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revision 425 by gross, Tue Jan 10 04:10:39 2006 UTC revision 1703 by artak, Thu Aug 14 05:34:25 2008 UTC
# Line 1  Line 1 
1    #
2  # $Id$  # $Id$
   
3  #  #
4  #      COPYRIGHT ACcESS 2004 -  All Rights Reserved  #######################################################
5    #
6    #           Copyright 2003-2007 by ACceSS MNRF
7    #       Copyright 2007 by University of Queensland
8  #  #
9  #   This software is the property of ACcESS.  No part of this code  #                http://esscc.uq.edu.au
10  #   may be copied in any form or by any means without the expressed written  #        Primary Business: Queensland, Australia
11  #   consent of ACcESS.  Copying, use or modification of this software  #  Licensed under the Open Software License version 3.0
12  #   by any unauthorised person is illegal unless that  #     http://www.opensource.org/licenses/osl-3.0.php
 #   person has a software license agreement with ACcESS.  
13  #  #
14    #######################################################
15    #
16    
17  """  """
18  The module provides an interface to define and solve linear partial  The module provides an interface to define and solve linear partial
19  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
# Line 17  the PDE solver library defined through t Line 22  the PDE solver library defined through t
22  The general interface is provided through the L{LinearPDE} class. The  The general interface is provided through the L{LinearPDE} class. The
23  L{AdvectivePDE} which is derived from the L{LinearPDE} class  L{AdvectivePDE} which is derived from the L{LinearPDE} class
24  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},
25  L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}  L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
26  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
27  to define of solve these sepecial PDEs.  to define of solve these sepecial PDEs.
28    
29  @var __author__: name of author  @var __author__: name of author
30  @var __licence__: licence agreement  @var __copyright__: copyrights
31    @var __license__: licence agreement
32  @var __url__: url entry point on documentation  @var __url__: url entry point on documentation
33  @var __version__: version  @var __version__: version
34  @var __date__: date of the version  @var __date__: date of the version
35  """  """
36    
37    import math
38  import escript  import escript
39  import util  import util
40  import numarray  import numarray
41    
42  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
43  __licence__="contact: esys@access.uq.edu.au"  __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
44  __url__="http://www.iservo.edu.au/esys/escript"                      http://www.access.edu.au
45                    Primary Business: Queensland, Australia"""
46    __license__="""Licensed under the Open Software License version 3.0
47                 http://www.opensource.org/licenses/osl-3.0.php"""
48    __url__="http://www.iservo.edu.au/esys"
49  __version__="$Revision$"  __version__="$Revision$"
50  __date__="$Date$"  __date__="$Date$"
51    
# Line 43  class IllegalCoefficient(ValueError): Line 54  class IllegalCoefficient(ValueError):
54     """     """
55     raised if an illegal coefficient of the general ar particular PDE is requested.     raised if an illegal coefficient of the general ar particular PDE is requested.
56     """     """
57       pass
58    
59  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
60     """     """
61     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
62     """     """
63       pass
64    
65    class IllegalCoefficientFunctionSpace(ValueError):
66       """
67       raised if an incorrect function space for a coefficient is used.
68       """
69    
70  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
71     """     """
72     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
73     """     """
74       pass
75    
76  class PDECoefficient(object):  class PDECoefficient(object):
77      """      """
# Line 61  class PDECoefficient(object): Line 80  class PDECoefficient(object):
80      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
81      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
82      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
83        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
84        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
85        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
86      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
87      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
88      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
# Line 82  class PDECoefficient(object): Line 104  class PDECoefficient(object):
104      OPERATOR=10      OPERATOR=10
105      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
106      BOTH=12      BOTH=12
107        INTERIOR_REDUCED=13
108        BOUNDARY_REDUCED=14
109        CONTACT_REDUCED=15
110    
111      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
112         """         """
113         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
114    
115         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
116         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
117                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
118         @param pattern: describes the shape of the coefficient and how the shape is build for a given         @param pattern: describes the shape of the coefficient and how the shape is build for a given
119                spatial dimension and numbers of equation and solution in then PDE. For instance,                spatial dimension and numbers of equation and solution in then PDE. For instance,
120                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
# Line 99  class PDECoefficient(object): Line 125  class PDECoefficient(object):
125         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
126         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
127         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
128           @param reduced: indicates if reduced
129           @type reduced: C{bool}
130         """         """
131         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
132         self.what=where         self.what=where
# Line 120  class PDECoefficient(object): Line 147  class PDECoefficient(object):
147         @param domain: domain on which the PDE uses the coefficient         @param domain: domain on which the PDE uses the coefficient
148         @type domain: L{Domain<escript.Domain>}         @type domain: L{Domain<escript.Domain>}
149         @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
150         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
151         @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
152         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
153         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
154         @rtype:  L{FunctionSpace<escript.FunctionSpace>}         @rtype:  L{FunctionSpace<escript.FunctionSpace>}
155         """         """
156         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
157              return escript.Function(domain)              return escript.Function(domain)
158           elif self.what==self.INTERIOR_REDUCED:
159                return escript.ReducedFunction(domain)
160         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
161              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
162           elif self.what==self.BOUNDARY_REDUCED:
163                return escript.ReducedFunctionOnBoundary(domain)
164         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
165              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
166           elif self.what==self.CONTACT_REDUCED:
167                return escript.ReducedFunctionOnContactZero(domain)
168         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
169              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
170                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 160  class PDECoefficient(object): Line 193  class PDECoefficient(object):
193         @param numSolutions: number of components of the PDE solution         @param numSolutions: number of components of the PDE solution
194         @type numSolutions: C{int}         @type numSolutions: C{int}
195         @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
196         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
197         @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
198         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
199         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
200         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
201         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
202           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
203         """         """
204         if newValue==None:         if newValue==None:
205             newValue=escript.Data()             newValue=escript.Data()
206         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
207             if not newValue.isEmpty():             if not newValue.isEmpty():
208                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
209                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
210                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
211                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
212                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
213         else:         else:
214             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
215         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 318  class LinearPDE(object): Line 353  class LinearPDE(object):
353    
354     For a single PDE with a solution with a single component the linear PDE is defined in the following form:     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
355    
356     M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
357    
358    
359     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
360     ie. summation over indexes appearing twice in a term of a sum is performed, is used.     ie. summation over indexes appearing twice in a term of a sum is performed, is used.
361     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
362     L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.     L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
363     M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.     L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
364       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
365       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
366    
367     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
368    
369     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
370    
371     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.     where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
    Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are  
    each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
372    
373    
374     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
# Line 344  class LinearPDE(object): Line 380  class LinearPDE(object):
380    
381     The PDE is symmetrical if     The PDE is symmetrical if
382    
383     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
384    
385     For a system of PDEs and a solution with several components the PDE has the form     For a system of PDEs and a solution with several components the PDE has the form
386    
387     M{-grad(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])[j]+C[i,k,l]*grad(u[k])[l]+D[i,k]*u[k] =-grad(X[i,j])[j]+Y[i] }     M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
388    
389     M{A} is a ramk four, M{B} and M{C} are each a rank three, M{D} and M{X} are each a rank two and M{Y} is a rank one.     M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
390     The natural boundary conditions take the form:     The natural boundary conditions take the form:
391    
392     M{n[j]*(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}     M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
393    
394    
395     The coefficient M{d} is a rank two and M{y} is a  rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form     The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
396    
397       Constraints take the form
398    
399     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
400    
# Line 366  class LinearPDE(object): Line 403  class LinearPDE(object):
403     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
404    
405          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
406            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
407          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
408            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
409          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
410            - M{D_reduced[i,k]=D_reduced[i,k]}
411          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
412            - M{d_reduced[i,k]=d_reduced[k,i]}
413    
414     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
415     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
416     defined as     defined as
417    
418     M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}     M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
419    
420     For the case of single solution component and single PDE M{J} is defined     For the case of single solution component and single PDE M{J} is defined
421    
422     M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}     M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
423    
424     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
425     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
426     the contact condition takes the form     the contact condition takes the form
427    
428     M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}     M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
429    
430     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
431     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
432     L{jump<util.jump>}.     L{jump<util.jump>}.
433     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
434       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
435     In case of a single PDE and a single component solution the contact condition takes the form     In case of a single PDE and a single component solution the contact condition takes the form
436    
437     M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}     M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
438    
439     In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar     In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
    both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
440    
441     @cvar DEFAULT: The default method used to solve the system of linear equations     @cvar DEFAULT: The default method used to solve the system of linear equations
442     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 404  class LinearPDE(object): Line 445  class LinearPDE(object):
445     @cvar CR: The conjugate residual method     @cvar CR: The conjugate residual method
446     @cvar CGS: The conjugate gardient square method     @cvar CGS: The conjugate gardient square method
447     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
448       @cvar TFQMR: Transport Free Quasi Minimal Residual method.
449     @cvar SSOR: The symmetric overrealaxtion method     @cvar SSOR: The symmetric overrealaxtion method
450     @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in     @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
451     @cvar ILUT: The incomplete LU factorization preconditioner with will in     @cvar ILUT: The incomplete LU factorization preconditioner with will in
# Line 418  class LinearPDE(object): Line 460  class LinearPDE(object):
460     @cvar SCSL: SGI SCSL solver library     @cvar SCSL: SGI SCSL solver library
461     @cvar MKL: Intel's MKL solver library     @cvar MKL: Intel's MKL solver library
462     @cvar UMFPACK: the UMFPACK library     @cvar UMFPACK: the UMFPACK library
463       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
464     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
465       @cvar AMG: algebraic multi grid
466       @cvar RILU: recursive ILU
467    
468     """     """
469     DEFAULT= 0     DEFAULT= 0
# Line 443  class LinearPDE(object): Line 488  class LinearPDE(object):
488     UMFPACK= 16     UMFPACK= 16
489     ITERATIVE= 20     ITERATIVE= 20
490     PASO= 21     PASO= 21
491       AMG= 22
492       RILU = 23
493       TRILINOS = 24
494       NONLINEAR_GMRES = 25
495       TFQMR = 26
496    
497     __TOL=1.e-13     SMALL_TOLERANCE=1.e-13
498     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
499     __METHOD_KEY="method"     __METHOD_KEY="method"
500     __SYMMETRY_KEY="symmetric"     __SYMMETRY_KEY="symmetric"
# Line 480  class LinearPDE(object): Line 530  class LinearPDE(object):
530         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
531         "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),
532         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
533           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
534           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
535           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
536           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
537           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
538           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
540           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
541           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
542           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
543         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
544         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
545    
# Line 665  class LinearPDE(object): Line 725  class LinearPDE(object):
725       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
726       """       """
727       if u==None:       if u==None:
728            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
729       else:       else:
730          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
731    
732     def getResidual(self,u=None):     def getResidual(self,u=None):
733       """       """
# Line 699  class LinearPDE(object): Line 759  class LinearPDE(object):
759        else:        else:
760           A=self.getCoefficientOfGeneralPDE("A")           A=self.getCoefficientOfGeneralPDE("A")
761           if not A.isEmpty():           if not A.isEmpty():
762              tol=util.Lsup(A)*self.__TOL              tol=util.Lsup(A)*self.SMALL_TOLERANCE
763              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
764                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
765                    for j in range(self.getDim()):                    for j in range(self.getDim()):
# Line 723  class LinearPDE(object): Line 783  class LinearPDE(object):
783              if verbose: print "non-symmetric PDE because C is not present but B is"              if verbose: print "non-symmetric PDE because C is not present but B is"
784              out=False              out=False
785           elif not B.isEmpty() and not C.isEmpty():           elif not B.isEmpty() and not C.isEmpty():
786              tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.              tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
787              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
788                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
789                     for j in range(self.getDim()):                     for j in range(self.getDim()):
# Line 739  class LinearPDE(object): Line 799  class LinearPDE(object):
799           if self.getNumSolutions()>1:           if self.getNumSolutions()>1:
800             D=self.getCoefficientOfGeneralPDE("D")             D=self.getCoefficientOfGeneralPDE("D")
801             if not D.isEmpty():             if not D.isEmpty():
802               tol=util.Lsup(D)*self.__TOL               tol=util.Lsup(D)*self.SMALL_TOLERANCE
803               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
804                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
805                    if util.Lsup(D[i,k]-D[k,i])>tol:                    if util.Lsup(D[i,k]-D[k,i])>tol:
# Line 747  class LinearPDE(object): Line 807  class LinearPDE(object):
807                        out=False                        out=False
808             d=self.getCoefficientOfGeneralPDE("d")             d=self.getCoefficientOfGeneralPDE("d")
809             if not d.isEmpty():             if not d.isEmpty():
810               tol=util.Lsup(d)*self.__TOL               tol=util.Lsup(d)*self.SMALL_TOLERANCE
811               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
812                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
813                    if util.Lsup(d[i,k]-d[k,i])>tol:                    if util.Lsup(d[i,k]-d[k,i])>tol:
# Line 755  class LinearPDE(object): Line 815  class LinearPDE(object):
815                        out=False                        out=False
816             d_contact=self.getCoefficientOfGeneralPDE("d_contact")             d_contact=self.getCoefficientOfGeneralPDE("d_contact")
817             if not d_contact.isEmpty():             if not d_contact.isEmpty():
818               tol=util.Lsup(d_contact)*self.__TOL               tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
819               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
820                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
821                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
822                        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)
823                        out=False                        out=False
824             # and now the reduced coefficients
825             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
826             if not A_reduced.isEmpty():
827                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
828                if self.getNumSolutions()>1:
829                   for i in range(self.getNumEquations()):
830                      for j in range(self.getDim()):
831                         for k in range(self.getNumSolutions()):
832                            for l in range(self.getDim()):
833                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
834                                   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)
835                                   out=False
836                else:
837                   for j in range(self.getDim()):
838                      for l in range(self.getDim()):
839                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
840                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
841                            out=False
842             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
843             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
844             if B_reduced.isEmpty() and not C_reduced.isEmpty():
845                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
846                out=False
847             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
848                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
849                out=False
850             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
851                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
852                if self.getNumSolutions()>1:
853                   for i in range(self.getNumEquations()):
854                       for j in range(self.getDim()):
855                          for k in range(self.getNumSolutions()):
856                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
857                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
858                                  out=False
859                else:
860                   for j in range(self.getDim()):
861                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
862                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
863                         out=False
864             if self.getNumSolutions()>1:
865               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
866               if not D_reduced.isEmpty():
867                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
868                 for i in range(self.getNumEquations()):
869                    for k in range(self.getNumSolutions()):
870                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
871                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
872                          out=False
873               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
874               if not d_reduced.isEmpty():
875                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
876                 for i in range(self.getNumEquations()):
877                    for k in range(self.getNumSolutions()):
878                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
879                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
880                          out=False
881               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
882               if not d_contact_reduced.isEmpty():
883                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
884                 for i in range(self.getNumEquations()):
885                    for k in range(self.getNumSolutions()):
886                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
887                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
888                          out=False
889        return out        return out
890    
891     def getSolution(self,**options):     def getSolution(self,**options):
# Line 800  class LinearPDE(object): Line 925  class LinearPDE(object):
925       """       """
926       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
927    
928       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]}
929    
930       or       or
931    
932       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]}
933    
934       @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.
935       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 812  class LinearPDE(object): Line 937  class LinearPDE(object):
937       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
938       """       """
939       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
940       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))) \
941               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
942               -util.self.getCoefficientOfGeneralPDE("X") \
943               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
944               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
945               -util.self.getCoefficientOfGeneralPDE("X_reduced")
946     # =============================================================================     # =============================================================================
947     #   solver settings:     #   solver settings:
948     # =============================================================================     # =============================================================================
# Line 821  class LinearPDE(object): Line 951  class LinearPDE(object):
951         sets a new solver         sets a new solver
952    
953         @param solver: sets a new solver method.         @param solver: sets a new solver method.
954         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}.         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{TFQMR}, L{PRES20}, L{LUMPING}, L{AMG}
955         @param preconditioner: sets a new solver method.         @param preconditioner: sets a new solver method.
956         @type solver: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
957         """         """
958         if solver==None: solve=self.DEFAULT         if solver==None: solver=self.__solver_method
959           if preconditioner==None: preconditioner=self.__preconditioner
960           if solver==None: solver=self.DEFAULT
961         if preconditioner==None: preconditioner=self.DEFAULT         if preconditioner==None: preconditioner=self.DEFAULT
962         if not (solver,preconditioner)==self.getSolverMethod():         if not (solver,preconditioner)==self.getSolverMethod():
963             self.__solver_method=solver             self.__solver_method=solver
# Line 849  class LinearPDE(object): Line 981  class LinearPDE(object):
981         elif m[0]==self.ITERATIVE: method= "ITERATIVE"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
982         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
983         elif m[0]==self.PCG: method= "PCG"         elif m[0]==self.PCG: method= "PCG"
984           elif m[0]==self.PCG: method= "TFQMR"
985         elif m[0]==self.CR: method= "CR"         elif m[0]==self.CR: method= "CR"
986         elif m[0]==self.CGS: method= "CGS"         elif m[0]==self.CGS: method= "CGS"
987         elif m[0]==self.BICGSTAB: method= "BICGSTAB"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
# Line 856  class LinearPDE(object): Line 989  class LinearPDE(object):
989         elif m[0]==self.GMRES: method= "GMRES"         elif m[0]==self.GMRES: method= "GMRES"
990         elif m[0]==self.PRES20: method= "PRES20"         elif m[0]==self.PRES20: method= "PRES20"
991         elif m[0]==self.LUMPING: method= "LUMPING"         elif m[0]==self.LUMPING: method= "LUMPING"
992           elif m[0]==self.AMG: method= "AMG"
993         if m[1]==self.DEFAULT: method+="+DEFAULT"         if m[1]==self.DEFAULT: method+="+DEFAULT"
994         elif m[1]==self.JACOBI: method+= "+JACOBI"         elif m[1]==self.JACOBI: method+= "+JACOBI"
995         elif m[1]==self.ILU0: method+= "+ILU0"         elif m[1]==self.ILU0: method+= "+ILU0"
996         elif m[1]==self.ILUT: method+= "+ILUT"         elif m[1]==self.ILUT: method+= "+ILUT"
997         elif m[1]==self.SSOR: method+= "+SSOR"         elif m[1]==self.SSOR: method+= "+SSOR"
998           elif m[1]==self.AMG: method+= "+AMG"
999           elif m[1]==self.RILU: method+= "+RILU"
1000         if p==self.DEFAULT: package="DEFAULT"         if p==self.DEFAULT: package="DEFAULT"
1001         elif p==self.PASO: package= "PASO"         elif p==self.PASO: package= "PASO"
1002         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
1003         elif p==self.SCSL: package= "SCSL"         elif p==self.SCSL: package= "SCSL"
1004         elif p==self.UMFPACK: package= "UMFPACK"         elif p==self.UMFPACK: package= "UMFPACK"
1005           elif p==self.TRILINOS: package= "TRILINOS"
1006         else : method="unknown"         else : method="unknown"
1007         return "%s solver of %s package"%(method,package)         return "%s solver of %s package"%(method,package)
1008    
# Line 883  class LinearPDE(object): Line 1020  class LinearPDE(object):
1020         """         """
1021         sets a new solver package         sets a new solver package
1022    
1023         @param solver: sets a new solver method.         @param package: sets a new solver method.
1024         @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}, L{TRILINOS}
1025         """         """
1026         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1027         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
1028             self.__solver_method=solver             self.__solver_package=package
1029             self.__checkMatrixType()             self.__checkMatrixType()
1030             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
1031    
# Line 921  class LinearPDE(object): Line 1058  class LinearPDE(object):
1058         @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
1059                     the system will be resolved.                     the system will be resolved.
1060         @type tol: positive C{float}         @type tol: positive C{float}
1061         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1062         """         """
1063         if not tol>0:         if not tol>0:
1064             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1065         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1066         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1067         self.__tolerance=tol         self.__tolerance=tol
# Line 1205  class LinearPDE(object): Line 1342  class LinearPDE(object):
1342         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1343             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1344         else:         else:
1345             self.__righthandside*=0             self.__righthandside.setToZero()
1346             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1347         return self.__righthandside         return self.__righthandside
1348    
# Line 1255  class LinearPDE(object): Line 1392  class LinearPDE(object):
1392       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1393       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1394       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1395                    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},
1396                      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}.
1397       """       """
1398       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1399          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1283  class LinearPDE(object): Line 1421  class LinearPDE(object):
1421       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1422       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1423       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1424                    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},
1425                      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}.
1426       """       """
1427       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1428          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1299  class LinearPDE(object): Line 1438  class LinearPDE(object):
1438       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1439       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1440       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1441                    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},
1442                      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}.
1443       """       """
1444       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1445          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1315  class LinearPDE(object): Line 1455  class LinearPDE(object):
1455       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1456       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1457       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1458                    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},
1459                      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}.
1460       """       """
1461       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1462          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 1445  class LinearPDE(object): Line 1586  class LinearPDE(object):
1586        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1587        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1588        @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>}.
1589          @keyword A_reduced: value for coefficient A_reduced.
1590          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1591        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1592        @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>}.
1593          @keyword B_reduced: value for coefficient B_reduced
1594          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1595        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1596        @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>}.
1597          @keyword C_reduced: value for coefficient C_reduced
1598          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1599        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1600        @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>}.
1601          @keyword D_reduced: value for coefficient D_reduced
1602          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1603        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1604        @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>}.
1605          @keyword X_reduced: value for coefficient X_reduced
1606          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1607        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1608        @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>}.
1609          @keyword Y_reduced: value for coefficient Y_reduced
1610          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1611        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1612        @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>}.
1613          @keyword d_reduced: value for coefficient d_reduced
1614          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1615        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1616        @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>}.
1617        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1618        @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>}.
1619                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1620          @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>}.
1621        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1622        @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>}.
1623                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1624          @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>}.
1625        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1626        @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>}
1627                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1499  class LinearPDE(object): Line 1656  class LinearPDE(object):
1656        # 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:
1657        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1658          try:          try:
1659             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1660                                             self.getNumEquations(),self.getNumSolutions(),
1661                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1662               self.alteredCoefficient(i)
1663            except IllegalCoefficientFunctionSpace,m:
1664                # if the function space is wrong then we try the reduced version:
1665                i_red=i+"_reduced"
1666                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1667                    try:
1668                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1669                                                          self.getNumEquations(),self.getNumSolutions(),
1670                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1671                        self.alteredCoefficient(i_red)
1672                    except IllegalCoefficientValue,m:
1673                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1674                    except IllegalCoefficientFunctionSpace,m:
1675                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1676                else:
1677                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1678          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1679             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1680        self.__altered_coefficients=True        self.__altered_coefficients=True
1681        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1682        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1511  class LinearPDE(object): Line 1684  class LinearPDE(object):
1684           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1685           homogeneous_constraint=True           homogeneous_constraint=True
1686           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1687               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1688                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1689                 self.__invalidateSystem()                 self.__invalidateSystem()
1690    
# Line 1525  class LinearPDE(object): Line 1698  class LinearPDE(object):
1698         if not self.__operator_is_Valid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1699            if self.isUsingLumping():            if self.isUsingLumping():
1700                if not self.__operator_is_Valid:                if not self.__operator_is_Valid:
1701                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1702                   if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Using coefficient A in lumped matrix can produce wrong results"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1703                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1704                   if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Using coefficient C in lumped matrix can produce wrong results"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1705                   mat=self.__getNewOperator()                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1706                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient B in lumped matrix may not be present."
1707                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1708                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient C in lumped matrix may not be present."
1709                             self.getCoefficientOfGeneralPDE("C"), \                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1710                             self.getCoefficientOfGeneralPDE("D"), \                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1711                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1712                             escript.Data(), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1713                             self.getCoefficientOfGeneralPDE("d"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1714                             escript.Data(),\                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1715                             self.getCoefficientOfGeneralPDE("d_contact"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1716                             escript.Data())                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1717                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1718                   del mat                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1719                     D=self.getCoefficientOfGeneralPDE("D")
1720                     d=self.getCoefficientOfGeneralPDE("d")
1721                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1723                     if not D.isEmpty():
1724                         if self.getNumSolutions()>1:
1725                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1726                         else:
1727                            D_times_e=D
1728                     else:
1729                        D_times_e=escript.Data()
1730                     if not d.isEmpty():
1731                         if self.getNumSolutions()>1:
1732                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1733                         else:
1734                            d_times_e=d
1735                     else:
1736                        d_times_e=escript.Data()
1737          
1738                     if not D_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            D_reduced_times_e=D_reduced
1743                     else:
1744                        D_reduced_times_e=escript.Data()
1745                     if not d_reduced.isEmpty():
1746                         if self.getNumSolutions()>1:
1747                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1748                         else:
1749                            d_reduced_times_e=d_reduced
1750                     else:
1751                        d_reduced_times_e=escript.Data()
1752    
1753                     self.__operator=self.__getNewRightHandSide()
1754                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1755                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1756                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1757                     else:
1758                        self.getDomain().addPDEToRHS(self.__operator, \
1759                                                     escript.Data(), \
1760                                                     D_times_e, \
1761                                                     d_times_e,\
1762                                                     escript.Data())
1763                        self.getDomain().addPDEToRHS(self.__operator, \
1764                                                     escript.Data(), \
1765                                                     D_reduced_times_e, \
1766                                                     d_reduced_times_e,\
1767                                                     escript.Data())
1768                     self.__operator=1./self.__operator
1769                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1770                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
1771                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
# Line 1551  class LinearPDE(object): Line 1774  class LinearPDE(object):
1774                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1775                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1776                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1777                     self.getDomain().addPDEToRHS(self.__righthandside, \
1778                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1779                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1780                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1781                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1782                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1783                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1784            else:            else:
# Line 1566  class LinearPDE(object): Line 1794  class LinearPDE(object):
1794                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1795                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1796                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1797                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1798                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1806                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1808                   self.__applyConstraint()                   self.__applyConstraint()
1809                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1810                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1577  class LinearPDE(object): Line 1816  class LinearPDE(object):
1816                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1817                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1818                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1819                     self.getDomain().addPDEToRHS(self.__righthandside, \
1820                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1821                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1822                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1823                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1824                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1825                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1826                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1592  class LinearPDE(object): Line 1836  class LinearPDE(object):
1836                              escript.Data(),\                              escript.Data(),\
1837                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1838                              escript.Data())                              escript.Data())
1839                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1840                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1841                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1842                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1843                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1844                                escript.Data(), \
1845                                escript.Data(), \
1846                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1847                                escript.Data(),\
1848                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1849                                escript.Data())
1850                   self.__applyConstraint()                   self.__applyConstraint()
1851                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1852                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1625  class Poisson(LinearPDE): Line 1880  class Poisson(LinearPDE):
1880       """       """
1881       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1882       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1883                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1884                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1885       self.setSymmetryOn()       self.setSymmetryOn()
1886    
1887     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1673  class Poisson(LinearPDE): Line 1929  class Poisson(LinearPDE):
1929           return escript.Data()           return escript.Data()
1930       elif name == "y_contact" :       elif name == "y_contact" :
1931           return escript.Data()           return escript.Data()
1932         elif name == "A_reduced" :
1933             return escript.Data()
1934         elif name == "B_reduced" :
1935             return escript.Data()
1936         elif name == "C_reduced" :
1937             return escript.Data()
1938         elif name == "D_reduced" :
1939             return escript.Data()
1940         elif name == "X_reduced" :
1941             return escript.Data()
1942         elif name == "Y_reduced" :
1943             return self.getCoefficient("f_reduced")
1944         elif name == "d_reduced" :
1945             return escript.Data()
1946         elif name == "y_reduced" :
1947             return escript.Data()
1948         elif name == "d_contact_reduced" :
1949             return escript.Data()
1950         elif name == "y_contact_reduced" :
1951             return escript.Data()
1952       elif name == "r" :       elif name == "r" :
1953           return escript.Data()           return escript.Data()
1954       elif name == "q" :       elif name == "q" :
# Line 1709  class Helmholtz(LinearPDE): Line 1985  class Helmholtz(LinearPDE):
1985       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1986                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1987                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1993                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1994       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1772  class Helmholtz(LinearPDE): Line 2050  class Helmholtz(LinearPDE):
2050           return escript.Data()           return escript.Data()
2051       elif name == "y_contact" :       elif name == "y_contact" :
2052           return escript.Data()           return escript.Data()
2053         elif name == "A_reduced" :
2054             return escript.Data()
2055         elif name == "B_reduced" :
2056             return escript.Data()
2057         elif name == "C_reduced" :
2058             return escript.Data()
2059         elif name == "D_reduced" :
2060             return escript.Data()
2061         elif name == "X_reduced" :
2062             return escript.Data()
2063         elif name == "Y_reduced" :
2064             return self.getCoefficient("f_reduced")
2065         elif name == "d_reduced" :
2066             return escript.Data()
2067         elif name == "y_reduced" :
2068            return self.getCoefficient("g_reduced")
2069         elif name == "d_contact_reduced" :
2070             return escript.Data()
2071         elif name == "y_contact_reduced" :
2072             return escript.Data()
2073       elif name == "r" :       elif name == "r" :
2074           return self.getCoefficient("r")           return self.getCoefficient("r")
2075       elif name == "q" :       elif name == "q" :
# Line 1783  class LameEquation(LinearPDE): Line 2081  class LameEquation(LinearPDE):
2081     """     """
2082     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2083    
2084     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] }
2085    
2086     with natural boundary conditons:     with natural boundary conditons:
2087    
2088     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] }
2089    
2090     and constraints:     and constraints:
2091    
# Line 1807  class LameEquation(LinearPDE): Line 2105  class LameEquation(LinearPDE):
2105                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2106        self.setSymmetryOn()        self.setSymmetryOn()
2107    
2108     def setValue(self,**coefficients):     def setValues(self,**coefficients):
2109       """       """
2110       sets new values to coefficients       sets new values to coefficients
2111    
# Line 1830  class LameEquation(LinearPDE): Line 2128  class LameEquation(LinearPDE):
2128                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
2129       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2130       """       """
2131       super(LameEquation, self).setValue(**coefficients)       super(LameEquation, self).setValues(**coefficients)
2132    
2133     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2134       """       """
# Line 1870  class LameEquation(LinearPDE): Line 2168  class LameEquation(LinearPDE):
2168           return escript.Data()           return escript.Data()
2169       elif name == "y_contact" :       elif name == "y_contact" :
2170           return escript.Data()           return escript.Data()
2171         elif name == "A_reduced" :
2172             return escript.Data()
2173         elif name == "B_reduced" :
2174             return escript.Data()
2175         elif name == "C_reduced" :
2176             return escript.Data()
2177         elif name == "D_reduced" :
2178             return escript.Data()
2179         elif name == "X_reduced" :
2180             return escript.Data()
2181         elif name == "Y_reduced" :
2182             return escript.Data()
2183         elif name == "d_reduced" :
2184             return escript.Data()
2185         elif name == "y_reduced" :
2186             return escript.Data()
2187         elif name == "d_contact_reduced" :
2188             return escript.Data()
2189         elif name == "y_contact_reduced" :
2190             return escript.Data()
2191       elif name == "r" :       elif name == "r" :
2192           return self.getCoefficient("r")           return self.getCoefficient("r")
2193       elif name == "q" :       elif name == "q" :
# Line 1877  class LameEquation(LinearPDE): Line 2195  class LameEquation(LinearPDE):
2195       else:       else:
2196          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2197    
2198  class AdvectivePDE(LinearPDE):  def LinearSinglePDE(domain,debug=False):
2199     """     """
2200     In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}     defines a single linear PDEs
    up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.  
   
    In the following we set  
   
    M{Z[j]=C[j]-B[j]}  
   
    or  
   
    M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}  
   
    To measure the dominance of the advective terms over the diffusive term M{A} the  
    X{Pelclet number} M{P} is used. It is defined as  
   
    M{P=h|Z|/(2|A|)}  
   
    where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size  
    from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.  
   
    From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:  
   
    M{S{Xi}=S{xi}(P) h/|Z|}  
   
    where M{S{xi}} is a suitable function of the Peclet number.  
   
    In the case of a single PDE the coefficient are up-dated in the following way:  
          - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}  
          - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}  
          - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}  
          - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}  
   
    Similar for the case of a systems of PDEs:  
          - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}  
          - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}  
          - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}  
          - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}  
   
    where M{S{delta}} is L{kronecker}.  
    Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}  
    but with the intension to stabilize the solution.  
2201    
2202       @param domain: domain of the PDE
2203       @type domain: L{Domain<escript.Domain>}
2204       @param debug: if True debug informations are printed.
2205       @rtype: L{LinearPDE}
2206     """     """
2207     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
       """  
       creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}  
   
       @param domain: domain of the PDE  
       @type domain: L{Domain<escript.Domain>}  
       @param numEquations: number of equations. If numEquations==None the number of equations  
                            is exracted from the PDE coefficients.  
       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components  
                            is exracted from the PDE coefficients.  
       @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the  
                  M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.  
       @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.  
       @param debug: if True debug informations are printed.  
       """  
       super(AdvectivePDE, self).__init__(domain,\  
                                          numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def setValue(**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)  
2208    
2209     def ELMAN_RAMAGE(self,P):  def LinearPDESystem(domain,debug=False):
      """  
      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 __calculateXi(self,peclet_factor,flux,h):  
        flux=util.Lsup(flux)  
        if flux_max>0.:  
           return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)  
        else:  
           return 0.  
   
    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():  
                 flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       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  
                       # flux=C-util.reorderComponents(B,[0,2,1])  
                    else:  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2  
                       # flux=C-B  
                 else:  
                    if self.getNumSolutions()>1:  
                       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])  
                    else:  
                       for l in range(self.getDim()): flux2+=(C[l]-B[l])**2  
                       #flux=C-B  
                 length_of_flux=util.sqrt(flux2)  
             elif C.isEmpty():  
               length_of_flux=util.length(B)  
               #flux=B  
             else:  
               length_of_flux=util.length(C)  
               #flux=C  
   
             #length_of_flux=util.length(flux)  
             flux_max=util.Lsup(length_of_flux)  
             if flux_max>0.:  
                # 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.__TOL)  
                else:  
                     inv_A=1./self.__TOL  
                peclet_number=length_of_flux*h/2*inv_A  
                xi=self.__xi(peclet_number)  
                self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)  
                self.trace("preclet number = %e"%util.Lsup(peclet_number))  
       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.createNewCoefficient("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:  
                 for j in range(self.getDim()):  
                    for l in range(self.getDim()):  
                       if not C.isEmpty() and not B.isEmpty():  
                           Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])  
                       elif C.isEmpty():  
                           Aout[j,l]+=Xi*B[j]*B[l]  
                       else:  
                           Aout[j,l]+=Xi*C[j]*C[l]  
                  # if not C.isEmpty() and not B.isEmpty():  
                  #    tmp=C-B  
                  #    Aout=Aout+Xi*util.outer(tmp,tmp)  
                  # elif C.isEmpty():  
                  #    Aout=Aout+Xi*util.outer(B,B)  
                  # else:  
                  # Aout=Aout+Xi*util.outer(C,C)  
          return Aout  
      elif name == "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.createNewCoefficient("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:  
                tmp=Xi*D  
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
                # Bout=Bout+Xi*D*C  
          return Bout  
      elif name == "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.createNewCoefficient("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:  
                tmp=Xi*D  
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
                # Cout=Cout+tmp*D*B  
          return Cout  
      elif name == "D" :  
          return self.getCoefficient("D")  
      elif name == "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.createNewCoefficient("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:  
                  tmp=Xi*Y  
                  for j in range(self.getDim()):  
                     if not C.isEmpty() and not B.isEmpty():  
                        Xout[j]+=tmp*(C[j]-B[j])  
                        # Xout=Xout+Xi*Y*(C-B)  
                     elif C.isEmpty():  
                        Xout[j]-=tmp*B[j]  
                        # Xout=Xout-Xi*Y*B  
                     else:  
                        Xout[j]+=tmp*C[j]  
                        # Xout=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  
   
 class AdvectionDiffusion(LinearPDE):  
2210     """     """
2211     Class to define PDE equation of the unisotropic advection-diffusion problem, which is genear L{LinearPDE} of the form     defines a system of linear PDEs
   
    M{S{omega}*u + inner(v,grad(u))- grad(matrixmult(k_bar,grad(u))[j])[j] = f}  
   
    with natural boundary conditons  
   
    M{n[j]*matrixmult(k,grad(u))[j] = g- S{alpha}u }  
   
    and constraints:  
   
    M{u=r} where M{q>0}  
   
    and  
   
    M{k_bar[i,j]=k[i,j]+upwind[i]*upwind[j]}  
2212    
2213       @param domain: domain of the PDE
2214       @type domain: L{Domain<escript.Domain>}
2215       @param debug: if True debug informations are printed.
2216       @rtype: L{LinearPDE}
2217     """     """
2218       return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2219    
2220     def __init__(self,domain,debug=False):  class TransportPDE(object):
      """  
      initializes a new Poisson equation  
   
      @param domain: domain of the PDE  
      @type domain: L{Domain<escript.Domain>}  
      @param debug: if True debug informations are printed.  
   
2221       """       """
2222       super(AdvectionDiffusion, self).__init__(domain,1,1,debug)       Warning: This is still a very experimental. The class is still changing!
      self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),  
                         "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),  
                         "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
                         "v": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),  
                         "upwind": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_DIM,),PDECoefficient.OPERATOR),  
                         "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),  
                         "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),  
                         "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),  
                         "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}  
2223    
2224     def setValue(self,**coefficients):       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2225       """      
2226       sets new values to coefficients       u=r where q>0
2227        
2228       @param coefficients: new values assigned to coefficients       all coefficients are constant over time.
2229       @keyword omega: value for coefficient M{S{omega}}  
2230       @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.       typical usage:
2231       @keyword k: value for coefficient M{k}  
2232       @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.           p=TransportPDE(dom)
2233       @keyword v: value for coefficient M{v}           p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2234       @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2235       @keyword upwind: value for upwind term M{upwind}           t=0
2236       @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.           dt=0.1
2237       @keyword f: value for right hand side M{f}           while (t<1.):
2238       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.                u=p.solve(dt)
2239       @keyword alpha: value for right hand side M{S{alpha}}  
2240       @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.       """
2241       @keyword g: value for right hand side M{g}       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2242       @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.          self.__domain=domain
2243       @keyword r: prescribed values M{r} for the solution in constraints.          self.__num_equations=num_equations
2244       @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}          self.__useSUPG=useSUPG
2245                 depending of reduced order is used for the representation of the equation.          self.__trace=trace
2246       @keyword q: mask for location of constraints          self.__theta=theta
2247       @type q: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}          self.__matrix_type=0
2248                 depending of reduced order is used for the representation of the equation.          self.__reduced=True
2249       @raise IllegalCoefficient: if an unknown coefficient keyword is used.          self.__reassemble=True
2250       """          if self.__useSUPG:
2251       super(AdvectionDiffusion, self).setValue(**coefficients)             self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2252               self.__pde.setSymmetryOn()
2253               self.__pde.setReducedOrderOn()
2254            else:
2255               self.__transport_problem=self.__getNewTransportProblem()
2256            self.setTolerance()
2257            self.__M=escript.Data()
2258            self.__A=escript.Data()
2259            self.__B=escript.Data()
2260            self.__C=escript.Data()
2261            self.__D=escript.Data()
2262            self.__X=escript.Data()
2263            self.__Y=escript.Data()
2264            self.__d=escript.Data()
2265            self.__y=escript.Data()
2266            self.__d_contact=escript.Data()
2267            self.__y_contact=escript.Data()
2268            self.__r=escript.Data()
2269            self.__q=escript.Data()
2270    
2271         def trace(self,text):
2272                 if self.__trace: print text
2273         def getSafeTimeStepSize(self):
2274            if self.__useSUPG:
2275                if self.__reassemble:
2276                   h=self.__domain.getSize()
2277                   dt=None
2278                   if not self.__A.isEmpty():
2279                      dt2=util.inf(h**2*self.__M/util.length(self.__A))
2280                      if dt == None:
2281                         dt = dt2
2282                      else:
2283                         dt=1./(1./dt+1./dt2)
2284                   if not self.__B.isEmpty():
2285                      dt2=util.inf(h*self.__M/util.length(self.__B))
2286                      if dt == None:
2287                         dt = dt2
2288                      else:
2289                         dt=1./(1./dt+1./dt2)
2290                   if not  self.__C.isEmpty():
2291                      dt2=util.inf(h*self.__M/util.length(self.__C))
2292                      if dt == None:
2293                         dt = dt2
2294                      else:
2295                         dt=1./(1./dt+1./dt2)
2296                   if not self.__D.isEmpty():
2297                      dt2=util.inf(self.__M/util.length(self.__D))
2298                      if dt == None:
2299                         dt = dt2
2300                      else:
2301                         dt=1./(1./dt+1./dt2)
2302                   self.__dt = dt/2
2303                return self.__dt
2304            else:
2305                return self.__getTransportProblem().getSafeTimeStepSize()
2306         def getDomain(self):
2307            return self.__domain
2308         def getTheta(self):
2309            return self.__theta
2310         def getNumEquations(self):
2311            return self.__num_equations
2312         def setReducedOn(self):
2313              if not self.reduced():
2314                  if self.__useSUPG:
2315                     self.__pde.setReducedOrderOn()
2316                  else:
2317                     self.__transport_problem=self.__getNewTransportProblem()
2318              self.__reduced=True
2319         def setReducedOff(self):
2320              if self.reduced():
2321                  if self.__useSUPG:
2322                     self.__pde.setReducedOrderOff()
2323                  else:
2324                     self.__transport_problem=self.__getNewTransportProblem()
2325              self.__reduced=False
2326         def reduced(self):
2327             return self.__reduced
2328         def getFunctionSpace(self):
2329            if self.reduced():
2330               return escript.ReducedSolution(self.getDomain())
2331            else:
2332               return escript.Solution(self.getDomain())
2333    
2334     def getCoefficientOfGeneralPDE(self,name):       def setTolerance(self,tol=1.e-8):
2335       """          self.__tolerance=tol
2336       return the value of the coefficient name of the general PDE          if self.__useSUPG:
2337                  self.__pde.setTolerance(self.__tolerance)
2338    
2339       @param name: name of the coefficient requested.       def __getNewTransportProblem(self):
2340       @type name: C{string}         """
2341       @return: the value of the coefficient  name         returns an instance of a new operator
2342       @rtype: L{Data<escript.Data>}         """
2343       @raise IllegalCoefficient: if name is not one of coefficients         self.trace("New Transport problem is allocated.")
2344                    "A", M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.         return self.getDomain().newTransportProblem( \
2345       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.                                 self.getTheta(),
2346       """                                 self.getNumEquations(), \
2347       if name == "A" :                                 self.getFunctionSpace(), \
2348           return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))                                 self.__matrix_type)
2349       elif name == "B" :            
2350           return escript.Data()       def __getNewSolutionVector(self):
2351       elif name == "C" :           if self.getNumEquations() ==1 :
2352           return self.getCoefficient("v")                  out=escript.Data(0.0,(),self.getFunctionSpace())
2353       elif name == "D" :           else:
2354           return self.getCoefficient("omega")                  out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2355       elif name == "X" :           return out
          return escript.Data()  
      elif name == "Y" :  
          return self.getCoefficient("f")  
      elif name == "d" :  
          return self.getCoefficient("alpha")  
      elif name == "y" :  
          return self.getCoefficient("g")  
      elif name == "d_contact" :  
          return escript.Data()  
      elif name == "y_contact" :  
          return escript.Data()  
      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  
2356    
2357         def __getTransportProblem(self):
2358           if self.__reassemble:
2359                 self.__source=self.__getNewSolutionVector()
2360                 self.__transport_problem.reset()
2361                 self.getDomain().addPDEToTransportProblem(
2362                             self.__transport_problem,
2363                             self.__source,
2364                             self.__M,
2365                             self.__A,
2366                             self.__B,
2367                             self.__C,
2368                             self.__D,
2369                             self.__X,
2370                             self.__Y,
2371                             self.__d,
2372                             self.__y,
2373                             self.__d_contact,
2374                             self.__y_contact)
2375                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2376                 self.__reassemble=False
2377           return self.__transport_problem
2378         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2379                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2380                 if not M==None:
2381                      self.__reassemble=True
2382                      self.__M=M
2383                 if not A==None:
2384                      self.__reassemble=True
2385                      self.__A=A
2386                 if not B==None:
2387                      self.__reassemble=True
2388                      self.__B=B
2389                 if not C==None:
2390                      self.__reassemble=True
2391                      self.__C=C
2392                 if not D==None:
2393                      self.__reassemble=True
2394                      self.__D=D
2395                 if not X==None:
2396                      self.__reassemble=True
2397                      self.__X=X
2398                 if not Y==None:
2399                      self.__reassemble=True
2400                      self.__Y=Y
2401                 if not d==None:
2402                      self.__reassemble=True
2403                      self.__d=d
2404                 if not y==None:
2405                      self.__reassemble=True
2406                      self.__y=y
2407                 if not d_contact==None:
2408                      self.__reassemble=True
2409                      self.__d_contact=d_contact
2410                 if not y_contact==None:
2411                      self.__reassemble=True
2412                      self.__y_contact=y_contact
2413                 if not q==None:
2414                      self.__reassemble=True
2415                      self.__q=q
2416                 if not r==None:
2417                      self.__reassemble=True
2418                      self.__r=r
2419    
2420         def setInitialSolution(self,u):
2421                 if self.__useSUPG:
2422                     self.__u=util.interpolate(u,self.getFunctionSpace())
2423                 else:
2424                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2425    
2426  # $Log$       def solve(self,dt,**kwarg):
2427  # Revision 1.14  2005/09/22 01:54:57  jgs             if self.__useSUPG:
2428  # Merge of development branch dev-02 back to main trunk on 2005-09-22                  if self.__reassemble:
2429  #                      self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2430  # Revision 1.13  2005/09/15 03:44:19  jgs                      self.__reassemble=False
2431  # Merge of development branch dev-02 back to main trunk on 2005-09-15                  dt2=self.getSafeTimeStepSize()
2432  #                  nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2433  # Revision 1.12  2005/09/01 03:31:28  jgs                  dt2=dt/nn
2434  # Merge of development branch dev-02 back to main trunk on 2005-09-01                  nnn=0
2435  #                  u=self.__u
2436  # Revision 1.11  2005/08/23 01:24:28  jgs                  self.trace("number of substeps is %d."%nn)
2437  # Merge of development branch dev-02 back to main trunk on 2005-08-23                  while nnn<nn :
2438  #                      self.__setSUPG(u,u,dt2/2)
2439  # Revision 1.10  2005/08/12 01:45:36  jgs                      u_half=self.__pde.getSolution(verbose=True)
2440  # erge of development branch dev-02 back to main trunk on 2005-08-12                      self.__setSUPG(u,u_half,dt2)
2441  #                      u=self.__pde.getSolution(verbose=True)
2442  # Revision 1.9.2.17  2005/09/21 07:03:33  matt                      nnn+=1
2443  # PDECoefficient and LinearPDE are now new style classes (introduced in Python                  self.__u=u
2444  # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been                  return self.__u
2445  # modified to instead use portable/cooperative "super" calls to extend base             else:
2446  # class methods.                 kwarg["tolerance"]=self.__tolerance
2447  #                 tp=self.__getTransportProblem()
2448  # Revision 1.9.2.16  2005/09/16 01:54:37  matt                 return tp.solve(self.__source,dt,kwarg)
2449  # Removed redundant if-loop.       def __setSUPG(self,u0,u,dt):
2450  #              g=util.grad(u)
2451  # Revision 1.9.2.15  2005/09/14 08:09:18  matt              X=0
2452  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.              Y=self.__M*u0
2453  #              X=0
2454  # Revision 1.9.2.14  2005/09/07 06:26:16  gross              self.__pde.setValue(r=u0)
2455  # the solver from finley are put into the standalone package paso now              if not self.__A.isEmpty():
2456  #                 X=X+dt*util.matrixmult(self.__A,g)
2457  # Revision 1.9.2.13  2005/08/31 08:45:03  gross              if not self.__B.isEmpty():
2458  # in the case of lumping no new system is allocated if the constraint is changed.                 X=X+dt*self.__B*u
2459  #              if not  self.__C.isEmpty():
2460  # Revision 1.9.2.12  2005/08/31 07:10:23  gross                 Y=Y+dt*util.inner(self.__C,g)
2461  # test for Lumping added              if not self.__D.isEmpty():
2462  #                 Y=Y+dt*self.__D*u
2463  # Revision 1.9.2.11  2005/08/30 01:53:45  gross              if not self.__X.isEmpty():
2464  # bug in format fixed.                 X=X+dt*self.__X
2465  #              if not self.__Y.isEmpty():
2466  # Revision 1.9.2.10  2005/08/26 07:14:17  gross                 Y=Y+dt*self.__Y
2467  # a few more bugs in linearPDE fixed. remaining problem are finley problems              self.__pde.setValue(X=X,Y=Y)
2468  #              if not self.__y.isEmpty():
2469  # Revision 1.9.2.9  2005/08/26 06:30:45  gross                 self.__pde.setValue(y=dt*self.__y)
2470  # fix for reported bug  0000004. test_linearPDE passes a few more tests              if not self.__y_contact.isEmpty():
2471  #                 self.__pde.setValue(y=dt*self.__y_contact)
2472  # Revision 1.9.2.8  2005/08/26 04:30:13  gross              self.__pde.setValue(r=u0)
 # 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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