of development branch dev-02 back to main trunk on 2005-09-01                           self.__A,
2364  #                           self.__B,
2365  # Revision 1.11  2005/08/23 01:24:28  jgs                           self.__C,
2366  # Merge of development branch dev-02 back to main trunk on 2005-08-23                           self.__D,
2367  #                           self.__X,
2368  # Revision 1.10  2005/08/12 01:45:36  jgs                           self.__Y,
2369  # erge of development branch dev-02 back to main trunk on 2005-08-12                           self.__d,
2370  #                           self.__y,
2371  # Revision 1.9.2.17  2005/09/21 07:03:33  matt                           self.__d_contact,
2372  # PDECoefficient and LinearPDE are now new style classes (introduced in Python                           self.__y_contact)
2373  # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been               self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2374  # modified to instead use portable/cooperative "super" calls to extend base               self.__reassemble=False
2375  # class methods.         return self.__transport_problem
2376  #       def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2377  # Revision 1.9.2.16  2005/09/16 01:54:37  matt                    d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2378  # Removed redundant if-loop.               if not M==None:
2379  #                    self.__reassemble=True
2380  # Revision 1.9.2.15  2005/09/14 08:09:18  matt                    self.__M=M
2381  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.               if not A==None:
2382  #                    self.__reassemble=True
2383  # Revision 1.9.2.14  2005/09/07 06:26:16  gross                    self.__A=A
2384  # the solver from finley are put into the standalone package paso now               if not B==None:
2385  #                    self.__reassemble=True
2386  # Revision 1.9.2.13  2005/08/31 08:45:03  gross                    self.__B=B
2387  # in the case of lumping no new system is allocated if the constraint is changed.               if not C==None:
2388  #                    self.__reassemble=True
2389  # Revision 1.9.2.12  2005/08/31 07:10:23  gross                    self.__C=C
2390  # test for Lumping added               if not D==None:
2391  #                    self.__reassemble=True
2392  # Revision 1.9.2.11  2005/08/30 01:53:45  gross                    self.__D=D
2393  # bug in format fixed.               if not X==None:
2394  #                    self.__reassemble=True
2395  # Revision 1.9.2.10  2005/08/26 07:14:17  gross                    self.__X=X
2396  # a few more bugs in linearPDE fixed. remaining problem are finley problems               if not Y==None:
2397  #                    self.__reassemble=True
2398  # Revision 1.9.2.9  2005/08/26 06:30:45  gross                    self.__Y=Y
2399  # fix for reported bug  0000004. test_linearPDE passes a few more tests               if not d==None:
2400  #                    self.__reassemble=True
2401  # Revision 1.9.2.8  2005/08/26 04:30:13  gross                    self.__d=d
2402  # gneric unit testing for linearPDE               if not y==None:
2403  #                    self.__reassemble=True
2404  # Revision 1.9.2.7  2005/08/25 07:06:50  gross                    self.__y=y
2405  # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so               if not d_contact==None:
2406  #                    self.__reassemble=True
2407  # Revision 1.9.2.6  2005/08/24 05:01:24  gross                    self.__d_contact=d_contact
2408  # problem with resetting the matrix in case of resetting its values to 0 fixed.               if not y_contact==None:
2409  #                    self.__reassemble=True
2410  # Revision 1.9.2.5  2005/08/24 02:03:28  gross                    self.__y_contact=y_contact
2411  # epydoc mark up partially fixed               if not q==None:
2412  #                    self.__reassemble=True
2413  # Revision 1.9.2.4  2005/08/22 07:11:09  gross                    self.__q=q
2414  # some problems with LinearPDEs fixed.               if not r==None:
2415  #                    self.__reassemble=True
2416  # Revision 1.9.2.3  2005/08/18 04:48:48  gross                    self.__r=r
2417  # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  
2418  #       def setInitialSolution(self,u):
2419  # Revision 1.9.2.2  2005/08/18 04:39:32  gross               if self.__useSUPG:
2420  # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now                   self.__u=util.interpolate(u,self.getFunctionSpace())
2421  #               else:
2422  # Revision 1.9.2.1  2005/07/29 07:10:27  gross                   self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2423  # new functions in util and a new pde type in linearPDEs  
2424  #       def solve(self,dt,**kwarg):
2425  # Revision 1.1.2.25  2005/07/28 04:21:09  gross             if self.__useSUPG:
2426  # Lame equation: (linear elastic, isotropic) added                  if self.__reassemble:
2427  #                      self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2428  # Revision 1.1.2.24  2005/07/22 06:37:11  gross                      self.__reassemble=False
2429  # some extensions to modellib and linearPDEs                  dt2=self.getSafeTimeStepSize()
2430  #                  nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2431  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane                  dt2=dt/nn
2432  # Fixed up some docstrings.  Moved module-level functions to top of file so                  nnn=0
2433  # that epydoc and doxygen can pick them up properly.                  u=self.__u
2434  #                  self.trace("number of substeps is %d."%nn)
2435  # Revision 1.1.2.22  2005/05/12 11:41:30  gross                  while nnn<nn :
2436  # some basic Models have been added                      self.__setSUPG(u,u,dt2/2)
2437  #                      u_half=self.__pde.getSolution(verbose=True)
2438  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane                      self.__setSUPG(u,u_half,dt2)
2439  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of                      u=self.__pde.getSolution(verbose=True)
2440  # file so that the AdvectivePDE class is picked up by doxygen.  Some                      nnn+=1
2441  # reformatting of docstrings.  Addition of code to make equations come out                  self.__u=u
2442  # as proper LaTeX.                  return self.__u
2443  #             else:
2444  # Revision 1.1.2.20  2005/04/15 07:09:08  gross                 kwarg["tolerance"]=self.__tolerance
2445  # some problems with functionspace and linearPDEs fixed.                 tp=self.__getTransportProblem()
2446  #                 return tp.solve(self.__source,dt,kwarg)
2447  # Revision 1.1.2.19  2005/03/04 05:27:07  gross       def __setSUPG(self,u0,u,dt):
2448  # bug in SystemPattern fixed.              g=util.grad(u)
2449  #              X=0
2450  # Revision 1.1.2.18  2005/02/08 06:16:45  gross              Y=self.__M*u0
2451  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed              X=0
2452  #              self.__pde.setValue(r=u0)
2453  # Revision 1.1.2.17  2005/02/08 05:56:19  gross              if not self.__A.isEmpty():
2454  # Reference Number handling added                 X=X+dt*util.matrixmult(self.__A,g)
2455  #              if not self.__B.isEmpty():
2456  # Revision 1.1.2.16  2005/02/07 04:41:28  gross                 X=X+dt*self.__B*u
2457  # some function exposed to python to make mesh merging running              if not  self.__C.isEmpty():
2458  #                 Y=Y+dt*util.inner(self.__C,g)
2459  # Revision 1.1.2.15  2005/02/03 00:14:44  gross              if not self.__D.isEmpty():
2460  # timeseries add and ESySParameter.py renames esysXML.py for consistence                 Y=Y+dt*self.__D*u
2461  #              if not self.__X.isEmpty():
2462  # Revision 1.1.2.14  2005/02/01 06:44:10  gross                 X=X+dt*self.__X
2463  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working              if not self.__Y.isEmpty():
2464  #                 Y=Y+dt*self.__Y
2465  # Revision 1.1.2.13  2005/01/25 00:47:07  gross              self.__pde.setValue(X=X,Y=Y)
2466  # updates in the documentation              if not self.__y.isEmpty():
2467  #                 self.__pde.setValue(y=dt*self.__y)
2468  # Revision 1.1.2.12  2005/01/12 01:28:04  matt              if not self.__y_contact.isEmpty():
2469  # Added createCoefficient method for linearPDEs.                 self.__pde.setValue(y=dt*self.__y_contact)
2470  #              self.__pde.setValue(r=u0)
 # Revision 1.1.2.11  2005/01/11 01:55:34  gross  
 # a problem in linearPDE class fixed  
 #  
 # Revision 1.1.2.10  2005/01/07 01:13:29  gross  
 # some bugs in linearPDE fixed  
 #  
 # Revision 1.1.2.9  2005/01/06 06:24:58  gross  
 # some bugs in slicing fixed  
 #  
 # Revision 1.1.2.8  2005/01/05 04:21:40  gross  
 # FunctionSpace checking/matchig in slicing added  
 #  
 # Revision 1.1.2.7  2004/12/29 10:03:41  gross  
 # bug in setValue fixed  
 #  
 # Revision 1.1.2.6  2004/12/29 05:29:59  gross  
 # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()  
 #  
 # Revision 1.1.2.5  2004/12/29 00:18:41  gross  
 # AdvectivePDE added  
 #  
 # Revision 1.1.2.4  2004/12/24 06:05:41  gross  
 # some changes in linearPDEs to add AdevectivePDE  
 #  
 # Revision 1.1.2.3  2004/12/16 00:12:34  gross  
 # __init__ of LinearPDE does not accept any coefficient anymore  
 #  
 # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  
 # *** empty log message ***  
 #  
 # Revision 1.1.2.1  2004/12/12 22:53:47  gross  
 # linearPDE has been renamed LinearPDE  
 #  
 # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross  
 # GMRES added  
 #  
 # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross  
 # options for GMRES and PRES20 added  
 #  
 # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross  
 # some small changes  
 #  
 # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross  
 # Finley solves 4M unknowns now  
 #  
 # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross  
 # poisson solver added  
 #  
 # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross  
 # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry  
 #  
 # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross  
 # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed  
 #  
 # Revision 1.1.1.1  2004/10/26 06:53:56  jgs  
 # initial import of project esys2  
 #  
 # Revision 1.3.2.3  2004/10/26 06:43:48  jgs  
 # committing Lutz's and Paul's changes to brach jgs  
 #  
 # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane  
 # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.  
 #  
 # Revision 1.3  2004/09/23 00:53:23  jgs  
 # minor fixes  
 #  
 # Revision 1.1  2004/08/28 12:58:06  gross  
 # SimpleSolve is not running yet: problem with == of functionsspace  
 #  

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