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revision 614 by elspeth, Wed Mar 22 01:37:07 2006 UTC revision 1513 by gross, Tue Apr 15 08:47:57 2008 UTC
# Line 1  Line 1 
1    #
2  # $Id$  # $Id$
3    #
4    #######################################################
5    #
6    #           Copyright 2003-2007 by ACceSS MNRF
7    #       Copyright 2007 by University of Queensland
8    #
9    #                http://esscc.uq.edu.au
10    #        Primary Business: Queensland, Australia
11    #  Licensed under the Open Software License version 3.0
12    #     http://www.opensource.org/licenses/osl-3.0.php
13    #
14    #######################################################
15    #
16    
17  """  """
18  The module provides an interface to define and solve linear partial  The module provides an interface to define and solve linear partial
19  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
# Line 7  the PDE solver library defined through t Line 22  the PDE solver library defined through t
22  The general interface is provided through the L{LinearPDE} class. The  The general interface is provided through the L{LinearPDE} class. The
23  L{AdvectivePDE} which is derived from the L{LinearPDE} class  L{AdvectivePDE} which is derived from the L{LinearPDE} class
24  provides an interface to PDE dominated by its advective terms. The L{Poisson},  provides an interface to PDE dominated by its advective terms. The L{Poisson},
25  L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}  L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
26  classs which are also derived form the L{LinearPDE} class should be used  classs which are also derived form the L{LinearPDE} class should be used
27  to define of solve these sepecial PDEs.  to define of solve these sepecial PDEs.
28    
29  @var __author__: name of author  @var __author__: name of author
30    @var __copyright__: copyrights
31  @var __license__: licence agreement  @var __license__: licence agreement
32  @var __url__: url entry point on documentation  @var __url__: url entry point on documentation
33  @var __version__: version  @var __version__: version
34  @var __date__: date of the version  @var __date__: date of the version
35  """  """
36    
37    import math
38  import escript  import escript
39  import util  import util
40  import numarray  import numarray
# Line 28  __copyright__="""  Copyright (c) 2006 by Line 45  __copyright__="""  Copyright (c) 2006 by
45                  Primary Business: Queensland, Australia"""                  Primary Business: Queensland, Australia"""
46  __license__="""Licensed under the Open Software License version 3.0  __license__="""Licensed under the Open Software License version 3.0
47               http://www.opensource.org/licenses/osl-3.0.php"""               http://www.opensource.org/licenses/osl-3.0.php"""
48  __url__="http://www.iservo.edu.au/esys/escript"  __url__="http://www.iservo.edu.au/esys"
49  __version__="$Revision$"  __version__="$Revision$"
50  __date__="$Date$"  __date__="$Date$"
51    
# Line 37  class IllegalCoefficient(ValueError): Line 54  class IllegalCoefficient(ValueError):
54     """     """
55     raised if an illegal coefficient of the general ar particular PDE is requested.     raised if an illegal coefficient of the general ar particular PDE is requested.
56     """     """
57       pass
58    
59  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
60     """     """
61     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
62     """     """
63       pass
64    
65    class IllegalCoefficientFunctionSpace(ValueError):
66       """
67       raised if an incorrect function space for a coefficient is used.
68       """
69    
70  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
71     """     """
72     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
73     """     """
74       pass
75    
76  class PDECoefficient(object):  class PDECoefficient(object):
77      """      """
# Line 55  class PDECoefficient(object): Line 80  class PDECoefficient(object):
80      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
81      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
82      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
83        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
84        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
85        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
86      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
87      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
88      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
# Line 76  class PDECoefficient(object): Line 104  class PDECoefficient(object):
104      OPERATOR=10      OPERATOR=10
105      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
106      BOTH=12      BOTH=12
107        INTERIOR_REDUCED=13
108        BOUNDARY_REDUCED=14
109        CONTACT_REDUCED=15
110    
111      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
112         """         """
113         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
114    
115         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
116         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
117                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
118         @param pattern: describes the shape of the coefficient and how the shape is build for a given         @param pattern: describes the shape of the coefficient and how the shape is build for a given
119                spatial dimension and numbers of equation and solution in then PDE. For instance,                spatial dimension and numbers of equation and solution in then PDE. For instance,
120                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
# Line 93  class PDECoefficient(object): Line 125  class PDECoefficient(object):
125         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
126         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
127         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
128           @param reduced: indicates if reduced
129           @type reduced: C{bool}
130         """         """
131         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
132         self.what=where         self.what=where
# Line 114  class PDECoefficient(object): Line 147  class PDECoefficient(object):
147         @param domain: domain on which the PDE uses the coefficient         @param domain: domain on which the PDE uses the coefficient
148         @type domain: L{Domain<escript.Domain>}         @type domain: L{Domain<escript.Domain>}
149         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
150         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
151         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
152         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
153         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
154         @rtype:  L{FunctionSpace<escript.FunctionSpace>}         @rtype:  L{FunctionSpace<escript.FunctionSpace>}
155         """         """
156         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
157              return escript.Function(domain)              return escript.Function(domain)
158           elif self.what==self.INTERIOR_REDUCED:
159                return escript.ReducedFunction(domain)
160         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
161              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
162           elif self.what==self.BOUNDARY_REDUCED:
163                return escript.ReducedFunctionOnBoundary(domain)
164         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
165              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
166           elif self.what==self.CONTACT_REDUCED:
167                return escript.ReducedFunctionOnContactZero(domain)
168         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
169              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
170                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 154  class PDECoefficient(object): Line 193  class PDECoefficient(object):
193         @param numSolutions: number of components of the PDE solution         @param numSolutions: number of components of the PDE solution
194         @type numSolutions: C{int}         @type numSolutions: C{int}
195         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
196         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
197         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
198         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
199         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
200         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
201         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
202           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
203         """         """
204         if newValue==None:         if newValue==None:
205             newValue=escript.Data()             newValue=escript.Data()
206         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
207             if not newValue.isEmpty():             if not newValue.isEmpty():
208                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
209                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
210                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
211                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
212                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
213         else:         else:
214             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
215         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 312  class LinearPDE(object): Line 353  class LinearPDE(object):
353    
354     For a single PDE with a solution with a single component the linear PDE is defined in the following form:     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
355    
356     M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
357    
358    
359     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
360     ie. summation over indexes appearing twice in a term of a sum is performed, is used.     ie. summation over indexes appearing twice in a term of a sum is performed, is used.
361     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
362     L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.     L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
363     M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.     L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
364       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
365       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
366    
367     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
368    
369     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
370    
371     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.     where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
    Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are  
    each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
372    
373    
374     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
# Line 338  class LinearPDE(object): Line 380  class LinearPDE(object):
380    
381     The PDE is symmetrical if     The PDE is symmetrical if
382    
383     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
384    
385     For a system of PDEs and a solution with several components the PDE has the form     For a system of PDEs and a solution with several components the PDE has the form
386    
387     M{-grad(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])[j]+C[i,k,l]*grad(u[k])[l]+D[i,k]*u[k] =-grad(X[i,j])[j]+Y[i] }     M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
388    
389     M{A} is a ramk four, M{B} and M{C} are each a rank three, M{D} and M{X} are each a rank two and M{Y} is a rank one.     M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
390     The natural boundary conditions take the form:     The natural boundary conditions take the form:
391    
392     M{n[j]*(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}     M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
393    
394    
395     The coefficient M{d} is a rank two and M{y} is a  rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form     The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
396    
397       Constraints take the form
398    
399     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
400    
# Line 360  class LinearPDE(object): Line 403  class LinearPDE(object):
403     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
404    
405          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
406            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
407          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
408            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
409          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
410            - M{D_reduced[i,k]=D_reduced[i,k]}
411          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
412            - M{d_reduced[i,k]=d_reduced[k,i]}
413    
414     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
415     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
416     defined as     defined as
417    
418     M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}     M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
419    
420     For the case of single solution component and single PDE M{J} is defined     For the case of single solution component and single PDE M{J} is defined
421    
422     M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}     M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
423    
424     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
425     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
426     the contact condition takes the form     the contact condition takes the form
427    
428     M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}     M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
429    
430     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
431     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
432     L{jump<util.jump>}.     L{jump<util.jump>}.
433     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
434       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
435     In case of a single PDE and a single component solution the contact condition takes the form     In case of a single PDE and a single component solution the contact condition takes the form
436    
437     M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}     M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
438    
439     In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar     In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
    both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
440    
441     @cvar DEFAULT: The default method used to solve the system of linear equations     @cvar DEFAULT: The default method used to solve the system of linear equations
442     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 412  class LinearPDE(object): Line 459  class LinearPDE(object):
459     @cvar SCSL: SGI SCSL solver library     @cvar SCSL: SGI SCSL solver library
460     @cvar MKL: Intel's MKL solver library     @cvar MKL: Intel's MKL solver library
461     @cvar UMFPACK: the UMFPACK library     @cvar UMFPACK: the UMFPACK library
462       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
463     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
464     @cvar AMG: algebraic multi grid     @cvar AMG: algebraic multi grid
465     @cvar RILU: recursive ILU     @cvar RILU: recursive ILU
# Line 441  class LinearPDE(object): Line 489  class LinearPDE(object):
489     PASO= 21     PASO= 21
490     AMG= 22     AMG= 22
491     RILU = 23     RILU = 23
492       TRILINOS = 24
493    
494     SMALL_TOLERANCE=1.e-13     SMALL_TOLERANCE=1.e-13
495     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
# Line 478  class LinearPDE(object): Line 527  class LinearPDE(object):
527         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
528         "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),
529         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
530           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
531           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
532           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
533           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
535           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
536           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
537           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
538           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
541         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
542    
# Line 663  class LinearPDE(object): Line 722  class LinearPDE(object):
722       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
723       """       """
724       if u==None:       if u==None:
725            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
726       else:       else:
727          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
728    
729     def getResidual(self,u=None):     def getResidual(self,u=None):
730       """       """
# Line 759  class LinearPDE(object): Line 818  class LinearPDE(object):
818                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
819                        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)
820                        out=False                        out=False
821             # and now the reduced coefficients
822             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
823             if not A_reduced.isEmpty():
824                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
825                if self.getNumSolutions()>1:
826                   for i in range(self.getNumEquations()):
827                      for j in range(self.getDim()):
828                         for k in range(self.getNumSolutions()):
829                            for l in range(self.getDim()):
830                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
831                                   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)
832                                   out=False
833                else:
834                   for j in range(self.getDim()):
835                      for l in range(self.getDim()):
836                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
837                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
838                            out=False
839             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
840             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
841             if B_reduced.isEmpty() and not C_reduced.isEmpty():
842                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
843                out=False
844             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
845                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
846                out=False
847             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
848                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
849                if self.getNumSolutions()>1:
850                   for i in range(self.getNumEquations()):
851                       for j in range(self.getDim()):
852                          for k in range(self.getNumSolutions()):
853                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
854                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
855                                  out=False
856                else:
857                   for j in range(self.getDim()):
858                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
859                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
860                         out=False
861             if self.getNumSolutions()>1:
862               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
863               if not D_reduced.isEmpty():
864                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
865                 for i in range(self.getNumEquations()):
866                    for k in range(self.getNumSolutions()):
867                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
868                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
869                          out=False
870               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
871               if not d_reduced.isEmpty():
872                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
873                 for i in range(self.getNumEquations()):
874                    for k in range(self.getNumSolutions()):
875                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
876                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
877                          out=False
878               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
879               if not d_contact_reduced.isEmpty():
880                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
881                 for i in range(self.getNumEquations()):
882                    for k in range(self.getNumSolutions()):
883                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
884                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
885                          out=False
886        return out        return out
887    
888     def getSolution(self,**options):     def getSolution(self,**options):
# Line 798  class LinearPDE(object): Line 922  class LinearPDE(object):
922       """       """
923       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
924    
925       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]}
926    
927       or       or
928    
929       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]}
930    
931       @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.
932       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 810  class LinearPDE(object): Line 934  class LinearPDE(object):
934       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
935       """       """
936       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
937       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))) \
938               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
939               -util.self.getCoefficientOfGeneralPDE("X") \
940               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
941               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
942               -util.self.getCoefficientOfGeneralPDE("X_reduced")
943     # =============================================================================     # =============================================================================
944     #   solver settings:     #   solver settings:
945     # =============================================================================     # =============================================================================
# Line 823  class LinearPDE(object): Line 952  class LinearPDE(object):
952         @param preconditioner: sets a new solver method.         @param preconditioner: sets a new solver method.
953         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
954         """         """
955         if solver==None: solve=self.DEFAULT         if solver==None: solver=self.__solver_method
956           if preconditioner==None: preconditioner=self.__preconditioner
957           if solver==None: solver=self.DEFAULT
958         if preconditioner==None: preconditioner=self.DEFAULT         if preconditioner==None: preconditioner=self.DEFAULT
959         if not (solver,preconditioner)==self.getSolverMethod():         if not (solver,preconditioner)==self.getSolverMethod():
960             self.__solver_method=solver             self.__solver_method=solver
# Line 867  class LinearPDE(object): Line 998  class LinearPDE(object):
998         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
999         elif p==self.SCSL: package= "SCSL"         elif p==self.SCSL: package= "SCSL"
1000         elif p==self.UMFPACK: package= "UMFPACK"         elif p==self.UMFPACK: package= "UMFPACK"
1001           elif p==self.TRILINOS: package= "TRILINOS"
1002         else : method="unknown"         else : method="unknown"
1003         return "%s solver of %s package"%(method,package)         return "%s solver of %s package"%(method,package)
1004    
# Line 884  class LinearPDE(object): Line 1016  class LinearPDE(object):
1016         """         """
1017         sets a new solver package         sets a new solver package
1018    
1019         @param solver: sets a new solver method.         @param package: sets a new solver method.
1020         @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}
1021         """         """
1022         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1023         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
1024             self.__solver_method=solver             self.__solver_package=package
1025             self.__checkMatrixType()             self.__checkMatrixType()
1026             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
1027    
# Line 922  class LinearPDE(object): Line 1054  class LinearPDE(object):
1054         @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
1055                     the system will be resolved.                     the system will be resolved.
1056         @type tol: positive C{float}         @type tol: positive C{float}
1057         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1058         """         """
1059         if not tol>0:         if not tol>0:
1060             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1061         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1062         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1063         self.__tolerance=tol         self.__tolerance=tol
# Line 1206  class LinearPDE(object): Line 1338  class LinearPDE(object):
1338         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1339             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1340         else:         else:
1341             self.__righthandside*=0             self.__righthandside.setToZero()
1342             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1343         return self.__righthandside         return self.__righthandside
1344    
# Line 1256  class LinearPDE(object): Line 1388  class LinearPDE(object):
1388       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1389       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1390       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1391                    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},
1392                      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}.
1393       """       """
1394       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1395          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1284  class LinearPDE(object): Line 1417  class LinearPDE(object):
1417       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1418       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1419       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1420                    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},
1421                      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}.
1422       """       """
1423       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1424          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1300  class LinearPDE(object): Line 1434  class LinearPDE(object):
1434       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1435       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1436       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1437                    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},
1438                      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}.
1439       """       """
1440       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1441          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1316  class LinearPDE(object): Line 1451  class LinearPDE(object):
1451       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1452       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1453       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1454                    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},
1455                      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}.
1456       """       """
1457       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1458          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
# Line 1446  class LinearPDE(object): Line 1582  class LinearPDE(object):
1582        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1583        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1584        @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>}.
1585          @keyword A_reduced: value for coefficient A_reduced.
1586          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1587        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1588        @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>}.
1589          @keyword B_reduced: value for coefficient B_reduced
1590          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1591        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1592        @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>}.
1593          @keyword C_reduced: value for coefficient C_reduced
1594          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1595        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1596        @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>}.
1597          @keyword D_reduced: value for coefficient D_reduced
1598          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1599        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1600        @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>}.
1601          @keyword X_reduced: value for coefficient X_reduced
1602          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1603        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1604        @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>}.
1605          @keyword Y_reduced: value for coefficient Y_reduced
1606          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1607        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1608        @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>}.
1609          @keyword d_reduced: value for coefficient d_reduced
1610          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1611        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1612        @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>}.
1613        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1614        @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>}.
1615                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1616          @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>}.
1617        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1618        @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>}.
1619                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1620          @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>}.
1621        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1622        @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>}
1623                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1500  class LinearPDE(object): Line 1652  class LinearPDE(object):
1652        # 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:
1653        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1654          try:          try:
1655             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1656                                             self.getNumEquations(),self.getNumSolutions(),
1657                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1658               self.alteredCoefficient(i)
1659            except IllegalCoefficientFunctionSpace,m:
1660                # if the function space is wrong then we try the reduced version:
1661                i_red=i+"_reduced"
1662                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1663                    try:
1664                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1665                                                          self.getNumEquations(),self.getNumSolutions(),
1666                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1667                        self.alteredCoefficient(i_red)
1668                    except IllegalCoefficientValue,m:
1669                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1670                    except IllegalCoefficientFunctionSpace,m:
1671                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1672                else:
1673                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1674          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1675             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1676        self.__altered_coefficients=True        self.__altered_coefficients=True
1677        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1678        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1512  class LinearPDE(object): Line 1680  class LinearPDE(object):
1680           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1681           homogeneous_constraint=True           homogeneous_constraint=True
1682           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1683               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1684                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1685                 self.__invalidateSystem()                 self.__invalidateSystem()
1686    
# Line 1531  class LinearPDE(object): Line 1699  class LinearPDE(object):
1699                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1700                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient A in lumped matrix may not be present."
1701                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1702                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient B in lumped matrix may not be present."
1703                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1704                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient C in lumped matrix may not be present."
1705                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1706                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1707                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1708                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1709                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1710                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1711                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1712                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1713                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1714                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1715                   D=self.getCoefficientOfGeneralPDE("D")                   D=self.getCoefficientOfGeneralPDE("D")
1716                     d=self.getCoefficientOfGeneralPDE("d")
1717                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1718                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1719                   if not D.isEmpty():                   if not D.isEmpty():
1720                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1721                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1722                       else:                       else:
1723                          D_times_e=D                          D_times_e=D
1724                   else:                   else:
1725                      D_times_e=escript.Data()                      D_times_e=escript.Data()
                  d=self.getCoefficientOfGeneralPDE("d")  
1726                   if not d.isEmpty():                   if not d.isEmpty():
1727                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1728                          d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1729                       else:                       else:
1730                          d_times_e=d                          d_times_e=d
1731                   else:                   else:
1732                      d_times_e=escript.Data()                      d_times_e=escript.Data()
1733                   d_contact=self.getCoefficientOfGeneralPDE("d_contact")        
1734                   if not d_contact.isEmpty():                   if not D_reduced.isEmpty():
1735                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1736                          d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))                          D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1737                       else:                       else:
1738                          d_contact_times_e=d_contact                          D_reduced_times_e=D_reduced
1739                   else:                   else:
1740                      d_contact_times_e=escript.Data()                      D_reduced_times_e=escript.Data()
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    
1749                   self.__operator=self.__getNewRightHandSide()                   self.__operator=self.__getNewRightHandSide()
1750                   self.getDomain().addPDEToRHS(self.__operator, \                   if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1751                                                escript.Data(), \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1752                                                D_times_e, \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1753                                                d_times_e,\                   else:
1754                                                d_contact_times_e)                      self.getDomain().addPDEToRHS(self.__operator, \
1755                                                     escript.Data(), \
1756                                                     D_times_e, \
1757                                                     d_times_e,\
1758                                                     escript.Data())
1759                        self.getDomain().addPDEToRHS(self.__operator, \
1760                                                     escript.Data(), \
1761                                                     D_reduced_times_e, \
1762                                                     d_reduced_times_e,\
1763                                                     escript.Data())
1764                   self.__operator=1./self.__operator                   self.__operator=1./self.__operator
1765                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1766                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1574  class LinearPDE(object): Line 1770  class LinearPDE(object):
1770                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1771                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1772                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1773                     self.getDomain().addPDEToRHS(self.__righthandside, \
1774                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1775                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1776                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1777                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1778                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1779                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1780            else:            else:
# Line 1589  class LinearPDE(object): Line 1790  class LinearPDE(object):
1790                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1791                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1792                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1793                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1794                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1804                   self.__applyConstraint()                   self.__applyConstraint()
1805                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1806                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1600  class LinearPDE(object): Line 1812  class LinearPDE(object):
1812                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1813                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1814                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1815                     self.getDomain().addPDEToRHS(self.__righthandside, \
1816                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1817                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1818                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1819                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1820                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1821                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1822                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1615  class LinearPDE(object): Line 1832  class LinearPDE(object):
1832                              escript.Data(),\                              escript.Data(),\
1833                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1834                              escript.Data())                              escript.Data())
1835                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1836                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1837                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1839                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1840                                escript.Data(), \
1841                                escript.Data(), \
1842                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1843                                escript.Data(),\
1844                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1845                                escript.Data())
1846                   self.__applyConstraint()                   self.__applyConstraint()
1847                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1848                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1648  class Poisson(LinearPDE): Line 1876  class Poisson(LinearPDE):
1876       """       """
1877       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1878       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1879                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1880                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1881       self.setSymmetryOn()       self.setSymmetryOn()
1882    
1883     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1696  class Poisson(LinearPDE): Line 1925  class Poisson(LinearPDE):
1925           return escript.Data()           return escript.Data()
1926       elif name == "y_contact" :       elif name == "y_contact" :
1927           return escript.Data()           return escript.Data()
1928         elif name == "A_reduced" :
1929             return escript.Data()
1930         elif name == "B_reduced" :
1931             return escript.Data()
1932         elif name == "C_reduced" :
1933             return escript.Data()
1934         elif name == "D_reduced" :
1935             return escript.Data()
1936         elif name == "X_reduced" :
1937             return escript.Data()
1938         elif name == "Y_reduced" :
1939             return self.getCoefficient("f_reduced")
1940         elif name == "d_reduced" :
1941             return escript.Data()
1942         elif name == "y_reduced" :
1943             return escript.Data()
1944         elif name == "d_contact_reduced" :
1945             return escript.Data()
1946         elif name == "y_contact_reduced" :
1947             return escript.Data()
1948       elif name == "r" :       elif name == "r" :
1949           return escript.Data()           return escript.Data()
1950       elif name == "q" :       elif name == "q" :
# Line 1732  class Helmholtz(LinearPDE): Line 1981  class Helmholtz(LinearPDE):
1981       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1982                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1983                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1984                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1985                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1986                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1989                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1990       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1795  class Helmholtz(LinearPDE): Line 2046  class Helmholtz(LinearPDE):
2046           return escript.Data()           return escript.Data()
2047       elif name == "y_contact" :       elif name == "y_contact" :
2048           return escript.Data()           return escript.Data()
2049         elif name == "A_reduced" :
2050             return escript.Data()
2051         elif name == "B_reduced" :
2052             return escript.Data()
2053         elif name == "C_reduced" :
2054             return escript.Data()
2055         elif name == "D_reduced" :
2056             return escript.Data()
2057         elif name == "X_reduced" :
2058             return escript.Data()
2059         elif name == "Y_reduced" :
2060             return self.getCoefficient("f_reduced")
2061         elif name == "d_reduced" :
2062             return escript.Data()
2063         elif name == "y_reduced" :
2064            return self.getCoefficient("g_reduced")
2065         elif name == "d_contact_reduced" :
2066             return escript.Data()
2067         elif name == "y_contact_reduced" :
2068             return escript.Data()
2069       elif name == "r" :       elif name == "r" :
2070           return self.getCoefficient("r")           return self.getCoefficient("r")
2071       elif name == "q" :       elif name == "q" :
# Line 1806  class LameEquation(LinearPDE): Line 2077  class LameEquation(LinearPDE):
2077     """     """
2078     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2079    
2080     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] }
2081    
2082     with natural boundary conditons:     with natural boundary conditons:
2083    
2084     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] }
2085    
2086     and constraints:     and constraints:
2087    
# Line 1893  class LameEquation(LinearPDE): Line 2164  class LameEquation(LinearPDE):
2164           return escript.Data()           return escript.Data()
2165       elif name == "y_contact" :       elif name == "y_contact" :
2166           return escript.Data()           return escript.Data()
2167         elif name == "A_reduced" :
2168             return escript.Data()
2169         elif name == "B_reduced" :
2170             return escript.Data()
2171         elif name == "C_reduced" :
2172             return escript.Data()
2173         elif name == "D_reduced" :
2174             return escript.Data()
2175         elif name == "X_reduced" :
2176             return escript.Data()
2177         elif name == "Y_reduced" :
2178             return escript.Data()
2179         elif name == "d_reduced" :
2180             return escript.Data()
2181         elif name == "y_reduced" :
2182             return escript.Data()
2183         elif name == "d_contact_reduced" :
2184             return escript.Data()
2185         elif name == "y_contact_reduced" :
2186             return escript.Data()
2187       elif name == "r" :       elif name == "r" :
2188           return self.getCoefficient("r")           return self.getCoefficient("r")
2189       elif name == "q" :       elif name == "q" :
# Line 1900  class LameEquation(LinearPDE): Line 2191  class LameEquation(LinearPDE):
2191       else:       else:
2192          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2193    
2194  class AdvectivePDE(LinearPDE):  def LinearSinglePDE(domain,debug=False):
2195     """     """
2196     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.  
2197    
2198       @param domain: domain of the PDE
2199       @type domain: L{Domain<escript.Domain>}
2200       @param debug: if True debug informations are printed.
2201       @rtype: L{LinearPDE}
2202     """     """
2203     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()  
2204    
2205     def setValue(self,**coefficients):  def LinearPDESystem(domain,debug=False):
2206        """     """
2207        sets new values to coefficients     defines a system of linear PDEs
   
       @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.  
2208    
2209        """     @param domain: domain of the PDE
2210        if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()     @type domain: L{Domain<escript.Domain>}
2211        super(AdvectivePDE, self).setValue(**coefficients)     @param debug: if True debug informations are printed.
2212       @rtype: L{LinearPDE}
2213       """
2214       return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2215    
2216     def ELMAN_RAMAGE(self,P):  class TransportPDE(object):
2217       """       """
2218       Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.       Warning: This is still a very experimental. The class is still changing!
      This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)  
           - M{S{xi}(P)=0} for M{P<1}  
           - M{S{xi}(P)=(1-1/P)/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))  
   
    def SIMPLIFIED_BROOK_HUGHES(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      The original methods is  
   
      M{S{xi}(P)=coth(P)-1/P}  
   
      As the evaluation of M{coth} is expensive we are using the approximation:  
   
          - M{S{xi}(P)=P/3} where M{P<3}  
          - M{S{xi}(P)=1/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      c=util.whereNegative(P-3.)  
      return P/6.*c+1./2.*(1.-c)  
   
    def HALF(self,P):  
      """  
      Predefined function to set value M{1/2} for M{S{xi}}  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return escript.Scalar(0.5,P.getFunctionSpace())  
   
    def __getXi(self):  
       if self.__Xi.isEmpty():  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          A=self.getCoefficient("A")  
          h=self.getDomain().getSize()  
          self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))  
          if not C.isEmpty() or not B.isEmpty():  
             if not C.isEmpty() and not B.isEmpty():  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for i in range(self.getNumEquations()):  
                          for k in range(self.getNumSolutions()):  
                             for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2  
                       length_of_flux=util.sqrt(flux2)  
                       # flux=C-util.reorderComponents(B,[0,2,1])  
                    else:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2  
                       length_of_flux=util.sqrt(flux2)  
                       # flux=C-B  
                 else:  
                    if self.getNumSolutions()>1:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2  
                       # flux=C-util.reorderComponents(B,[1,0])  
                       length_of_flux=util.sqrt(flux2)  
                    else:  
                       length_of_flux=util.length(C-B)  
             elif C.isEmpty():  
               length_of_flux=util.length(B)  
             else:  
               length_of_flux=util.length(C)  
             flux_max=util.Lsup(length_of_flux)  
             if flux_max>0.:  
               if A.isEmpty():  
                   inv_A=1./self.SMALL_TOLERANCE  
                   peclet_number=escript.Scalar(inv_A,length_of_flux.getFunctionSpace())  
                   xi=self.__xi(self,peclet_number)  
               else:  
                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))  
                   length_of_A=util.length(A)  
                   A_max=util.Lsup(length_of_A)  
                   if A_max>0:  
                        inv_A=1./(length_of_A+A_max*self.SMALL_TOLERANCE)  
                   else:  
                        inv_A=1./self.SMALL_TOLERANCE  
                   peclet_number=length_of_flux*h/2*inv_A  
                   xi=self.__xi(self,peclet_number)  
               self.__Xi=h*xi/(length_of_flux+flux_max*self.SMALL_TOLERANCE)  
               self.trace("preclet number = %e"%util.Lsup(peclet_number))  
             else:  
               self.__Xi=escript.Scalar(0.,length_of_flux.getFunctionSpace())  
       return self.__Xi  
2219    
2220         Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2221        
2222         u=r where q>0
2223        
2224         all coefficients are constant over time.
2225    
2226         typical usage:
2227    
2228             p=TransportPDE(dom)
2229             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2230             p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2231             t=0
2232             dt=0.1
2233             while (t<1.):
2234                  u=p.solve(dt)
2235    
2236         """
2237         def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2238            self.__domain=domain
2239            self.__num_equations=num_equations
2240            self.__useSUPG=useSUPG
2241            self.__trace=trace
2242            self.__theta=theta
2243            self.__matrix_type=0
2244            self.__reduced=True
2245            self.__reassemble=True
2246            if self.__useSUPG:
2247               self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2248               self.__pde.setSymmetryOn()
2249               self.__pde.setReducedOrderOn()
2250            else:
2251               self.__transport_problem=self.__getNewTransportProblem()
2252            self.setTolerance()
2253            self.__M=escript.Data()
2254            self.__A=escript.Data()
2255            self.__B=escript.Data()
2256            self.__C=escript.Data()
2257            self.__D=escript.Data()
2258            self.__X=escript.Data()
2259            self.__Y=escript.Data()
2260            self.__d=escript.Data()
2261            self.__y=escript.Data()
2262            self.__d_contact=escript.Data()
2263            self.__y_contact=escript.Data()
2264            self.__r=escript.Data()
2265            self.__q=escript.Data()
2266    
2267         def trace(self,text):
2268                 if self.__trace: print text
2269         def getSafeTimeStepSize(self):
2270            if self.__useSUPG:
2271                if self.__reassemble:
2272                   h=self.__domain.getSize()
2273                   dt=None
2274                   if not self.__A.isEmpty():
2275                      dt2=util.inf(h**2*self.__M/util.length(self.__A))
2276                      if dt == None:
2277                         dt = dt2
2278                      else:
2279                         dt=1./(1./dt+1./dt2)
2280                   if not self.__B.isEmpty():
2281                      dt2=util.inf(h*self.__M/util.length(self.__B))
2282                      if dt == None:
2283                         dt = dt2
2284                      else:
2285                         dt=1./(1./dt+1./dt2)
2286                   if not  self.__C.isEmpty():
2287                      dt2=util.inf(h*self.__M/util.length(self.__C))
2288                      if dt == None:
2289                         dt = dt2
2290                      else:
2291                         dt=1./(1./dt+1./dt2)
2292                   if not self.__D.isEmpty():
2293                      dt2=util.inf(self.__M/util.length(self.__D))
2294                      if dt == None:
2295                         dt = dt2
2296                      else:
2297                         dt=1./(1./dt+1./dt2)
2298                   self.__dt = dt/2
2299                return self.__dt
2300            else:
2301                return self.__getTransportProblem().getSafeTimeStepSize()
2302         def getDomain(self):
2303            return self.__domain
2304         def getTheta(self):
2305            return self.__theta
2306         def getNumEquations(self):
2307            return self.__num_equations
2308         def setReducedOn(self):
2309              if not self.reduced():
2310                  if self.__useSUPG:
2311                     self.__pde.setReducedOrderOn()
2312                  else:
2313                     self.__transport_problem=self.__getNewTransportProblem()
2314              self.__reduced=True
2315         def setReducedOff(self):
2316              if self.reduced():
2317                  if self.__useSUPG:
2318                     self.__pde.setReducedOrderOff()
2319                  else:
2320                     self.__transport_problem=self.__getNewTransportProblem()
2321              self.__reduced=False
2322         def reduced(self):
2323             return self.__reduced
2324         def getFunctionSpace(self):
2325            if self.reduced():
2326               return escript.ReducedSolution(self.getDomain())
2327            else:
2328               return escript.Solution(self.getDomain())
2329    
2330     def getCoefficientOfGeneralPDE(self,name):       def setTolerance(self,tol=1.e-8):
2331       """          self.__tolerance=tol
2332       return the value of the coefficient name of the general PDE          if self.__useSUPG:
2333                  self.__pde.setTolerance(self.__tolerance)
      @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."  
2334    
2335       if name == "A" :       def __getNewTransportProblem(self):
2336           A=self.getCoefficient("A")         """
2337           B=self.getCoefficient("B")         returns an instance of a new operator
2338           C=self.getCoefficient("C")         """
2339           if B.isEmpty() and C.isEmpty():         self.trace("New Transport problem is allocated.")
2340              Aout=A         return self.getDomain().newTransportProblem( \
2341           else:                                 self.getTheta(),
2342              if A.isEmpty():                                 self.getNumEquations(), \
2343                 Aout=self.createCoefficientOfGeneralPDE("A")                                 self.getFunctionSpace(), \
2344              else:                                 self.__matrix_type)
2345                 Aout=A[:]            
2346              Xi=self.__getXi()       def __getNewSolutionVector(self):
2347              if self.getNumEquations()>1:           if self.getNumEquations() ==1 :
2348                  for i in range(self.getNumEquations()):                  out=escript.Data(0.0,(),self.getFunctionSpace())
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()):  
                             if not C.isEmpty() and not B.isEmpty():  
                                # tmp=C-util.reorderComponents(B,[0,2,1])  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k])  
                             elif C.isEmpty():  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)  
                             else:  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)  
             else:  
                if not C.isEmpty() and not B.isEmpty():  
                    delta=(C-B)  
                    Aout+=util.outer(Xi*delta,delta)  
                elif not B.isEmpty():  
                    Aout+=util.outer(Xi*B,B)  
                elif not C.isEmpty():  
                    Aout+=util.outer(Xi*C,C)  
          return Aout  
      elif name == "B" :  
          # return self.getCoefficient("B")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if C.isEmpty() or D.isEmpty():  
             Bout=B  
          else:  
             Xi=self.__getXi()  
             if B.isEmpty():  
                 Bout=self.createCoefficientOfGeneralPDE("B")  
             else:  
                 Bout=B[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                   for p in range(self.getNumEquations()):  
                      tmp=Xi*D[p,k]  
                      for i in range(self.getNumEquations()):  
                         for j in range(self.getDim()):  
                            Bout[i,j,k]+=tmp*C[p,i,j]  
                            # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)  
             else:  
                Bout+=(Xi*D)*C  
          return Bout  
      elif name == "C" :  
          # return self.getCoefficient("C")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if B.isEmpty() or D.isEmpty():  
             Cout=C  
          else:  
             Xi=self.__getXi()  
             if C.isEmpty():  
                 Cout=self.createCoefficientOfGeneralPDE("C")  
             else:  
                 Cout=C[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                    for p in range(self.getNumEquations()):  
                       tmp=Xi*D[p,k]  
                       for i in range(self.getNumEquations()):  
                         for l in range(self.getDim()):  
                                  Cout[i,k,l]+=tmp*B[p,l,i]  
                                  # Cout=Cout+Xi*B[p,l,i]*D[p,k]  
             else:  
                Cout+=(Xi*D)*B  
          return Cout  
      elif name == "D" :  
          return self.getCoefficient("D")  
      elif name == "X" :  
          # return self.getCoefficient("X")  
          X=self.getCoefficient("X")  
          Y=self.getCoefficient("Y")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):  
             Xout=X  
2349           else:           else:
2350              if X.isEmpty():                  out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2351                  Xout=self.createCoefficientOfGeneralPDE("X")           return out
             else:  
                 Xout=X[:]  
             Xi=self.__getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                              # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                              # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
                              # Xout=X_out+Xi*util.inner(Y,C,offset=1)  
             else:  
               if not C.isEmpty() and not B.isEmpty():  
                 Xout+=(Xi*Y)*(C-B)  
               elif C.isEmpty():  
                 Xout-=(Xi*Y)*B  
               else:  
                 Xout+=(Xi*Y)*C  
          return Xout  
      elif name == "Y" :  
          return self.getCoefficient("Y")  
      elif name == "d" :  
          return self.getCoefficient("d")  
      elif name == "y" :  
          return self.getCoefficient("y")  
      elif name == "d_contact" :  
          return self.getCoefficient("d_contact")  
      elif name == "y_contact" :  
          return self.getCoefficient("y_contact")  
      elif name == "r" :  
          return self.getCoefficient("r")  
      elif name == "q" :  
          return self.getCoefficient("q")  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2352    
2353  # $Log$       def __getTransportProblem(self):
2354  # Revision 1.14  2005/09/22 01:54:57  jgs         if self.__reassemble:
2355  # Merge of development branch dev-02 back to main trunk on 2005-09-22               self.__source=self.__getNewSolutionVector()
2356  #               self.__transport_problem.reset()
2357  # Revision 1.13  2005/09/15 03:44:19  jgs               self.getDomain().addPDEToTransportProblem(
2358  # Merge of development branch dev-02 back to main trunk on 2005-09-15                           self.__transport_problem,
2359  #                           self.__source,
2360  # Revision 1.12  2005/09/01 03:31:28  jgs                           self.__M,
2361  # Merge of development branch dev-02 back to main trunk on 2005-09-01                           self.__A,
2362  #                           self.__B,
2363  # Revision 1.11  2005/08/23 01:24:28  jgs                           self.__C,
2364  # Merge of development branch dev-02 back to main trunk on 2005-08-23                           self.__D,
2365  #                           self.__X,
2366  # Revision 1.10  2005/08/12 01:45:36  jgs                           self.__Y,
2367  # erge of development branch dev-02 back to main trunk on 2005-08-12                           self.__d,
2368  #                           self.__y,
2369  # Revision 1.9.2.17  2005/09/21 07:03:33  matt                           self.__d_contact,
2370  # PDECoefficient and LinearPDE are now new style classes (introduced in Python                           self.__y_contact)
2371  # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been               self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2372  # modified to instead use portable/cooperative "super" calls to extend base               self.__reassemble=False
2373  # class methods.         return self.__transport_problem
2374  #       def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2375  # Revision 1.9.2.16  2005/09/16 01:54:37  matt                    d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2376  # Removed redundant if-loop.               if not M==None:
2377  #                    self.__reassemble=True
2378  # Revision 1.9.2.15  2005/09/14 08:09:18  matt                    self.__M=M
2379  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.               if not A==None:
2380  #                    self.__reassemble=True
2381  # Revision 1.9.2.14  2005/09/07 06:26:16  gross                    self.__A=A
2382  # the solver from finley are put into the standalone package paso now               if not B==None:
2383  #                    self.__reassemble=True
2384  # Revision 1.9.2.13  2005/08/31 08:45:03  gross                    self.__B=B
2385  # in the case of lumping no new system is allocated if the constraint is changed.               if not C==None:
2386  #                    self.__reassemble=True
2387  # Revision 1.9.2.12  2005/08/31 07:10:23  gross                    self.__C=C
2388  # test for Lumping added               if not D==None:
2389  #                    self.__reassemble=True
2390  # Revision 1.9.2.11  2005/08/30 01:53:45  gross                    self.__D=D
2391  # bug in format fixed.               if not X==None:
2392  #                    self.__reassemble=True
2393  # Revision 1.9.2.10  2005/08/26 07:14:17  gross                    self.__X=X
2394  # a few more bugs in linearPDE fixed. remaining problem are finley problems               if not Y==None:
2395  #                    self.__reassemble=True
2396  # Revision 1.9.2.9  2005/08/26 06:30:45  gross                    self.__Y=Y
2397  # fix for reported bug  0000004. test_linearPDE passes a few more tests               if not d==None:
2398  #                    self.__reassemble=True
2399  # Revision 1.9.2.8  2005/08/26 04:30:13  gross                    self.__d=d
2400  # gneric unit testing for linearPDE               if not y==None:
2401  #                    self.__reassemble=True
2402  # Revision 1.9.2.7  2005/08/25 07:06:50  gross                    self.__y=y
2403  # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so               if not d_contact==None:
2404  #                    self.__reassemble=True
2405  # Revision 1.9.2.6  2005/08/24 05:01:24  gross                    self.__d_contact=d_contact
2406  # problem with resetting the matrix in case of resetting its values to 0 fixed.               if not y_contact==None:
2407  #                    self.__reassemble=True
2408  # Revision 1.9.2.5  2005/08/24 02:03:28  gross                    self.__y_contact=y_contact
2409  # epydoc mark up partially fixed               if not q==None:
2410  #                    self.__reassemble=True
2411  # Revision 1.9.2.4  2005/08/22 07:11:09  gross                    self.__q=q
2412  # some problems with LinearPDEs fixed.               if not r==None:
2413  #                    self.__reassemble=True
2414  # Revision 1.9.2.3  2005/08/18 04:48:48  gross                    self.__r=r
2415  # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  
2416  #       def setInitialSolution(self,u):
2417  # Revision 1.9.2.2  2005/08/18 04:39:32  gross               if self.__useSUPG:
2418  # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now                   self.__u=util.interpolate(u,self.getFunctionSpace())
2419  #               else:
2420  # Revision 1.9.2.1  2005/07/29 07:10:27  gross                   self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2421  # new functions in util and a new pde type in linearPDEs  
2422  #       def solve(self,dt,**kwarg):
2423  # Revision 1.1.2.25  2005/07/28 04:21:09  gross             if self.__useSUPG:
2424  # Lame equation: (linear elastic, isotropic) added                  if self.__reassemble:
2425  #                      self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q)
2426  # Revision 1.1.2.24  2005/07/22 06:37:11  gross                      self.__reassemble=False
2427  # some extensions to modellib and linearPDEs                  dt2=self.getSafeTimeStepSize()
2428  #                  nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2429  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane                  dt2=dt/nn
2430  # Fixed up some docstrings.  Moved module-level functions to top of file so                  nnn=0
2431  # that epydoc and doxygen can pick them up properly.                  u=self.__u
2432  #                  self.trace("number of substeps is %d."%nn)
2433  # Revision 1.1.2.22  2005/05/12 11:41:30  gross                  while nnn<nn :
2434  # some basic Models have been added                      self.__setSUPG(u,u,dt2/2)
2435  #                      u_half=self.__pde.getSolution(verbose=True)
2436  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane                      self.__setSUPG(u,u_half,dt2)
2437  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of                      u=self.__pde.getSolution(verbose=True)
2438  # file so that the AdvectivePDE class is picked up by doxygen.  Some                      nnn+=1
2439  # reformatting of docstrings.  Addition of code to make equations come out                  self.__u=u
2440  # as proper LaTeX.                  return self.__u
2441  #             else:
2442  # Revision 1.1.2.20  2005/04/15 07:09:08  gross                 kwarg["tolerance"]=self.__tolerance
2443  # some problems with functionspace and linearPDEs fixed.                 tp=self.__getTransportProblem()
2444  #                 return tp.solve(self.__source,dt,kwarg)
2445  # Revision 1.1.2.19  2005/03/04 05:27:07  gross       def __setSUPG(self,u0,u,dt):
2446  # bug in SystemPattern fixed.              g=util.grad(u)
2447  #              X=0
2448  # Revision 1.1.2.18  2005/02/08 06:16:45  gross              Y=self.__M*u0
2449  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed              X=0
2450  #              if not self.__A.isEmpty():
2451  # Revision 1.1.2.17  2005/02/08 05:56:19  gross                 X=X+dt*util.matrixmult(self.__A,g)
2452  # Reference Number handling added              if not self.__B.isEmpty():
2453  #                 X=X+dt*self.__B*u
2454  # Revision 1.1.2.16  2005/02/07 04:41:28  gross              if not  self.__C.isEmpty():
2455  # some function exposed to python to make mesh merging running                 Y=Y+dt*util.inner(self.__C,g)
2456  #              if not self.__D.isEmpty():
2457  # Revision 1.1.2.15  2005/02/03 00:14:44  gross                 Y=Y+dt*self.__D*u
2458  # timeseries add and ESySParameter.py renames esysXML.py for consistence              if not self.__X.isEmpty():
2459  #                 X=X+dt*self.__X
2460  # Revision 1.1.2.14  2005/02/01 06:44:10  gross              if not self.__Y.isEmpty():
2461  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working                 Y=Y+dt*self.__Y
2462  #              self.__pde.setValue(X=X,Y=Y)
2463  # Revision 1.1.2.13  2005/01/25 00:47:07  gross              if not self.__y.isEmpty():
2464  # updates in the documentation                 self.__pde.setValue(y=dt*self.__y)
2465  #              if not self.__y_contact.isEmpty():
2466  # Revision 1.1.2.12  2005/01/12 01:28:04  matt                 self.__pde.setValue(y=dt*self.__y_contact)
2467  # Added createCoefficient method for linearPDEs.              self.__pde.setValue(r=u0)
 #  
 # Revision 1.1.2.11  2005/01/11 01:55:34  gross  
 # a problem in linearPDE class fixed  
 #  
 # Revision 1.1.2.10  2005/01/07 01:13:29  gross  
 # some bugs in linearPDE fixed  
 #  
 # Revision 1.1.2.9  2005/01/06 06:24:58  gross  
 # some bugs in slicing fixed  
 #  
 # Revision 1.1.2.8  2005/01/05 04:21:40  gross  
 # FunctionSpace checking/matchig in slicing added  
 #  
 # Revision 1.1.2.7  2004/12/29 10:03:41  gross  
 # bug in setValue fixed  
 #  
 # Revision 1.1.2.6  2004/12/29 05:29:59  gross  
 # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()  
 #  
 # Revision 1.1.2.5  2004/12/29 00:18:41  gross  
 # AdvectivePDE added  
 #  
 # Revision 1.1.2.4  2004/12/24 06:05:41  gross  
 # some changes in linearPDEs to add AdevectivePDE  
 #  
 # Revision 1.1.2.3  2004/12/16 00:12:34  gross  
 # __init__ of LinearPDE does not accept any coefficient anymore  
 #  
 # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  
 # *** empty log message ***  
 #  
 # Revision 1.1.2.1  2004/12/12 22:53:47  gross  
 # linearPDE has been renamed LinearPDE  
 #  
 # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross  
 # GMRES added  
 #  
 # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross  
 # options for GMRES and PRES20 added  
 #  
 # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross  
 # some small changes  
 #  
 # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross  
 # Finley solves 4M unknowns now  
 #  
 # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross  
 # poisson solver added  
 #  
 # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross  
 # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry  
 #  
 # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross  
 # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed  
 #  
 # Revision 1.1.1.1  2004/10/26 06:53:56  jgs  
 # initial import of project esys2  
 #  
 # Revision 1.3.2.3  2004/10/26 06:43:48  jgs  
 # committing Lutz's and Paul's changes to brach jgs  
 #  
 # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane  
 # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.  
 #  
 # Revision 1.3  2004/09/23 00:53:23  jgs  
 # minor fixes  
 #  
 # Revision 1.1  2004/08/28 12:58:06  gross  
 # SimpleSolve is not running yet: problem with == of functionsspace  
 #  

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