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revision 614 by elspeth, Wed Mar 22 01:37:07 2006 UTC revision 1204 by gross, Sat Jun 23 11:43:12 2007 UTC
# Line 7  the PDE solver library defined through t Line 7  the PDE solver library defined through t
7  The general interface is provided through the L{LinearPDE} class. The  The general interface is provided through the L{LinearPDE} class. The
8  L{AdvectivePDE} which is derived from the L{LinearPDE} class  L{AdvectivePDE} which is derived from the L{LinearPDE} class
9  provides an interface to PDE dominated by its advective terms. The L{Poisson},  provides an interface to PDE dominated by its advective terms. The L{Poisson},
10  L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}  L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
11  classs which are also derived form the L{LinearPDE} class should be used  classs which are also derived form the L{LinearPDE} class should be used
12  to define of solve these sepecial PDEs.  to define of solve these sepecial PDEs.
13    
14  @var __author__: name of author  @var __author__: name of author
15    @var __copyright__: copyrights
16  @var __license__: licence agreement  @var __license__: licence agreement
17  @var __url__: url entry point on documentation  @var __url__: url entry point on documentation
18  @var __version__: version  @var __version__: version
# Line 28  __copyright__="""  Copyright (c) 2006 by Line 29  __copyright__="""  Copyright (c) 2006 by
29                  Primary Business: Queensland, Australia"""                  Primary Business: Queensland, Australia"""
30  __license__="""Licensed under the Open Software License version 3.0  __license__="""Licensed under the Open Software License version 3.0
31               http://www.opensource.org/licenses/osl-3.0.php"""               http://www.opensource.org/licenses/osl-3.0.php"""
32  __url__="http://www.iservo.edu.au/esys/escript"  __url__="http://www.iservo.edu.au/esys"
33  __version__="$Revision$"  __version__="$Revision$"
34  __date__="$Date$"  __date__="$Date$"
35    
# Line 37  class IllegalCoefficient(ValueError): Line 38  class IllegalCoefficient(ValueError):
38     """     """
39     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.
40     """     """
41       pass
42    
43  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
44     """     """
45     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
46     """     """
47       pass
48    
49    class IllegalCoefficientFunctionSpace(ValueError):
50       """
51       raised if an incorrect function space for a coefficient is used.
52       """
53    
54  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
55     """     """
56     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
57     """     """
58       pass
59    
60  class PDECoefficient(object):  class PDECoefficient(object):
61      """      """
# Line 55  class PDECoefficient(object): Line 64  class PDECoefficient(object):
64      @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
65      @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
66      @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
67        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
68        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
69        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
70      @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
71      @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
72      @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 76  class PDECoefficient(object): Line 88  class PDECoefficient(object):
88      OPERATOR=10      OPERATOR=10
89      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
90      BOTH=12      BOTH=12
91        INTERIOR_REDUCED=13
92        BOUNDARY_REDUCED=14
93        CONTACT_REDUCED=15
94    
95      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
96         """         """
97         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
98    
99         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
100         @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},
101                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
102         @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
103                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,
104                (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 93  class PDECoefficient(object): Line 109  class PDECoefficient(object):
109         @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}
110         @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
111         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
112           @param reduced: indicates if reduced
113           @type reduced: C{bool}
114         """         """
115          
116         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
117         self.what=where         self.what=where
118         self.pattern=pattern         self.pattern=pattern
# Line 114  class PDECoefficient(object): Line 132  class PDECoefficient(object):
132         @param domain: domain on which the PDE uses the coefficient         @param domain: domain on which the PDE uses the coefficient
133         @type domain: L{Domain<escript.Domain>}         @type domain: L{Domain<escript.Domain>}
134         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
135         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
136         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
137         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
138         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
139         @rtype:  L{FunctionSpace<escript.FunctionSpace>}         @rtype:  L{FunctionSpace<escript.FunctionSpace>}
140         """         """
141         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
142              return escript.Function(domain)              return escript.Function(domain)
143           elif self.what==self.INTERIOR_REDUCED:
144                return escript.ReducedFunction(domain)
145         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
146              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
147           elif self.what==self.BOUNDARY_REDUCED:
148                return escript.ReducedFunctionOnBoundary(domain)
149         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
150              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
151           elif self.what==self.CONTACT_REDUCED:
152                return escript.ReducedFunctionOnContactZero(domain)
153         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
154              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
155                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 154  class PDECoefficient(object): Line 178  class PDECoefficient(object):
178         @param numSolutions: number of components of the PDE solution         @param numSolutions: number of components of the PDE solution
179         @type numSolutions: C{int}         @type numSolutions: C{int}
180         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
181         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
182         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
183         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
184         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
185         @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>}
186         @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
187           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
188         """         """
189         if newValue==None:         if newValue==None:
190             newValue=escript.Data()             newValue=escript.Data()
191         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
192             if not newValue.isEmpty():             if not newValue.isEmpty():
193                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
194                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
195                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
196                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
197                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
198         else:         else:
199             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
200         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 312  class LinearPDE(object): Line 338  class LinearPDE(object):
338    
339     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:
340    
341     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)}
342    
343    
344     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,
345     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.
346     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
347     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
348     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
349       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
350       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.
351    
352     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
353    
354     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}
355    
356     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>}.  
357    
358    
359     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 338  class LinearPDE(object): Line 365  class LinearPDE(object):
365    
366     The PDE is symmetrical if     The PDE is symmetrical if
367    
368     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]
369    
370     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
371    
372     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] }
373    
374     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.
375     The natural boundary conditions take the form:     The natural boundary conditions take the form:
376    
377     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]}
378    
379    
380     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>}.
381    
382       Constraints take the form
383    
384     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
385    
# Line 360  class LinearPDE(object): Line 388  class LinearPDE(object):
388     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
389    
390          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
391            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
392          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
393            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
394          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
395            - M{D_reduced[i,k]=D_reduced[i,k]}
396          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
397            - M{d_reduced[i,k]=d_reduced[k,i]}
398    
399     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
400     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
401     defined as     defined as
402    
403     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]}
404    
405     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
406    
407     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]}
408    
409     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
410     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
411     the contact condition takes the form     the contact condition takes the form
412    
413     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]}
414    
415     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
416     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
417     L{jump<util.jump>}.     L{jump<util.jump>}.
418     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>}.
419        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>}.
420     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
421    
422     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)}
423    
424     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>}.  
425    
426     @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
427     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 478  class LinearPDE(object): Line 510  class LinearPDE(object):
510         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
511         "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),
512         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
513           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
514           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
515           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
516           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
517           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
518           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
519           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
520           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
521           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
522           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
523         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
524         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
525    
# Line 663  class LinearPDE(object): Line 705  class LinearPDE(object):
705       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
706       """       """
707       if u==None:       if u==None:
708            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
709       else:       else:
710          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
711    
712     def getResidual(self,u=None):     def getResidual(self,u=None):
713       """       """
# Line 759  class LinearPDE(object): Line 801  class LinearPDE(object):
801                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
802                        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)
803                        out=False                        out=False
804             # and now the reduced coefficients
805             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
806             if not A_reduced.isEmpty():
807                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
808                if self.getNumSolutions()>1:
809                   for i in range(self.getNumEquations()):
810                      for j in range(self.getDim()):
811                         for k in range(self.getNumSolutions()):
812                            for l in range(self.getDim()):
813                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
814                                   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)
815                                   out=False
816                else:
817                   for j in range(self.getDim()):
818                      for l in range(self.getDim()):
819                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
820                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
821                            out=False
822             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
823             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
824             if B_reduced.isEmpty() and not C_reduced.isEmpty():
825                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
826                out=False
827             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
828                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
829                out=False
830             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
831                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
832                if self.getNumSolutions()>1:
833                   for i in range(self.getNumEquations()):
834                       for j in range(self.getDim()):
835                          for k in range(self.getNumSolutions()):
836                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
837                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
838                                  out=False
839                else:
840                   for j in range(self.getDim()):
841                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
842                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
843                         out=False
844             if self.getNumSolutions()>1:
845               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
846               if not D_reduced.isEmpty():
847                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
848                 for i in range(self.getNumEquations()):
849                    for k in range(self.getNumSolutions()):
850                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
851                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
852                          out=False
853               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
854               if not d_reduced.isEmpty():
855                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
856                 for i in range(self.getNumEquations()):
857                    for k in range(self.getNumSolutions()):
858                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
859                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
860                          out=False
861               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
862               if not d_contact_reduced.isEmpty():
863                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
864                 for i in range(self.getNumEquations()):
865                    for k in range(self.getNumSolutions()):
866                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
867                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
868                          out=False
869        return out        return out
870    
871     def getSolution(self,**options):     def getSolution(self,**options):
# Line 798  class LinearPDE(object): Line 905  class LinearPDE(object):
905       """       """
906       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
907    
908       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]}
909    
910       or       or
911    
912       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]}
913    
914       @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.
915       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 810  class LinearPDE(object): Line 917  class LinearPDE(object):
917       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
918       """       """
919       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
920       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))) \
921               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
922               -util.self.getCoefficientOfGeneralPDE("X") \
923               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
924               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
925               -util.self.getCoefficientOfGeneralPDE("X_reduced")
926     # =============================================================================     # =============================================================================
927     #   solver settings:     #   solver settings:
928     # =============================================================================     # =============================================================================
# Line 884  class LinearPDE(object): Line 996  class LinearPDE(object):
996         """         """
997         sets a new solver package         sets a new solver package
998    
999         @param solver: sets a new solver method.         @param package: sets a new solver method.
1000         @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}         @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
1001         """         """
1002         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1003         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
1004             self.__solver_method=solver             self.__solver_package=package
1005             self.__checkMatrixType()             self.__checkMatrixType()
1006             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
1007    
# Line 922  class LinearPDE(object): Line 1034  class LinearPDE(object):
1034         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1035                     the system will be resolved.                     the system will be resolved.
1036         @type tol: positive C{float}         @type tol: positive C{float}
1037         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1038         """         """
1039         if not tol>0:         if not tol>0:
1040             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1041         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1042         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1043         self.__tolerance=tol         self.__tolerance=tol
# Line 1206  class LinearPDE(object): Line 1318  class LinearPDE(object):
1318         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1319             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1320         else:         else:
1321             self.__righthandside*=0             self.__righthandside.setToZero()
1322             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1323         return self.__righthandside         return self.__righthandside
1324    
# Line 1256  class LinearPDE(object): Line 1368  class LinearPDE(object):
1368       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1369       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1370       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1371                    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},
1372                      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}.
1373       """       """
1374       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1375          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1284  class LinearPDE(object): Line 1397  class LinearPDE(object):
1397       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1398       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1399       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1400                    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},
1401                      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}.
1402       """       """
1403       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1404          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1300  class LinearPDE(object): Line 1414  class LinearPDE(object):
1414       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1415       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1416       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1417                    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},
1418                      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}.
1419       """       """
1420       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1421          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1316  class LinearPDE(object): Line 1431  class LinearPDE(object):
1431       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1432       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1433       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1434                    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},
1435                      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}.
1436       """       """
1437       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1438          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 1446  class LinearPDE(object): Line 1562  class LinearPDE(object):
1562        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1563        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1564        @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>}.
1565          @keyword A_reduced: value for coefficient A_reduced.
1566          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1567        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1568        @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>}.
1569          @keyword B_reduced: value for coefficient B_reduced
1570          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1571        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1572        @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>}.
1573          @keyword C_reduced: value for coefficient C_reduced
1574          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1575        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1576        @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>}.
1577          @keyword D_reduced: value for coefficient D_reduced
1578          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1579        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1580        @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>}.
1581          @keyword X_reduced: value for coefficient X_reduced
1582          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1583        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1584        @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>}.
1585          @keyword Y_reduced: value for coefficient Y_reduced
1586          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1587        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1588        @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>}.
1589          @keyword d_reduced: value for coefficient d_reduced
1590          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1591        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1592        @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>}.
1593        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1594        @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>}.
1595                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1596          @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>}.
1597        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1598        @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>}.
1599                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1600          @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>}.
1601        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1602        @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>}
1603                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1500  class LinearPDE(object): Line 1632  class LinearPDE(object):
1632        # 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:
1633        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1634          try:          try:
1635             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1636                                             self.getNumEquations(),self.getNumSolutions(),
1637                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1638               self.alteredCoefficient(i)
1639            except IllegalCoefficientFunctionSpace,m:
1640                # if the function space is wrong then we try the reduced version:
1641                i_red=i+"_reduced"
1642                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1643                    try:
1644                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1645                                                          self.getNumEquations(),self.getNumSolutions(),
1646                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1647                        self.alteredCoefficient(i_red)
1648                    except IllegalCoefficientValue,m:
1649                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1650                    except IllegalCoefficientFunctionSpace,m:
1651                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1652                else:
1653                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1654          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1655             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1656        self.__altered_coefficients=True        self.__altered_coefficients=True
1657        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1658        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1512  class LinearPDE(object): Line 1660  class LinearPDE(object):
1660           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1661           homogeneous_constraint=True           homogeneous_constraint=True
1662           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1663               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1664                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1665                 self.__invalidateSystem()                 self.__invalidateSystem()
1666    
# Line 1531  class LinearPDE(object): Line 1679  class LinearPDE(object):
1679                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1680                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient A in lumped matrix may not be present."
1681                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1682                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient B in lumped matrix may not be present."
1683                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1684                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient C in lumped matrix may not be present."
1685                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1686                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1687                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1688                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1689                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1690                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1691                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1692                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1693                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1694                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1695                   D=self.getCoefficientOfGeneralPDE("D")                   D=self.getCoefficientOfGeneralPDE("D")
1696                     d=self.getCoefficientOfGeneralPDE("d")
1697                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1698                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1699                   if not D.isEmpty():                   if not D.isEmpty():
1700                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1701                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1702                       else:                       else:
1703                          D_times_e=D                          D_times_e=D
1704                   else:                   else:
1705                      D_times_e=escript.Data()                      D_times_e=escript.Data()
                  d=self.getCoefficientOfGeneralPDE("d")  
1706                   if not d.isEmpty():                   if not d.isEmpty():
1707                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1708                          d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1709                       else:                       else:
1710                          d_times_e=d                          d_times_e=d
1711                   else:                   else:
1712                      d_times_e=escript.Data()                      d_times_e=escript.Data()
1713                   d_contact=self.getCoefficientOfGeneralPDE("d_contact")        
1714                   if not d_contact.isEmpty():                   if not D_reduced.isEmpty():
1715                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1716                          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(),)))
1717                       else:                       else:
1718                          d_contact_times_e=d_contact                          D_reduced_times_e=D_reduced
1719                   else:                   else:
1720                      d_contact_times_e=escript.Data()                      D_reduced_times_e=escript.Data()
1721                         if not d_reduced.isEmpty():
1722                         if self.getNumSolutions()>1:
1723                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1724                         else:
1725                            d_reduced_times_e=d_reduced
1726                     else:
1727                        d_reduced_times_e=escript.Data()
1728    
1729                   self.__operator=self.__getNewRightHandSide()                   self.__operator=self.__getNewRightHandSide()
1730                   self.getDomain().addPDEToRHS(self.__operator, \                   if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1731                                                escript.Data(), \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1732                                                D_times_e, \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1733                                                d_times_e,\                   else:
1734                                                d_contact_times_e)                      self.getDomain().addPDEToRHS(self.__operator, \
1735                                                     escript.Data(), \
1736                                                     D_times_e, \
1737                                                     d_times_e,\
1738                                                     escript.Data())
1739                        self.getDomain().addPDEToRHS(self.__operator, \
1740                                                     escript.Data(), \
1741                                                     D_reduced_times_e, \
1742                                                     d_reduced_times_e,\
1743                                                     escript.Data())
1744                   self.__operator=1./self.__operator                   self.__operator=1./self.__operator
1745                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1746                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1574  class LinearPDE(object): Line 1750  class LinearPDE(object):
1750                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1751                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1752                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1753                     self.getDomain().addPDEToRHS(self.__righthandside, \
1754                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1755                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1756                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1757                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1758                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1759                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1760            else:            else:
# Line 1589  class LinearPDE(object): Line 1770  class LinearPDE(object):
1770                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1771                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1772                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1773                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1774                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1775                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1776                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1777                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1778                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1779                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1780                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1781                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1782                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1783                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1784                   self.__applyConstraint()                   self.__applyConstraint()
1785                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1786                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1600  class LinearPDE(object): Line 1792  class LinearPDE(object):
1792                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1793                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1794                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1795                     self.getDomain().addPDEToRHS(self.__righthandside, \
1796                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1798                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1799                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1800                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1801                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1802                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1615  class LinearPDE(object): Line 1812  class LinearPDE(object):
1812                              escript.Data(),\                              escript.Data(),\
1813                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1814                              escript.Data())                              escript.Data())
1815                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1816                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1817                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1818                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1819                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1820                                escript.Data(), \
1821                                escript.Data(), \
1822                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1823                                escript.Data(),\
1824                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1825                                escript.Data())
1826                   self.__applyConstraint()                   self.__applyConstraint()
1827                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1828                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1648  class Poisson(LinearPDE): Line 1856  class Poisson(LinearPDE):
1856       """       """
1857       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1858       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1859                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1860                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1861       self.setSymmetryOn()       self.setSymmetryOn()
1862    
1863     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1696  class Poisson(LinearPDE): Line 1905  class Poisson(LinearPDE):
1905           return escript.Data()           return escript.Data()
1906       elif name == "y_contact" :       elif name == "y_contact" :
1907           return escript.Data()           return escript.Data()
1908         elif name == "A_reduced" :
1909             return escript.Data()
1910         elif name == "B_reduced" :
1911             return escript.Data()
1912         elif name == "C_reduced" :
1913             return escript.Data()
1914         elif name == "D_reduced" :
1915             return escript.Data()
1916         elif name == "X_reduced" :
1917             return escript.Data()
1918         elif name == "Y_reduced" :
1919             return self.getCoefficient("f_reduced")
1920         elif name == "d_reduced" :
1921             return escript.Data()
1922         elif name == "y_reduced" :
1923             return escript.Data()
1924         elif name == "d_contact_reduced" :
1925             return escript.Data()
1926         elif name == "y_contact_reduced" :
1927             return escript.Data()
1928       elif name == "r" :       elif name == "r" :
1929           return escript.Data()           return escript.Data()
1930       elif name == "q" :       elif name == "q" :
# Line 1732  class Helmholtz(LinearPDE): Line 1961  class Helmholtz(LinearPDE):
1961       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1962                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1963                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1964                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1965                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1966                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1967                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1968                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1969                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1970       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1795  class Helmholtz(LinearPDE): Line 2026  class Helmholtz(LinearPDE):
2026           return escript.Data()           return escript.Data()
2027       elif name == "y_contact" :       elif name == "y_contact" :
2028           return escript.Data()           return escript.Data()
2029         elif name == "A_reduced" :
2030             return escript.Data()
2031         elif name == "B_reduced" :
2032             return escript.Data()
2033         elif name == "C_reduced" :
2034             return escript.Data()
2035         elif name == "D_reduced" :
2036             return escript.Data()
2037         elif name == "X_reduced" :
2038             return escript.Data()
2039         elif name == "Y_reduced" :
2040             return self.getCoefficient("f_reduced")
2041         elif name == "d_reduced" :
2042             return escript.Data()
2043         elif name == "y_reduced" :
2044            return self.getCoefficient("g_reduced")
2045         elif name == "d_contact_reduced" :
2046             return escript.Data()
2047         elif name == "y_contact_reduced" :
2048             return escript.Data()
2049       elif name == "r" :       elif name == "r" :
2050           return self.getCoefficient("r")           return self.getCoefficient("r")
2051       elif name == "q" :       elif name == "q" :
# Line 1806  class LameEquation(LinearPDE): Line 2057  class LameEquation(LinearPDE):
2057     """     """
2058     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2059    
2060     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[j])[i])[j] = F_i -grad(S{sigma}[i,j])[j] }     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[k])[k])[j] = F_i -grad(S{sigma}[ij])[j] }
2061    
2062     with natural boundary conditons:     with natural boundary conditons:
2063    
2064     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) - S{lambda}*grad(u[j])[i]) = f_i -n[j]*S{sigma}[i,j] }     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
2065    
2066     and constraints:     and constraints:
2067    
# Line 1893  class LameEquation(LinearPDE): Line 2144  class LameEquation(LinearPDE):
2144           return escript.Data()           return escript.Data()
2145       elif name == "y_contact" :       elif name == "y_contact" :
2146           return escript.Data()           return escript.Data()
2147         elif name == "A_reduced" :
2148             return escript.Data()
2149         elif name == "B_reduced" :
2150             return escript.Data()
2151         elif name == "C_reduced" :
2152             return escript.Data()
2153         elif name == "D_reduced" :
2154             return escript.Data()
2155         elif name == "X_reduced" :
2156             return escript.Data()
2157         elif name == "Y_reduced" :
2158             return escript.Data()
2159         elif name == "d_reduced" :
2160             return escript.Data()
2161         elif name == "y_reduced" :
2162             return escript.Data()
2163         elif name == "d_contact_reduced" :
2164             return escript.Data()
2165         elif name == "y_contact_reduced" :
2166             return escript.Data()
2167       elif name == "r" :       elif name == "r" :
2168           return self.getCoefficient("r")           return self.getCoefficient("r")
2169       elif name == "q" :       elif name == "q" :
# Line 1900  class LameEquation(LinearPDE): Line 2171  class LameEquation(LinearPDE):
2171       else:       else:
2172          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2173    
 class AdvectivePDE(LinearPDE):  
    """  
    In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}  
    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.  
   
    """  
    def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):  
       """  
       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  
   
       @param coefficients: new values assigned to coefficients  
       @keyword A: value for coefficient A.  
       @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @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.  
   
       """  
       if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()  
       super(AdvectivePDE, self).setValue(**coefficients)  
   
    def ELMAN_RAMAGE(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      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  
   
   
    def getCoefficientOfGeneralPDE(self,name):  
      """  
      return the value of the coefficient name of the general PDE  
   
      @param name: name of the coefficient requested.  
      @type name: C{string}  
      @return: the value of the coefficient name  
      @rtype: L{Data<escript.Data>}  
      @raise IllegalCoefficient: if name is not one of coefficients  
                   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}.  
      @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.  
      """  
      if not self.getNumEquations() == self.getNumSolutions():  
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
   
      if name == "A" :  
          A=self.getCoefficient("A")  
          B=self.getCoefficient("B")  
          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  
          else:  
             if X.isEmpty():  
                 Xout=self.createCoefficientOfGeneralPDE("X")  
             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  
   
 # $Log$  
 # Revision 1.14  2005/09/22 01:54:57  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-22  
 #  
 # Revision 1.13  2005/09/15 03:44:19  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-15  
 #  
 # Revision 1.12  2005/09/01 03:31:28  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-01  
 #  
 # Revision 1.11  2005/08/23 01:24:28  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-08-23  
 #  
 # Revision 1.10  2005/08/12 01:45:36  jgs  
 # erge of development branch dev-02 back to main trunk on 2005-08-12  
 #  
 # Revision 1.9.2.17  2005/09/21 07:03:33  matt  
 # PDECoefficient and LinearPDE are now new style classes (introduced in Python  
 # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been  
 # modified to instead use portable/cooperative "super" calls to extend base  
 # class methods.  
 #  
 # Revision 1.9.2.16  2005/09/16 01:54:37  matt  
 # Removed redundant if-loop.  
 #  
 # Revision 1.9.2.15  2005/09/14 08:09:18  matt  
 # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.  
 #  
 # Revision 1.9.2.14  2005/09/07 06:26:16  gross  
 # the solver from finley are put into the standalone package paso now  
 #  
 # Revision 1.9.2.13  2005/08/31 08:45:03  gross  
 # in the case of lumping no new system is allocated if the constraint is changed.  
 #  
 # Revision 1.9.2.12  2005/08/31 07:10:23  gross  
 # test for Lumping added  
 #  
 # Revision 1.9.2.11  2005/08/30 01:53:45  gross  
 # bug in format fixed.  
 #  
 # Revision 1.9.2.10  2005/08/26 07:14:17  gross  
 # a few more bugs in linearPDE fixed. remaining problem are finley problems  
 #  
 # Revision 1.9.2.9  2005/08/26 06:30:45  gross  
 # fix for reported bug  0000004. test_linearPDE passes a few more tests  
 #  
 # Revision 1.9.2.8  2005/08/26 04:30:13  gross  
 # gneric unit testing for linearPDE  
 #  
 # Revision 1.9.2.7  2005/08/25 07:06:50  gross  
 # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so  
 #  
 # Revision 1.9.2.6  2005/08/24 05:01:24  gross  
 # problem with resetting the matrix in case of resetting its values to 0 fixed.  
 #  
 # Revision 1.9.2.5  2005/08/24 02:03:28  gross  
 # epydoc mark up partially fixed  
 #  
 # Revision 1.9.2.4  2005/08/22 07:11:09  gross  
 # some problems with LinearPDEs fixed.  
 #  
 # Revision 1.9.2.3  2005/08/18 04:48:48  gross  
 # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  
 #  
 # Revision 1.9.2.2  2005/08/18 04:39:32  gross  
 # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now  
 #  
 # Revision 1.9.2.1  2005/07/29 07:10:27  gross  
 # new functions in util and a new pde type in linearPDEs  
 #  
 # Revision 1.1.2.25  2005/07/28 04:21:09  gross  
 # Lame equation: (linear elastic, isotropic) added  
 #  
 # Revision 1.1.2.24  2005/07/22 06:37:11  gross  
 # some extensions to modellib and linearPDEs  
 #  
 # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  
 # Fixed up some docstrings.  Moved module-level functions to top of file so  
 # that epydoc and doxygen can pick them up properly.  
 #  
 # Revision 1.1.2.22  2005/05/12 11:41:30  gross  
 # some basic Models have been added  
 #  
 # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane  
 # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of  
 # file so that the AdvectivePDE class is picked up by doxygen.  Some  
 # reformatting of docstrings.  Addition of code to make equations come out  
 # as proper LaTeX.  
 #  
 # Revision 1.1.2.20  2005/04/15 07:09:08  gross  
 # some problems with functionspace and linearPDEs fixed.  
 #  
 # Revision 1.1.2.19  2005/03/04 05:27:07  gross  
 # bug in SystemPattern fixed.  
 #  
 # Revision 1.1.2.18  2005/02/08 06:16:45  gross  
 # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed  
 #  
 # Revision 1.1.2.17  2005/02/08 05:56:19  gross  
 # Reference Number handling added  
 #  
 # Revision 1.1.2.16  2005/02/07 04:41:28  gross  
 # some function exposed to python to make mesh merging running  
 #  
 # Revision 1.1.2.15  2005/02/03 00:14:44  gross  
 # timeseries add and ESySParameter.py renames esysXML.py for consistence  
 #  
 # Revision 1.1.2.14  2005/02/01 06:44:10  gross  
 # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working  
 #  
 # Revision 1.1.2.13  2005/01/25 00:47:07  gross  
 # updates in the documentation  
 #  
 # Revision 1.1.2.12  2005/01/12 01:28:04  matt  
 # Added createCoefficient method for linearPDEs.  
 #  
 # 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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