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revision 425 by gross, Tue Jan 10 04:10:39 2006 UTC revision 1819 by artak, Tue Sep 30 05:58:06 2008 UTC
# Line 1  Line 1 
 # $Id$  
1    
2    ########################################################
3  #  #
4  #      COPYRIGHT ACcESS 2004 -  All Rights Reserved  # Copyright (c) 2003-2008 by University of Queensland
5  #  # Earth Systems Science Computational Center (ESSCC)
6  #   This software is the property of ACcESS.  No part of this code  # http://www.uq.edu.au/esscc
7  #   may be copied in any form or by any means without the expressed written  #
8  #   consent of ACcESS.  Copying, use or modification of this software  # Primary Business: Queensland, Australia
9  #   by any unauthorised person is illegal unless that  # Licensed under the Open Software License version 3.0
10  #   person has a software license agreement with ACcESS.  # http://www.opensource.org/licenses/osl-3.0.php
11  #  #
12    ########################################################
13    
14    __copyright__="""Copyright (c) 2003-2008 by University of Queensland
15    Earth Systems Science Computational Center (ESSCC)
16    http://www.uq.edu.au/esscc
17    Primary Business: Queensland, Australia"""
18    __license__="""Licensed under the Open Software License version 3.0
19    http://www.opensource.org/licenses/osl-3.0.php"""
20    __url__="http://www.uq.edu.au/esscc/escript-finley"
21    
22  """  """
23  The module provides an interface to define and solve linear partial  The module provides an interface to define and solve linear partial
24  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 27  the PDE solver library defined through t
27  The general interface is provided through the L{LinearPDE} class. The  The general interface is provided through the L{LinearPDE} class. The
28  L{AdvectivePDE} which is derived from the L{LinearPDE} class  L{AdvectivePDE} which is derived from the L{LinearPDE} class
29  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},
30  L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}  L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
31  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
32  to define of solve these sepecial PDEs.  to define of solve these sepecial PDEs.
33    
34  @var __author__: name of author  @var __author__: name of author
35  @var __licence__: licence agreement  @var __copyright__: copyrights
36    @var __license__: licence agreement
37  @var __url__: url entry point on documentation  @var __url__: url entry point on documentation
38  @var __version__: version  @var __version__: version
39  @var __date__: date of the version  @var __date__: date of the version
40  """  """
41    
42    import math
43  import escript  import escript
44  import util  import util
45  import numarray  import numarray
46    
47  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
 __licence__="contact: esys@access.uq.edu.au"  
 __url__="http://www.iservo.edu.au/esys/escript"  
 __version__="$Revision$"  
 __date__="$Date$"  
48    
49    
50  class IllegalCoefficient(ValueError):  class IllegalCoefficient(ValueError):
51     """     """
52     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.
53     """     """
54       pass
55    
56  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
57     """     """
58     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
59     """     """
60       pass
61    
62    class IllegalCoefficientFunctionSpace(ValueError):
63       """
64       raised if an incorrect function space for a coefficient is used.
65       """
66    
67  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
68     """     """
69     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
70     """     """
71       pass
72    
73  class PDECoefficient(object):  class PDECoefficient(object):
74      """      """
# Line 61  class PDECoefficient(object): Line 77  class PDECoefficient(object):
77      @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
78      @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
79      @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
80        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
81        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
82        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
83      @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
84      @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
85      @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 101  class PDECoefficient(object):
101      OPERATOR=10      OPERATOR=10
102      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
103      BOTH=12      BOTH=12
104        INTERIOR_REDUCED=13
105        BOUNDARY_REDUCED=14
106        CONTACT_REDUCED=15
107    
108      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
109         """         """
110         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
111    
112         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
113         @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},
114                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
115         @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
116                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,
117                (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 122  class PDECoefficient(object):
122         @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}
123         @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
124         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
125           @param reduced: indicates if reduced
126           @type reduced: C{bool}
127         """         """
128         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
129         self.what=where         self.what=where
# Line 120  class PDECoefficient(object): Line 144  class PDECoefficient(object):
144         @param domain: domain on which the PDE uses the coefficient         @param domain: domain on which the PDE uses the coefficient
145         @type domain: L{Domain<escript.Domain>}         @type domain: L{Domain<escript.Domain>}
146         @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
147         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
148         @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
149         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
150         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
151         @rtype:  L{FunctionSpace<escript.FunctionSpace>}         @rtype:  L{FunctionSpace<escript.FunctionSpace>}
152         """         """
153         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
154              return escript.Function(domain)              return escript.Function(domain)
155           elif self.what==self.INTERIOR_REDUCED:
156                return escript.ReducedFunction(domain)
157         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
158              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
159           elif self.what==self.BOUNDARY_REDUCED:
160                return escript.ReducedFunctionOnBoundary(domain)
161         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
162              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
163           elif self.what==self.CONTACT_REDUCED:
164                return escript.ReducedFunctionOnContactZero(domain)
165         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
166              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
167                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 160  class PDECoefficient(object): Line 190  class PDECoefficient(object):
190         @param numSolutions: number of components of the PDE solution         @param numSolutions: number of components of the PDE solution
191         @type numSolutions: C{int}         @type numSolutions: C{int}
192         @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
193         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
194         @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
195         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
196         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
197         @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>}
198         @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
199           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
200         """         """
201         if newValue==None:         if newValue==None:
202             newValue=escript.Data()             newValue=escript.Data()
203         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
204             if not newValue.isEmpty():             if not newValue.isEmpty():
205                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
206                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
207                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
208                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
209                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
210         else:         else:
211             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
212         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 318  class LinearPDE(object): Line 350  class LinearPDE(object):
350    
351     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:
352    
353     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)}
354    
355    
356     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,
357     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.
358     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
359     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
360     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
361       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
362       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.
363    
364     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
365    
366     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}
367    
368     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>}.  
369    
370    
371     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 377  class LinearPDE(object):
377    
378     The PDE is symmetrical if     The PDE is symmetrical if
379    
380     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]}
381    
382     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
383    
384     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] }
385    
386     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.
387     The natural boundary conditions take the form:     The natural boundary conditions take the form:
388    
389     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]}
390    
391    
392     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>}.
393    
394       Constraints take the form
395    
396     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
397    
# Line 366  class LinearPDE(object): Line 400  class LinearPDE(object):
400     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
401    
402          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
403            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
404          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
405            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
406          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
407            - M{D_reduced[i,k]=D_reduced[i,k]}
408          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
409            - M{d_reduced[i,k]=d_reduced[k,i]}
410    
411     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
412     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
413     defined as     defined as
414    
415     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]}
416    
417     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
418    
419     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]}
420    
421     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
422     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
423     the contact condition takes the form     the contact condition takes the form
424    
425     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]}
426    
427     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
428     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
429     L{jump<util.jump>}.     L{jump<util.jump>}.
430     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>}.
431       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>}.
432     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
433    
434     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)}
435    
436     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>}.  
437    
438     @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
439     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 404  class LinearPDE(object): Line 442  class LinearPDE(object):
442     @cvar CR: The conjugate residual method     @cvar CR: The conjugate residual method
443     @cvar CGS: The conjugate gardient square method     @cvar CGS: The conjugate gardient square method
444     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
445       @cvar TFQMR: Transport Free Quasi Minimal Residual method.
446       @cvar MINRES: Minimum residual method.
447     @cvar SSOR: The symmetric overrealaxtion method     @cvar SSOR: The symmetric overrealaxtion method
448     @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in     @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
449     @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 458  class LinearPDE(object):
458     @cvar SCSL: SGI SCSL solver library     @cvar SCSL: SGI SCSL solver library
459     @cvar MKL: Intel's MKL solver library     @cvar MKL: Intel's MKL solver library
460     @cvar UMFPACK: the UMFPACK library     @cvar UMFPACK: the UMFPACK library
461       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
462     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
463       @cvar AMG: algebraic multi grid
464       @cvar RILU: recursive ILU
465       @cvar GS: Gauss-Seidel solver
466    
467     """     """
468     DEFAULT= 0     DEFAULT= 0
# Line 443  class LinearPDE(object): Line 487  class LinearPDE(object):
487     UMFPACK= 16     UMFPACK= 16
488     ITERATIVE= 20     ITERATIVE= 20
489     PASO= 21     PASO= 21
490       AMG= 22
491       RILU = 23
492       TRILINOS = 24
493       NONLINEAR_GMRES = 25
494       TFQMR = 26
495       MINRES = 27
496       GS=28
497    
498     __TOL=1.e-13     SMALL_TOLERANCE=1.e-13
499     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
500     __METHOD_KEY="method"     __METHOD_KEY="method"
501     __SYMMETRY_KEY="symmetric"     __SYMMETRY_KEY="symmetric"
# Line 480  class LinearPDE(object): Line 531  class LinearPDE(object):
531         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
532         "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),
533         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
534           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
535           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
537           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
539           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
541           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
542           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
543           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
544         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
545         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
546    
# Line 665  class LinearPDE(object): Line 726  class LinearPDE(object):
726       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
727       """       """
728       if u==None:       if u==None:
729            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
730       else:       else:
731          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
732    
733     def getResidual(self,u=None):     def getResidual(self,u=None):
734       """       """
# Line 699  class LinearPDE(object): Line 760  class LinearPDE(object):
760        else:        else:
761           A=self.getCoefficientOfGeneralPDE("A")           A=self.getCoefficientOfGeneralPDE("A")
762           if not A.isEmpty():           if not A.isEmpty():
763              tol=util.Lsup(A)*self.__TOL              tol=util.Lsup(A)*self.SMALL_TOLERANCE
764              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
765                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
766                    for j in range(self.getDim()):                    for j in range(self.getDim()):
# Line 723  class LinearPDE(object): Line 784  class LinearPDE(object):
784              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"
785              out=False              out=False
786           elif not B.isEmpty() and not C.isEmpty():           elif not B.isEmpty() and not C.isEmpty():
787              tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.              tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
788              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
789                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
790                     for j in range(self.getDim()):                     for j in range(self.getDim()):
# Line 739  class LinearPDE(object): Line 800  class LinearPDE(object):
800           if self.getNumSolutions()>1:           if self.getNumSolutions()>1:
801             D=self.getCoefficientOfGeneralPDE("D")             D=self.getCoefficientOfGeneralPDE("D")
802             if not D.isEmpty():             if not D.isEmpty():
803               tol=util.Lsup(D)*self.__TOL               tol=util.Lsup(D)*self.SMALL_TOLERANCE
804               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
805                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
806                    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 808  class LinearPDE(object):
808                        out=False                        out=False
809             d=self.getCoefficientOfGeneralPDE("d")             d=self.getCoefficientOfGeneralPDE("d")
810             if not d.isEmpty():             if not d.isEmpty():
811               tol=util.Lsup(d)*self.__TOL               tol=util.Lsup(d)*self.SMALL_TOLERANCE
812               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
813                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
814                    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 816  class LinearPDE(object):
816                        out=False                        out=False
817             d_contact=self.getCoefficientOfGeneralPDE("d_contact")             d_contact=self.getCoefficientOfGeneralPDE("d_contact")
818             if not d_contact.isEmpty():             if not d_contact.isEmpty():
819               tol=util.Lsup(d_contact)*self.__TOL               tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
820               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
821                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
822                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
823                        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)
824                        out=False                        out=False
825             # and now the reduced coefficients
826             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
827             if not A_reduced.isEmpty():
828                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
829                if self.getNumSolutions()>1:
830                   for i in range(self.getNumEquations()):
831                      for j in range(self.getDim()):
832                         for k in range(self.getNumSolutions()):
833                            for l in range(self.getDim()):
834                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
835                                   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)
836                                   out=False
837                else:
838                   for j in range(self.getDim()):
839                      for l in range(self.getDim()):
840                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
841                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
842                            out=False
843             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
844             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
845             if B_reduced.isEmpty() and not C_reduced.isEmpty():
846                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
847                out=False
848             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
849                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
850                out=False
851             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
852                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
853                if self.getNumSolutions()>1:
854                   for i in range(self.getNumEquations()):
855                       for j in range(self.getDim()):
856                          for k in range(self.getNumSolutions()):
857                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
858                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
859                                  out=False
860                else:
861                   for j in range(self.getDim()):
862                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
863                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
864                         out=False
865             if self.getNumSolutions()>1:
866               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
867               if not D_reduced.isEmpty():
868                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
869                 for i in range(self.getNumEquations()):
870                    for k in range(self.getNumSolutions()):
871                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
872                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
873                          out=False
874               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
875               if not d_reduced.isEmpty():
876                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
877                 for i in range(self.getNumEquations()):
878                    for k in range(self.getNumSolutions()):
879                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
880                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
881                          out=False
882               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
883               if not d_contact_reduced.isEmpty():
884                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
885                 for i in range(self.getNumEquations()):
886                    for k in range(self.getNumSolutions()):
887                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
888                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
889                          out=False
890        return out        return out
891    
892     def getSolution(self,**options):     def getSolution(self,**options):
# Line 800  class LinearPDE(object): Line 926  class LinearPDE(object):
926       """       """
927       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
928    
929       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]}
930    
931       or       or
932    
933       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]}
934    
935       @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.
936       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 812  class LinearPDE(object): Line 938  class LinearPDE(object):
938       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
939       """       """
940       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
941       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))) \
942               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
943               -util.self.getCoefficientOfGeneralPDE("X") \
944               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
945               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
946               -util.self.getCoefficientOfGeneralPDE("X_reduced")
947     # =============================================================================     # =============================================================================
948     #   solver settings:     #   solver settings:
949     # =============================================================================     # =============================================================================
# Line 821  class LinearPDE(object): Line 952  class LinearPDE(object):
952         sets a new solver         sets a new solver
953    
954         @param solver: sets a new solver method.         @param solver: sets a new solver method.
955         @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{MINRES}, L{PRES20}, L{LUMPING}, L{AMG}
956         @param preconditioner: sets a new solver method.         @param preconditioner: sets a new solver method.
957         @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},  L{GS}
958         """         """
959         if solver==None: solve=self.DEFAULT         if solver==None: solver=self.__solver_method
960           if preconditioner==None: preconditioner=self.__preconditioner
961           if solver==None: solver=self.DEFAULT
962         if preconditioner==None: preconditioner=self.DEFAULT         if preconditioner==None: preconditioner=self.DEFAULT
963         if not (solver,preconditioner)==self.getSolverMethod():         if not (solver,preconditioner)==self.getSolverMethod():
964             self.__solver_method=solver             self.__solver_method=solver
# Line 849  class LinearPDE(object): Line 982  class LinearPDE(object):
982         elif m[0]==self.ITERATIVE: method= "ITERATIVE"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
983         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
984         elif m[0]==self.PCG: method= "PCG"         elif m[0]==self.PCG: method= "PCG"
985           elif m[0]==self.TFQMR: method= "TFQMR"
986           elif m[0]==self.MINRES: method= "MINRES"
987         elif m[0]==self.CR: method= "CR"         elif m[0]==self.CR: method= "CR"
988         elif m[0]==self.CGS: method= "CGS"         elif m[0]==self.CGS: method= "CGS"
989         elif m[0]==self.BICGSTAB: method= "BICGSTAB"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
# Line 856  class LinearPDE(object): Line 991  class LinearPDE(object):
991         elif m[0]==self.GMRES: method= "GMRES"         elif m[0]==self.GMRES: method= "GMRES"
992         elif m[0]==self.PRES20: method= "PRES20"         elif m[0]==self.PRES20: method= "PRES20"
993         elif m[0]==self.LUMPING: method= "LUMPING"         elif m[0]==self.LUMPING: method= "LUMPING"
994           elif m[0]==self.AMG: method= "AMG"
995         if m[1]==self.DEFAULT: method+="+DEFAULT"         if m[1]==self.DEFAULT: method+="+DEFAULT"
996         elif m[1]==self.JACOBI: method+= "+JACOBI"         elif m[1]==self.JACOBI: method+= "+JACOBI"
997         elif m[1]==self.ILU0: method+= "+ILU0"         elif m[1]==self.ILU0: method+= "+ILU0"
998         elif m[1]==self.ILUT: method+= "+ILUT"         elif m[1]==self.ILUT: method+= "+ILUT"
999         elif m[1]==self.SSOR: method+= "+SSOR"         elif m[1]==self.SSOR: method+= "+SSOR"
1000           elif m[1]==self.AMG: method+= "+AMG"
1001           elif m[1]==self.RILU: method+= "+RILU"
1002           elif m[1]==self.GS: method+= "+GS"
1003         if p==self.DEFAULT: package="DEFAULT"         if p==self.DEFAULT: package="DEFAULT"
1004         elif p==self.PASO: package= "PASO"         elif p==self.PASO: package= "PASO"
1005         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
1006         elif p==self.SCSL: package= "SCSL"         elif p==self.SCSL: package= "SCSL"
1007         elif p==self.UMFPACK: package= "UMFPACK"         elif p==self.UMFPACK: package= "UMFPACK"
1008           elif p==self.TRILINOS: package= "TRILINOS"
1009         else : method="unknown"         else : method="unknown"
1010         return "%s solver of %s package"%(method,package)         return "%s solver of %s package"%(method,package)
1011    
# Line 883  class LinearPDE(object): Line 1023  class LinearPDE(object):
1023         """         """
1024         sets a new solver package         sets a new solver package
1025    
1026         @param solver: sets a new solver method.         @param package: sets a new solver method.
1027         @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}
1028         """         """
1029         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1030         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
1031             self.__solver_method=solver             self.__solver_package=package
1032             self.__checkMatrixType()             self.__checkMatrixType()
1033             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
1034    
# Line 921  class LinearPDE(object): Line 1061  class LinearPDE(object):
1061         @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
1062                     the system will be resolved.                     the system will be resolved.
1063         @type tol: positive C{float}         @type tol: positive C{float}
1064         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1065         """         """
1066         if not tol>0:         if not tol>0:
1067             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1068         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1069         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1070         self.__tolerance=tol         self.__tolerance=tol
# Line 1205  class LinearPDE(object): Line 1345  class LinearPDE(object):
1345         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1346             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1347         else:         else:
1348             self.__righthandside*=0             self.__righthandside.setToZero()
1349             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1350         return self.__righthandside         return self.__righthandside
1351    
# Line 1255  class LinearPDE(object): Line 1395  class LinearPDE(object):
1395       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1396       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1397       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1398                    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},
1399                      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}.
1400       """       """
1401       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1402          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1283  class LinearPDE(object): Line 1424  class LinearPDE(object):
1424       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1425       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1426       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1427                    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},
1428                      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}.
1429       """       """
1430       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1431          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 1441  class LinearPDE(object):
1441       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1442       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1443       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1444                    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},
1445                      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}.
1446       """       """
1447       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1448          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 1458  class LinearPDE(object):
1458       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1459       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1460       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1461                    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},
1462                      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}.
1463       """       """
1464       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1465          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 1589  class LinearPDE(object):
1589        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1590        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1591        @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>}.
1592          @keyword A_reduced: value for coefficient A_reduced.
1593          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1594        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1595        @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>}.
1596          @keyword B_reduced: value for coefficient B_reduced
1597          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1598        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1599        @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>}.
1600          @keyword C_reduced: value for coefficient C_reduced
1601          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1602        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1603        @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>}.
1604          @keyword D_reduced: value for coefficient D_reduced
1605          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1606        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1607        @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>}.
1608          @keyword X_reduced: value for coefficient X_reduced
1609          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1610        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1611        @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>}.
1612          @keyword Y_reduced: value for coefficient Y_reduced
1613          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1614        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1615        @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>}.
1616          @keyword d_reduced: value for coefficient d_reduced
1617          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1618        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1619        @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>}.
1620        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1621        @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>}.
1622                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1623          @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>}.
1624        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1625        @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>}.
1626                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1627          @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>}.
1628        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1629        @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>}
1630                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1499  class LinearPDE(object): Line 1659  class LinearPDE(object):
1659        # 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:
1660        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1661          try:          try:
1662             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1663                                             self.getNumEquations(),self.getNumSolutions(),
1664                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1665               self.alteredCoefficient(i)
1666            except IllegalCoefficientFunctionSpace,m:
1667                # if the function space is wrong then we try the reduced version:
1668                i_red=i+"_reduced"
1669                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1670                    try:
1671                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1672                                                          self.getNumEquations(),self.getNumSolutions(),
1673                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1674                        self.alteredCoefficient(i_red)
1675                    except IllegalCoefficientValue,m:
1676                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1677                    except IllegalCoefficientFunctionSpace,m:
1678                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1679                else:
1680                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1681          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1682             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1683        self.__altered_coefficients=True        self.__altered_coefficients=True
1684        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1685        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1511  class LinearPDE(object): Line 1687  class LinearPDE(object):
1687           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1688           homogeneous_constraint=True           homogeneous_constraint=True
1689           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1690               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1691                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1692                 self.__invalidateSystem()                 self.__invalidateSystem()
1693    
# Line 1525  class LinearPDE(object): Line 1701  class LinearPDE(object):
1701         if not self.__operator_is_Valid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1702            if self.isUsingLumping():            if self.isUsingLumping():
1703                if not self.__operator_is_Valid:                if not self.__operator_is_Valid:
1704                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1705                   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"
1706                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1707                   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."
1708                   mat=self.__getNewOperator()                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1709                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient B in lumped matrix may not be present."
1710                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1711                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient C in lumped matrix may not be present."
1712                             self.getCoefficientOfGeneralPDE("C"), \                   if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1713                             self.getCoefficientOfGeneralPDE("D"), \                        raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1714                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1715                             escript.Data(), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1716                             self.getCoefficientOfGeneralPDE("d"), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1717                             escript.Data(),\                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1718                             self.getCoefficientOfGeneralPDE("d_contact"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1719                             escript.Data())                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1720                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                   if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1721                   del mat                        raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1722                     D=self.getCoefficientOfGeneralPDE("D")
1723                     d=self.getCoefficientOfGeneralPDE("d")
1724                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1725                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1726                     if not D.isEmpty():
1727                         if self.getNumSolutions()>1:
1728                            D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1729                         else:
1730                            D_times_e=D
1731                     else:
1732                        D_times_e=escript.Data()
1733                     if not d.isEmpty():
1734                         if self.getNumSolutions()>1:
1735                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1736                         else:
1737                            d_times_e=d
1738                     else:
1739                        d_times_e=escript.Data()
1740          
1741                     if not D_reduced.isEmpty():
1742                         if self.getNumSolutions()>1:
1743                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1744                         else:
1745                            D_reduced_times_e=D_reduced
1746                     else:
1747                        D_reduced_times_e=escript.Data()
1748                     if not d_reduced.isEmpty():
1749                         if self.getNumSolutions()>1:
1750                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1751                         else:
1752                            d_reduced_times_e=d_reduced
1753                     else:
1754                        d_reduced_times_e=escript.Data()
1755    
1756                     self.__operator=self.__getNewRightHandSide()
1757                     if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1758                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1759                        self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1760                     else:
1761                        self.getDomain().addPDEToRHS(self.__operator, \
1762                                                     escript.Data(), \
1763                                                     D_times_e, \
1764                                                     d_times_e,\
1765                                                     escript.Data())
1766                        self.getDomain().addPDEToRHS(self.__operator, \
1767                                                     escript.Data(), \
1768                                                     D_reduced_times_e, \
1769                                                     d_reduced_times_e,\
1770                                                     escript.Data())
1771                     self.__operator=1./self.__operator
1772                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1773                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
1774                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
# Line 1551  class LinearPDE(object): Line 1777  class LinearPDE(object):
1777                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1778                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1779                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1780                     self.getDomain().addPDEToRHS(self.__righthandside, \
1781                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1782                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1783                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1784                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1785                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1786                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1787            else:            else:
# Line 1566  class LinearPDE(object): Line 1797  class LinearPDE(object):
1797                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1798                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1799                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1800                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1801                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1806                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1808                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1809                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1810                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1811                   self.__applyConstraint()                   self.__applyConstraint()
1812                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1813                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1577  class LinearPDE(object): Line 1819  class LinearPDE(object):
1819                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1820                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1821                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1822                     self.getDomain().addPDEToRHS(self.__righthandside, \
1823                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1824                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1825                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1826                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1827                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1828                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1829                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1592  class LinearPDE(object): Line 1839  class LinearPDE(object):
1839                              escript.Data(),\                              escript.Data(),\
1840                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1841                              escript.Data())                              escript.Data())
1842                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1843                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1844                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1845                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1846                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1847                                escript.Data(), \
1848                                escript.Data(), \
1849                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1850                                escript.Data(),\
1851                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1852                                escript.Data())
1853                   self.__applyConstraint()                   self.__applyConstraint()
1854                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1855                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1625  class Poisson(LinearPDE): Line 1883  class Poisson(LinearPDE):
1883       """       """
1884       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1885       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1886                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1887                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1888       self.setSymmetryOn()       self.setSymmetryOn()
1889    
1890     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1673  class Poisson(LinearPDE): Line 1932  class Poisson(LinearPDE):
1932           return escript.Data()           return escript.Data()
1933       elif name == "y_contact" :       elif name == "y_contact" :
1934           return escript.Data()           return escript.Data()
1935         elif name == "A_reduced" :
1936             return escript.Data()
1937         elif name == "B_reduced" :
1938             return escript.Data()
1939         elif name == "C_reduced" :
1940             return escript.Data()
1941         elif name == "D_reduced" :
1942             return escript.Data()
1943         elif name == "X_reduced" :
1944             return escript.Data()
1945         elif name == "Y_reduced" :
1946             return self.getCoefficient("f_reduced")
1947         elif name == "d_reduced" :
1948             return escript.Data()
1949         elif name == "y_reduced" :
1950             return escript.Data()
1951         elif name == "d_contact_reduced" :
1952             return escript.Data()
1953         elif name == "y_contact_reduced" :
1954             return escript.Data()
1955       elif name == "r" :       elif name == "r" :
1956           return escript.Data()           return escript.Data()
1957       elif name == "q" :       elif name == "q" :
# Line 1709  class Helmholtz(LinearPDE): Line 1988  class Helmholtz(LinearPDE):
1988       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1989                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1993                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1994                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1995                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1996                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1997       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1772  class Helmholtz(LinearPDE): Line 2053  class Helmholtz(LinearPDE):
2053           return escript.Data()           return escript.Data()
2054       elif name == "y_contact" :       elif name == "y_contact" :
2055           return escript.Data()           return escript.Data()
2056         elif name == "A_reduced" :
2057             return escript.Data()
2058         elif name == "B_reduced" :
2059             return escript.Data()
2060         elif name == "C_reduced" :
2061             return escript.Data()
2062         elif name == "D_reduced" :
2063             return escript.Data()
2064         elif name == "X_reduced" :
2065             return escript.Data()
2066         elif name == "Y_reduced" :
2067             return self.getCoefficient("f_reduced")
2068         elif name == "d_reduced" :
2069             return escript.Data()
2070         elif name == "y_reduced" :
2071            return self.getCoefficient("g_reduced")
2072         elif name == "d_contact_reduced" :
2073             return escript.Data()
2074         elif name == "y_contact_reduced" :
2075             return escript.Data()
2076       elif name == "r" :       elif name == "r" :
2077           return self.getCoefficient("r")           return self.getCoefficient("r")
2078       elif name == "q" :       elif name == "q" :
# Line 1783  class LameEquation(LinearPDE): Line 2084  class LameEquation(LinearPDE):
2084     """     """
2085     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2086    
2087     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] }
2088    
2089     with natural boundary conditons:     with natural boundary conditons:
2090    
2091     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] }
2092    
2093     and constraints:     and constraints:
2094    
# Line 1807  class LameEquation(LinearPDE): Line 2108  class LameEquation(LinearPDE):
2108                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2109        self.setSymmetryOn()        self.setSymmetryOn()
2110    
2111     def setValue(self,**coefficients):     def setValues(self,**coefficients):
2112       """       """
2113       sets new values to coefficients       sets new values to coefficients
2114    
# Line 1830  class LameEquation(LinearPDE): Line 2131  class LameEquation(LinearPDE):
2131                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
2132       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2133       """       """
2134       super(LameEquation, self).setValue(**coefficients)       super(LameEquation, self).setValues(**coefficients)
2135    
2136     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2137       """       """
# Line 1870  class LameEquation(LinearPDE): Line 2171  class LameEquation(LinearPDE):
2171           return escript.Data()           return escript.Data()
2172       elif name == "y_contact" :       elif name == "y_contact" :
2173           return escript.Data()           return escript.Data()
2174         elif name == "A_reduced" :
2175             return escript.Data()
2176         elif name == "B_reduced" :
2177             return escript.Data()
2178         elif name == "C_reduced" :
2179             return escript.Data()
2180         elif name == "D_reduced" :
2181             return escript.Data()
2182         elif name == "X_reduced" :
2183             return escript.Data()
2184         elif name == "Y_reduced" :
2185             return escript.Data()
2186         elif name == "d_reduced" :
2187             return escript.Data()
2188         elif name == "y_reduced" :
2189             return escript.Data()
2190         elif name == "d_contact_reduced" :
2191             return escript.Data()
2192         elif name == "y_contact_reduced" :
2193             return escript.Data()
2194       elif name == "r" :       elif name == "r" :
2195           return self.getCoefficient("r")           return self.getCoefficient("r")
2196       elif name == "q" :       elif name == "q" :
# Line 1877  class LameEquation(LinearPDE): Line 2198  class LameEquation(LinearPDE):
2198       else:       else:
2199          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2200    
2201  class AdvectivePDE(LinearPDE):  def LinearSinglePDE(domain,debug=False):
2202     """     """
2203     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.  
2204    
2205       @param domain: domain of the PDE
2206       @type domain: L{Domain<escript.Domain>}
2207       @param debug: if True debug informations are printed.
2208       @rtype: L{LinearPDE}
2209     """     """
2210     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)  
   
    def ELMAN_RAMAGE(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)  
           - M{S{xi}(P)=0} for M{P<1}  
           - M{S{xi}(P)=(1-1/P)/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))  
   
    def SIMPLIFIED_BROOK_HUGHES(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      The original methods is  
   
      M{S{xi}(P)=coth(P)-1/P}  
   
      As the evaluation of M{coth} is expensive we are using the approximation:  
   
          - M{S{xi}(P)=P/3} where M{P<3}  
          - M{S{xi}(P)=1/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      c=util.whereNegative(P-3.)  
      return P/6.*c+1./2.*(1.-c)  
   
    def HALF(self,P):  
      """  
      Predefined function to set value M{1/2} for M{S{xi}}  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return escript.Scalar(0.5,P.getFunctionSpace())  
   
    def __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  
   
2211    
2212     def getCoefficientOfGeneralPDE(self,name):  def LinearPDESystem(domain,debug=False):
      """  
      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):  
2213     """     """
2214     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]}  
2215    
2216       @param domain: domain of the PDE
2217       @type domain: L{Domain<escript.Domain>}
2218       @param debug: if True debug informations are printed.
2219       @rtype: L{LinearPDE}
2220     """     """
2221       return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2222    
2223     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.  
   
      """  
      super(AdvectionDiffusion, self).__init__(domain,1,1,debug)  
      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)}  
   
    def setValue(self,**coefficients):  
2224       """       """
2225       sets new values to coefficients       Warning: This is still a very experimental. The class is still changing!
2226    
2227       @param coefficients: new values assigned to coefficients       Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2228       @keyword omega: value for coefficient M{S{omega}}      
2229       @type omega: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.       u=r where q>0
2230       @keyword k: value for coefficient M{k}      
2231       @type k: any type that can be casted to L{Tensor<escript.Tensor>} object on L{Function<escript.Function>}.       all coefficients are constant over time.
2232       @keyword v: value for coefficient M{v}  
2233       @type v: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.       typical usage:
2234       @keyword upwind: value for upwind term M{upwind}  
2235       @type upwind: any type that can be casted to L{Vector<escript.Vector>} object on L{Function<escript.Function>}.           p=TransportPDE(dom)
2236       @keyword f: value for right hand side M{f}           p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2237       @type f: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Function<escript.Function>}.           p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2238       @keyword alpha: value for right hand side M{S{alpha}}           t=0
2239       @type alpha: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.           dt=0.1
2240       @keyword g: value for right hand side M{g}           while (t<1.):
2241       @type g: any type that can be casted to L{Scalar<escript.Scalar>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.                u=p.solve(dt)
2242       @keyword r: prescribed values M{r} for the solution in constraints.  
2243       @type r: any type that can be casted to L{Scalar<escript.Scalar>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}       """
2244                 depending of reduced order is used for the representation of the equation.       def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2245       @keyword q: mask for location of constraints          self.__domain=domain
2246       @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.__num_equations=num_equations
2247                 depending of reduced order is used for the representation of the equation.          self.__useSUPG=useSUPG
2248       @raise IllegalCoefficient: if an unknown coefficient keyword is used.          self.__trace=trace
2249       """          self.__theta=theta
2250       super(AdvectionDiffusion, self).setValue(**coefficients)          self.__matrix_type=0
2251            self.__reduced=True
2252            self.__reassemble=True
2253            if self.__useSUPG:
2254               self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2255               self.__pde.setSymmetryOn()
2256               self.__pde.setReducedOrderOn()
2257            else:
2258               self.__transport_problem=self.__getNewTransportProblem()
2259            self.setTolerance()
2260            self.__M=escript.Data()
2261            self.__A=escript.Data()
2262            self.__B=escript.Data()
2263            self.__C=escript.Data()
2264            self.__D=escript.Data()
2265            self.__X=escript.Data()
2266            self.__Y=escript.Data()
2267            self.__d=escript.Data()
2268            self.__y=escript.Data()
2269            self.__d_contact=escript.Data()
2270            self.__y_contact=escript.Data()
2271            self.__r=escript.Data()
2272            self.__q=escript.Data()
2273    
2274         def trace(self,text):
2275                 if self.__trace: print text
2276         def getSafeTimeStepSize(self):
2277            if self.__useSUPG:
2278                if self.__reassemble:
2279                   h=self.__domain.getSize()
2280                   dt=None
2281                   if not self.__A.isEmpty():
2282                      dt2=util.inf(h**2*self.__M/util.length(self.__A))
2283                      if dt == None:
2284                         dt = dt2
2285                      else:
2286                         dt=1./(1./dt+1./dt2)
2287                   if not self.__B.isEmpty():
2288                      dt2=util.inf(h*self.__M/util.length(self.__B))
2289                      if dt == None:
2290                         dt = dt2
2291                      else:
2292                         dt=1./(1./dt+1./dt2)
2293                   if not  self.__C.isEmpty():
2294                      dt2=util.inf(h*self.__M/util.length(self.__C))
2295                      if dt == None:
2296                         dt = dt2
2297                      else:
2298                         dt=1./(1./dt+1./dt2)
2299                   if not self.__D.isEmpty():
2300                      dt2=util.inf(self.__M/util.length(self.__D))
2301                      if dt == None:
2302                         dt = dt2
2303                      else:
2304                         dt=1./(1./dt+1./dt2)
2305                   self.__dt = dt/2
2306                return self.__dt
2307            else:
2308                return self.__getTransportProblem().getSafeTimeStepSize()
2309         def getDomain(self):
2310            return self.__domain
2311         def getTheta(self):
2312            return self.__theta
2313         def getNumEquations(self):
2314            return self.__num_equations
2315         def setReducedOn(self):
2316              if not self.reduced():
2317                  if self.__useSUPG:
2318                     self.__pde.setReducedOrderOn()
2319                  else:
2320                     self.__transport_problem=self.__getNewTransportProblem()
2321              self.__reduced=True
2322         def setReducedOff(self):
2323              if self.reduced():
2324                  if self.__useSUPG:
2325                     self.__pde.setReducedOrderOff()
2326                  else:
2327                     self.__transport_problem=self.__getNewTransportProblem()
2328              self.__reduced=False
2329         def reduced(self):
2330             return self.__reduced
2331         def getFunctionSpace(self):
2332            if self.reduced():
2333               return escript.ReducedSolution(self.getDomain())
2334            else:
2335               return escript.Solution(self.getDomain())
2336    
2337     def getCoefficientOfGeneralPDE(self,name):       def setTolerance(self,tol=1.e-8):
2338       """          self.__tolerance=tol
2339       return the value of the coefficient name of the general PDE          if self.__useSUPG:
2340                  self.__pde.setTolerance(self.__tolerance)
2341    
2342       @param name: name of the coefficient requested.       def __getNewTransportProblem(self):
2343       @type name: C{string}         """
2344       @return: the value of the coefficient  name         returns an instance of a new operator
2345       @rtype: L{Data<escript.Data>}         """
2346       @raise IllegalCoefficient: if name is not one of coefficients         self.trace("New Transport problem is allocated.")
2347                    "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( \
2348       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.                                 self.getTheta(),
2349       """                                 self.getNumEquations(), \
2350       if name == "A" :                                 self.getFunctionSpace(), \
2351           return self.getCoefficient("k")+util.outer(self.getCoefficient("upwind"),self.getCoefficient("upwind"))                                 self.__matrix_type)
2352       elif name == "B" :            
2353           return escript.Data()       def __getNewSolutionVector(self):
2354       elif name == "C" :           if self.getNumEquations() ==1 :
2355           return self.getCoefficient("v")                  out=escript.Data(0.0,(),self.getFunctionSpace())
2356       elif name == "D" :           else:
2357           return self.getCoefficient("omega")                  out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2358       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  
2359    
2360         def __getTransportProblem(self):
2361           if self.__reassemble:
2362                 self.__source=self.__getNewSolutionVector()
2363                 self.__transport_problem.reset()
2364                 self.getDomain().addPDEToTransportProblem(
2365                             self.__transport_problem,
2366                             self.__source,
2367                             self.__M,
2368                             self.__A,
2369                             self.__B,
2370                             self.__C,
2371                             self.__D,
2372                             self.__X,
2373                             self.__Y,
2374                             self.__d,
2375                             self.__y,
2376                             self.__d_contact,
2377                             self.__y_contact)
2378                 self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2379                 self.__reassemble=False
2380           return self.__transport_problem
2381         def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2382                      d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2383                 if not M==None:
2384                      self.__reassemble=True
2385                      self.__M=M
2386                 if not A==None:
2387                      self.__reassemble=True
2388                      self.__A=A
2389                 if not B==None:
2390                      self.__reassemble=True
2391                      self.__B=B
2392                 if not C==None:
2393                      self.__reassemble=True
2394                      self.__C=C
2395                 if not D==None:
2396                      self.__reassemble=True
2397                      self.__D=D
2398                 if not X==None:
2399                      self.__reassemble=True
2400                      self.__X=X
2401                 if not Y==None:
2402                      self.__reassemble=True
2403                      self.__Y=Y
2404                 if not d==None:
2405                      self.__reassemble=True
2406                      self.__d=d
2407                 if not y==None:
2408                      self.__reassemble=True
2409                      self.__y=y
2410                 if not d_contact==None:
2411                      self.__reassemble=True
2412                      self.__d_contact=d_contact
2413                 if not y_contact==None:
2414                      self.__reassemble=True
2415                      self.__y_contact=y_contact
2416                 if not q==None:
2417                      self.__reassemble=True
2418                      self.__q=q
2419                 if not r==None:
2420                      self.__reassemble=True
2421                      self.__r=r
2422    
2423         def setInitialSolution(self,u):
2424                 if self.__useSUPG:
2425                     self.__u=util.interpolate(u,self.getFunctionSpace())
2426                 else:
2427                     self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2428    
2429  # $Log$       def solve(self,dt,**kwarg):
2430  # Revision 1.14  2005/09/22 01:54:57  jgs             if self.__useSUPG:
2431  # Merge of development branch dev-02 back to main trunk on 2005-09-22                  if self.__reassemble:
2432  #                      self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2433  # Revision 1.13  2005/09/15 03:44:19  jgs                      self.__reassemble=False
2434  # Merge of development branch dev-02 back to main trunk on 2005-09-15                  dt2=self.getSafeTimeStepSize()
2435  #                  nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2436  # Revision 1.12  2005/09/01 03:31:28  jgs                  dt2=dt/nn
2437  # Merge of development branch dev-02 back to main trunk on 2005-09-01                  nnn=0
2438  #                  u=self.__u
2439  # Revision 1.11  2005/08/23 01:24:28  jgs                  self.trace("number of substeps is %d."%nn)
2440  # Merge of development branch dev-02 back to main trunk on 2005-08-23                  while nnn<nn :
2441  #                      self.__setSUPG(u,u,dt2/2)
2442  # Revision 1.10  2005/08/12 01:45:36  jgs                      u_half=self.__pde.getSolution(verbose=True)
2443  # erge of development branch dev-02 back to main trunk on 2005-08-12                      self.__setSUPG(u,u_half,dt2)
2444  #                      u=self.__pde.getSolution(verbose=True)
2445  # Revision 1.9.2.17  2005/09/21 07:03:33  matt                      nnn+=1
2446  # PDECoefficient and LinearPDE are now new style classes (introduced in Python                  self.__u=u
2447  # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been                  return self.__u
2448  # modified to instead use portable/cooperative "super" calls to extend base             else:
2449  # class methods.                 kwarg["tolerance"]=self.__tolerance
2450  #                 tp=self.__getTransportProblem()
2451  # Revision 1.9.2.16  2005/09/16 01:54:37  matt                 return tp.solve(self.__source,dt,kwarg)
2452  # Removed redundant if-loop.       def __setSUPG(self,u0,u,dt):
2453  #              g=util.grad(u)
2454  # Revision 1.9.2.15  2005/09/14 08:09:18  matt              X=0
2455  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.              Y=self.__M*u0
2456  #              X=0
2457  # Revision 1.9.2.14  2005/09/07 06:26:16  gross              self.__pde.setValue(r=u0)
2458  # the solver from finley are put into the standalone package paso now              if not self.__A.isEmpty():
2459  #                 X=X+dt*util.matrixmult(self.__A,g)
2460  # Revision 1.9.2.13  2005/08/31 08:45:03  gross              if not self.__B.isEmpty():
2461  # in the case of lumping no new system is allocated if the constraint is changed.                 X=X+dt*self.__B*u
2462  #              if not  self.__C.isEmpty():
2463  # Revision 1.9.2.12  2005/08/31 07:10:23  gross                 Y=Y+dt*util.inner(self.__C,g)
2464  # test for Lumping added              if not self.__D.isEmpty():
2465  #                 Y=Y+dt*self.__D*u
2466  # Revision 1.9.2.11  2005/08/30 01:53:45  gross              if not self.__X.isEmpty():
2467  # bug in format fixed.                 X=X+dt*self.__X
2468  #              if not self.__Y.isEmpty():
2469  # Revision 1.9.2.10  2005/08/26 07:14:17  gross                 Y=Y+dt*self.__Y
2470  # a few more bugs in linearPDE fixed. remaining problem are finley problems              self.__pde.setValue(X=X,Y=Y)
2471  #              if not self.__y.isEmpty():
2472  # Revision 1.9.2.9  2005/08/26 06:30:45  gross                 self.__pde.setValue(y=dt*self.__y)
2473  # fix for reported bug  0000004. test_linearPDE passes a few more tests              if not self.__y_contact.isEmpty():
2474  #                 self.__pde.setValue(y=dt*self.__y_contact)
2475  # 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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