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revision 328 by gross, Wed Dec 7 04:41:53 2005 UTC revision 1072 by gross, Thu Mar 29 06:44:30 2007 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
   
 #  
 #      COPYRIGHT ACcESS 2004 -  All Rights Reserved  
 #  
 #   This software is the property of ACcESS.  No part of this code  
 #   may be copied in any form or by any means without the expressed written  
 #   consent of ACcESS.  Copying, use or modification of this software  
 #   by any unauthorised person is illegal unless that  
 #   person has a software license agreement with ACcESS.  
 #  
2  """  """
3  The module provides an interface to define and solve linear partial  The module provides an interface to define and solve linear partial
4  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
# Line 17  the PDE solver library defined through t Line 7  the PDE solver library defined through t
7  The general interface is provided through the L{LinearPDE} class. The  The general interface is provided through the L{LinearPDE} class. The
8  L{AdvectivePDE} which is derived from the L{LinearPDE} class  L{AdvectivePDE} which is derived from the L{LinearPDE} class
9  provides an interface to PDE dominated by its advective terms. The L{Poisson},  provides an interface to PDE dominated by its advective terms. The L{Poisson},
10  L{Helmholtz}, L{LameEquation}  L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
11  classs which are also derived form the L{LinearPDE} class should be used  classs which are also derived form the L{LinearPDE} class should be used
12  to define of solve these sepecial PDEs.  to define of solve these sepecial PDEs.
13    
14  @var __author__: name of author  @var __author__: name of author
15  @var __licence__: licence agreement  @var __copyright__: copyrights
16    @var __license__: licence agreement
17  @var __url__: url entry point on documentation  @var __url__: url entry point on documentation
18  @var __version__: version  @var __version__: version
19  @var __date__: date of the version  @var __date__: date of the version
# Line 33  import util Line 24  import util
24  import numarray  import numarray
25    
26  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
27  __licence__="contact: esys@access.uq.edu.au"  __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
28  __url__="http://www.iservo.edu.au/esys/escript"                      http://www.access.edu.au
29                    Primary Business: Queensland, Australia"""
30    __license__="""Licensed under the Open Software License version 3.0
31                 http://www.opensource.org/licenses/osl-3.0.php"""
32    __url__="http://www.iservo.edu.au/esys"
33  __version__="$Revision$"  __version__="$Revision$"
34  __date__="$Date$"  __date__="$Date$"
35    
# Line 43  class IllegalCoefficient(ValueError): Line 38  class IllegalCoefficient(ValueError):
38     """     """
39     raised if an illegal coefficient of the general ar particular PDE is requested.     raised if an illegal coefficient of the general ar particular PDE is requested.
40     """     """
41       pass
42    
43  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
44     """     """
45     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
46     """     """
47       pass
48    
49    class IllegalCoefficientFunctionSpace(ValueError):
50       """
51       raised if an incorrect function space for a coefficient is used.
52       """
53    
54  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
55     """     """
56     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
57     """     """
58       pass
59    
60  class PDECoefficient(object):  class PDECoefficient(object):
61      """      """
# Line 61  class PDECoefficient(object): Line 64  class PDECoefficient(object):
64      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
65      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
66      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
67        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
68        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
69        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
70      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
71      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
72      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
# Line 82  class PDECoefficient(object): Line 88  class PDECoefficient(object):
88      OPERATOR=10      OPERATOR=10
89      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
90      BOTH=12      BOTH=12
91        INTERIOR_REDUCED=13
92        BOUNDARY_REDUCED=14
93        CONTACT_REDUCED=15
94    
95      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
96         """         """
97         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
98    
99         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
100         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
101                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
102         @param pattern: describes the shape of the coefficient and how the shape is build for a given         @param pattern: describes the shape of the coefficient and how the shape is build for a given
103                spatial dimension and numbers of equation and solution in then PDE. For instance,                spatial dimension and numbers of equation and solution in then PDE. For instance,
104                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
# Line 99  class PDECoefficient(object): Line 109  class PDECoefficient(object):
109         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
110         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
111         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
112           @param reduced: indicates if reduced
113           @type reduced: C{bool}
114         """         """
115         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
116         self.what=where         self.what=where
# Line 120  class PDECoefficient(object): Line 131  class PDECoefficient(object):
131         @param domain: domain on which the PDE uses the coefficient         @param domain: domain on which the PDE uses the coefficient
132         @type domain: L{Domain<escript.Domain>}         @type domain: L{Domain<escript.Domain>}
133         @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
134         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
135         @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
136         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
137         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
138         @rtype:  L{FunctionSpace<escript.FunctionSpace>}         @rtype:  L{FunctionSpace<escript.FunctionSpace>}
139         """         """
140         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
141              return escript.Function(domain)              return escript.Function(domain)
142           elif self.what==self.INTERIOR_REDUCED:
143                return escript.ReducedFunction(domain)
144         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
145              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
146           elif self.what==self.BOUNDARY_REDUCED:
147                return escript.ReducedFunctionOnBoundary(domain)
148         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
149              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
150           elif self.what==self.CONTACT_REDUCED:
151                return escript.ReducedFunctionOnContactZero(domain)
152         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
153              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
154                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 160  class PDECoefficient(object): Line 177  class PDECoefficient(object):
177         @param numSolutions: number of components of the PDE solution         @param numSolutions: number of components of the PDE solution
178         @type numSolutions: C{int}         @type numSolutions: C{int}
179         @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
180         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
181         @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
182         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
183         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
184         @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>}
185         @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
186           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
187         """         """
188         if newValue==None:         if newValue==None:
189             newValue=escript.Data()             newValue=escript.Data()
190         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
191             if not newValue.isEmpty():             if not newValue.isEmpty():
192                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
193                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
194                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
195                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
196                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
197         else:         else:
198             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
199         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 318  class LinearPDE(object): Line 337  class LinearPDE(object):
337    
338     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:
339    
340     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)}
341    
342    
343     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,
344     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.
345     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
346     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
347     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
348       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
349       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.
350    
351     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
352    
353     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}
354    
355     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>}.  
356    
357    
358     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
# Line 344  class LinearPDE(object): Line 364  class LinearPDE(object):
364    
365     The PDE is symmetrical if     The PDE is symmetrical if
366    
367     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]
368    
369     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
370    
371     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] }
372    
373     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.
374     The natural boundary conditions take the form:     The natural boundary conditions take the form:
375    
376     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]}
377    
378    
379     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>}.
380    
381       Constraints take the form
382    
383     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
384    
# Line 366  class LinearPDE(object): Line 387  class LinearPDE(object):
387     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
388    
389          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
390            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
391          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
392            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
393          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
394            - M{D_reduced[i,k]=D_reduced[i,k]}
395          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
396            - M{d_reduced[i,k]=d_reduced[k,i]}
397    
398     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
399     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
400     defined as     defined as
401    
402     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]}
403    
404     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
405    
406     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]}
407    
408     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
409     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
410     the contact condition takes the form     the contact condition takes the form
411    
412     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]}
413    
414     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
415     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
416     L{jump<util.jump>}.     L{jump<util.jump>}.
417     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>}.
418        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>}.
419     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
420    
421     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)}
422    
423     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>}.  
424    
425     @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
426     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 419  class LinearPDE(object): Line 444  class LinearPDE(object):
444     @cvar MKL: Intel's MKL solver library     @cvar MKL: Intel's MKL solver library
445     @cvar UMFPACK: the UMFPACK library     @cvar UMFPACK: the UMFPACK library
446     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
447       @cvar AMG: algebraic multi grid
448       @cvar RILU: recursive ILU
449    
450     """     """
451     DEFAULT= 0     DEFAULT= 0
# Line 443  class LinearPDE(object): Line 470  class LinearPDE(object):
470     UMFPACK= 16     UMFPACK= 16
471     ITERATIVE= 20     ITERATIVE= 20
472     PASO= 21     PASO= 21
473       AMG= 22
474       RILU = 23
475    
476     __TOL=1.e-13     SMALL_TOLERANCE=1.e-13
477     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
478     __METHOD_KEY="method"     __METHOD_KEY="method"
479     __SYMMETRY_KEY="symmetric"     __SYMMETRY_KEY="symmetric"
480     __TOLERANCE_KEY="tolerance"     __TOLERANCE_KEY="tolerance"
481       __PRECONDITIONER_KEY="preconditioner"
482    
483    
484     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
# Line 479  class LinearPDE(object): Line 509  class LinearPDE(object):
509         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
510         "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),
511         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
512           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
513           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
514           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
515           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
516           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
517           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
518           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
519           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
520           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
521           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
522         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
523         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
524    
# Line 498  class LinearPDE(object): Line 538  class LinearPDE(object):
538       self.__tolerance=1.e-8       self.__tolerance=1.e-8
539       self.__solver_method=self.DEFAULT       self.__solver_method=self.DEFAULT
540       self.__solver_package=self.DEFAULT       self.__solver_package=self.DEFAULT
541         self.__preconditioner=self.DEFAULT
542       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
543       self.__sym=False       self.__sym=False
544    
# Line 663  class LinearPDE(object): Line 704  class LinearPDE(object):
704       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
705       """       """
706       if u==None:       if u==None:
707            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
708       else:       else:
709          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
710    
711     def getResidual(self,u=None):     def getResidual(self,u=None):
712       """       """
# Line 697  class LinearPDE(object): Line 738  class LinearPDE(object):
738        else:        else:
739           A=self.getCoefficientOfGeneralPDE("A")           A=self.getCoefficientOfGeneralPDE("A")
740           if not A.isEmpty():           if not A.isEmpty():
741              tol=util.Lsup(A)*self.__TOL              tol=util.Lsup(A)*self.SMALL_TOLERANCE
742              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
743                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
744                    for j in range(self.getDim()):                    for j in range(self.getDim()):
# Line 721  class LinearPDE(object): Line 762  class LinearPDE(object):
762              if verbose: print "non-symmetric PDE because C is not present but B is"              if verbose: print "non-symmetric PDE because C is not present but B is"
763              out=False              out=False
764           elif not B.isEmpty() and not C.isEmpty():           elif not B.isEmpty() and not C.isEmpty():
765              tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.              tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
766              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
767                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
768                     for j in range(self.getDim()):                     for j in range(self.getDim()):
# Line 737  class LinearPDE(object): Line 778  class LinearPDE(object):
778           if self.getNumSolutions()>1:           if self.getNumSolutions()>1:
779             D=self.getCoefficientOfGeneralPDE("D")             D=self.getCoefficientOfGeneralPDE("D")
780             if not D.isEmpty():             if not D.isEmpty():
781               tol=util.Lsup(D)*self.__TOL               tol=util.Lsup(D)*self.SMALL_TOLERANCE
782               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
783                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
784                    if util.Lsup(D[i,k]-D[k,i])>tol:                    if util.Lsup(D[i,k]-D[k,i])>tol:
# Line 745  class LinearPDE(object): Line 786  class LinearPDE(object):
786                        out=False                        out=False
787             d=self.getCoefficientOfGeneralPDE("d")             d=self.getCoefficientOfGeneralPDE("d")
788             if not d.isEmpty():             if not d.isEmpty():
789               tol=util.Lsup(d)*self.__TOL               tol=util.Lsup(d)*self.SMALL_TOLERANCE
790               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
791                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
792                    if util.Lsup(d[i,k]-d[k,i])>tol:                    if util.Lsup(d[i,k]-d[k,i])>tol:
# Line 753  class LinearPDE(object): Line 794  class LinearPDE(object):
794                        out=False                        out=False
795             d_contact=self.getCoefficientOfGeneralPDE("d_contact")             d_contact=self.getCoefficientOfGeneralPDE("d_contact")
796             if not d_contact.isEmpty():             if not d_contact.isEmpty():
797               tol=util.Lsup(d_contact)*self.__TOL               tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
798               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
799                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
800                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
801                        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)
802                        out=False                        out=False
803             # and now the reduced coefficients
804             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
805             if not A_reduced.isEmpty():
806                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
807                if self.getNumSolutions()>1:
808                   for i in range(self.getNumEquations()):
809                      for j in range(self.getDim()):
810                         for k in range(self.getNumSolutions()):
811                            for l in range(self.getDim()):
812                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
813                                   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)
814                                   out=False
815                else:
816                   for j in range(self.getDim()):
817                      for l in range(self.getDim()):
818                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
819                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
820                            out=False
821             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
822             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
823             if B_reduced.isEmpty() and not C_reduced.isEmpty():
824                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
825                out=False
826             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
827                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
828                out=False
829             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
830                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
831                if self.getNumSolutions()>1:
832                   for i in range(self.getNumEquations()):
833                       for j in range(self.getDim()):
834                          for k in range(self.getNumSolutions()):
835                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
836                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
837                                  out=False
838                else:
839                   for j in range(self.getDim()):
840                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
841                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
842                         out=False
843             if self.getNumSolutions()>1:
844               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
845               if not D_reduced.isEmpty():
846                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
847                 for i in range(self.getNumEquations()):
848                    for k in range(self.getNumSolutions()):
849                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
850                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
851                          out=False
852               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
853               if not d_reduced.isEmpty():
854                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
855                 for i in range(self.getNumEquations()):
856                    for k in range(self.getNumSolutions()):
857                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
858                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
859                          out=False
860               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
861               if not d_contact_reduced.isEmpty():
862                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
863                 for i in range(self.getNumEquations()):
864                    for k in range(self.getNumSolutions()):
865                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
866                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
867                          out=False
868        return out        return out
869    
870     def getSolution(self,**options):     def getSolution(self,**options):
# Line 772  class LinearPDE(object): Line 878  class LinearPDE(object):
878         @type verbose: C{bool}         @type verbose: C{bool}
879         @keyword reordering: reordering scheme to be used during elimination. Allowed values are         @keyword reordering: reordering scheme to be used during elimination. Allowed values are
880                              L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}                              L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
        @keyword preconditioner: preconditioner method to be used. Allowed values are  
                                 L{SSOR}, L{ILU0}, L{ILUT}, L{JACOBI}  
881         @keyword iter_max: maximum number of iteration steps allowed.         @keyword iter_max: maximum number of iteration steps allowed.
882         @keyword drop_tolerance: threshold for drupping in L{ILUT}         @keyword drop_tolerance: threshold for drupping in L{ILUT}
883         @keyword drop_storage: maximum of allowed memory in L{ILUT}         @keyword drop_storage: maximum of allowed memory in L{ILUT}
# Line 786  class LinearPDE(object): Line 890  class LinearPDE(object):
890               self.__solution=self.copyConstraint(f*mat)               self.__solution=self.copyConstraint(f*mat)
891            else:            else:
892               options[self.__TOLERANCE_KEY]=self.getTolerance()               options[self.__TOLERANCE_KEY]=self.getTolerance()
893               options[self.__METHOD_KEY]=self.getSolverMethod()               options[self.__METHOD_KEY]=self.getSolverMethod()[0]
894                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
895               options[self.__PACKAGE_KEY]=self.getSolverPackage()               options[self.__PACKAGE_KEY]=self.getSolverPackage()
896               options[self.__SYMMETRY_KEY]=self.isSymmetric()               options[self.__SYMMETRY_KEY]=self.isSymmetric()
897               self.trace("PDE is resolved.")               self.trace("PDE is resolved.")
# Line 799  class LinearPDE(object): Line 904  class LinearPDE(object):
904       """       """
905       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
906    
907       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]}
908    
909       or       or
910    
911       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]}
912    
913       @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.
914       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 811  class LinearPDE(object): Line 916  class LinearPDE(object):
916       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
917       """       """
918       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
919       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))) \
920               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
921               -util.self.getCoefficientOfGeneralPDE("X") \
922               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
923               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
924               -util.self.getCoefficientOfGeneralPDE("X_reduced")
925     # =============================================================================     # =============================================================================
926     #   solver settings:     #   solver settings:
927     # =============================================================================     # =============================================================================
928     def setSolverMethod(self,solver=None):     def setSolverMethod(self,solver=None,preconditioner=None):
929         """         """
930         sets a new solver         sets a new solver
931    
932         @param solver: sets a new solver method.         @param solver: sets a new solver method.
933         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}.         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, L{AMG}
934           @param preconditioner: sets a new solver method.
935           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
936         """         """
937         if solver==None: solve=self.DEFAULT         if solver==None: solve=self.DEFAULT
938         if not solver==self.getSolverMethod():         if preconditioner==None: preconditioner=self.DEFAULT
939           if not (solver,preconditioner)==self.getSolverMethod():
940             self.__solver_method=solver             self.__solver_method=solver
941               self.__preconditioner=preconditioner
942             self.__checkMatrixType()             self.__checkMatrixType()
943             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
944    
# Line 838  class LinearPDE(object): Line 952  class LinearPDE(object):
952    
953         m=self.getSolverMethod()         m=self.getSolverMethod()
954         p=self.getSolverPackage()         p=self.getSolverPackage()
955         if m==self.DEFAULT: method="DEFAULT"         method=""
956         elif m==self.DIRECT: method= "DIRECT"         if m[0]==self.DEFAULT: method="DEFAULT"
957         elif m==self.ITERATIVE: method= "ITERATIVE"         elif m[0]==self.DIRECT: method= "DIRECT"
958         elif m==self.CHOLEVSKY: method= "CHOLEVSKY"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
959         elif m==self.PCG: method= "PCG"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
960         elif m==self.CR: method= "CR"         elif m[0]==self.PCG: method= "PCG"
961         elif m==self.CGS: method= "CGS"         elif m[0]==self.CR: method= "CR"
962         elif m==self.BICGSTAB: method= "BICGSTAB"         elif m[0]==self.CGS: method= "CGS"
963         elif m==self.SSOR: method= "SSOR"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
964         elif m==self.GMRES: method= "GMRES"         elif m[0]==self.SSOR: method= "SSOR"
965         elif m==self.PRES20: method= "PRES20"         elif m[0]==self.GMRES: method= "GMRES"
966         elif m==self.LUMPING: method= "LUMPING"         elif m[0]==self.PRES20: method= "PRES20"
967         else : method="unknown"         elif m[0]==self.LUMPING: method= "LUMPING"
968           elif m[0]==self.AMG: method= "AMG"
969           if m[1]==self.DEFAULT: method+="+DEFAULT"
970           elif m[1]==self.JACOBI: method+= "+JACOBI"
971           elif m[1]==self.ILU0: method+= "+ILU0"
972           elif m[1]==self.ILUT: method+= "+ILUT"
973           elif m[1]==self.SSOR: method+= "+SSOR"
974           elif m[1]==self.AMG: method+= "+AMG"
975           elif m[1]==self.RILU: method+= "+RILU"
976         if p==self.DEFAULT: package="DEFAULT"         if p==self.DEFAULT: package="DEFAULT"
977         elif p==self.PASO: package= "PASO"         elif p==self.PASO: package= "PASO"
978         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
# Line 867  class LinearPDE(object): Line 989  class LinearPDE(object):
989         @return: the solver method currently be used.         @return: the solver method currently be used.
990         @rtype: C{int}         @rtype: C{int}
991         """         """
992         return self.__solver_method         return self.__solver_method,self.__preconditioner
993    
994     def setSolverPackage(self,package=None):     def setSolverPackage(self,package=None):
995         """         """
996         sets a new solver package         sets a new solver package
997    
998         @param solver: sets a new solver method.         @param package: sets a new solver method.
999         @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}
1000         """         """
1001         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1002         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
1003             self.__solver_method=solver             self.__solver_package=package
1004             self.__checkMatrixType()             self.__checkMatrixType()
1005             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
1006    
# Line 898  class LinearPDE(object): Line 1020  class LinearPDE(object):
1020        @return: True is lumping is currently used a solver method.        @return: True is lumping is currently used a solver method.
1021        @rtype: C{bool}        @rtype: C{bool}
1022        """        """
1023        return self.getSolverMethod()==self.LUMPING        return self.getSolverMethod()[0]==self.LUMPING
1024    
1025     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
1026         """         """
# Line 911  class LinearPDE(object): Line 1033  class LinearPDE(object):
1033         @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
1034                     the system will be resolved.                     the system will be resolved.
1035         @type tol: positive C{float}         @type tol: positive C{float}
1036         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1037         """         """
1038         if not tol>0:         if not tol>0:
1039             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1040         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1041         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1042         self.__tolerance=tol         self.__tolerance=tol
# Line 1091  class LinearPDE(object): Line 1213  class LinearPDE(object):
1213       """       """
1214       reassess the matrix type and, if a new matrix is needed, resets the system.       reassess the matrix type and, if a new matrix is needed, resets the system.
1215       """       """
1216       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.getSolverPackage(),self.isSymmetric())       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1217       if not new_matrix_type==self.__matrix_type:       if not new_matrix_type==self.__matrix_type:
1218           self.trace("Matrix type is now %d."%new_matrix_type)           self.trace("Matrix type is now %d."%new_matrix_type)
1219           self.__matrix_type=new_matrix_type           self.__matrix_type=new_matrix_type
# Line 1245  class LinearPDE(object): Line 1367  class LinearPDE(object):
1367       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1368       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1369       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1370                    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},
1371                      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}.
1372       """       """
1373       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1374          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1273  class LinearPDE(object): Line 1396  class LinearPDE(object):
1396       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1397       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1398       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1399                    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},
1400                      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}.
1401       """       """
1402       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1403          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1289  class LinearPDE(object): Line 1413  class LinearPDE(object):
1413       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1414       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1415       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1416                    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},
1417                      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}.
1418       """       """
1419       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1420          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1305  class LinearPDE(object): Line 1430  class LinearPDE(object):
1430       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1431       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1432       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1433                    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},
1434                      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}.
1435       """       """
1436       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1437          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 1435  class LinearPDE(object): Line 1561  class LinearPDE(object):
1561        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1562        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1563        @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>}.
1564          @keyword A_reduced: value for coefficient A_reduced.
1565          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1566        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1567        @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>}.
1568          @keyword B_reduced: value for coefficient B_reduced
1569          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1570        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1571        @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>}.
1572          @keyword C_reduced: value for coefficient C_reduced
1573          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1574        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1575        @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>}.
1576          @keyword D_reduced: value for coefficient D_reduced
1577          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1578        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1579        @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>}.
1580          @keyword X_reduced: value for coefficient X_reduced
1581          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1582        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1583        @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>}.
1584          @keyword Y_reduced: value for coefficient Y_reduced
1585          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1586        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1587        @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>}.
1588          @keyword d_reduced: value for coefficient d_reduced
1589          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1590        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1591        @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>}.
1592        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1593        @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>}.
1594                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1595          @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>}.
1596        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1597        @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>}.
1598                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1599          @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>}.
1600        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1601        @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>}
1602                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1489  class LinearPDE(object): Line 1631  class LinearPDE(object):
1631        # 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:
1632        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1633          try:          try:
1634             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1635                                             self.getNumEquations(),self.getNumSolutions(),
1636                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1637               self.alteredCoefficient(i)
1638            except IllegalCoefficientFunctionSpace,m:
1639                # if the function space is wrong then we try the reduced version:
1640                i_red=i+"_reduced"
1641                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1642                    try:
1643                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1644                                                          self.getNumEquations(),self.getNumSolutions(),
1645                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1646                        self.alteredCoefficient(i_red)
1647                    except IllegalCoefficientValue,m:
1648                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1649                    except IllegalCoefficientFunctionSpace,m:
1650                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1651                else:
1652                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1653          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1654             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1655        self.__altered_coefficients=True        self.__altered_coefficients=True
1656        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1657        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1501  class LinearPDE(object): Line 1659  class LinearPDE(object):
1659           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1660           homogeneous_constraint=True           homogeneous_constraint=True
1661           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1662               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1663                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1664                 self.__invalidateSystem()                 self.__invalidateSystem()
1665    
# Line 1515  class LinearPDE(object): Line 1673  class LinearPDE(object):
1673         if not self.__operator_is_Valid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1674            if self.isUsingLumping():            if self.isUsingLumping():
1675                if not self.__operator_is_Valid:                if not self.__operator_is_Valid:
1676                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1677                   if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Using coefficient A in lumped matrix can produce wrong results"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1678                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1679                   if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Using coefficient C in lumped matrix can produce wrong results"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1680                   mat=self.__getNewOperator()                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1681                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient B in lumped matrix may not be present."
1682                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1683                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient C in lumped matrix may not be present."
1684                             self.getCoefficientOfGeneralPDE("C"), \                   if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1685                             self.getCoefficientOfGeneralPDE("D"), \                        raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1686                             escript.Data(), \                   if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1687                             escript.Data(), \                        raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1688                             self.getCoefficientOfGeneralPDE("d"), \                   if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1689                             escript.Data(),\                        raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1690                             self.getCoefficientOfGeneralPDE("d_contact"), \                   D=self.getCoefficientOfGeneralPDE("D")
1691                             escript.Data())                   if not D.isEmpty():
1692                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                       if self.getNumSolutions()>1:
1693                   del mat                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1694                         else:
1695                            D_times_e=D
1696                     else:
1697                        D_times_e=escript.Data()
1698                     d=self.getCoefficientOfGeneralPDE("d")
1699                     if not d.isEmpty():
1700                         if self.getNumSolutions()>1:
1701                            d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1702                         else:
1703                            d_times_e=d
1704                     else:
1705                        d_times_e=escript.Data()
1706                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1707                     if not d_contact.isEmpty():
1708                         if self.getNumSolutions()>1:
1709                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1710                         else:
1711                            d_contact_times_e=d_contact
1712                     else:
1713                        d_contact_times_e=escript.Data()
1714        
1715                     self.__operator=self.__getNewRightHandSide()
1716                     self.getDomain().addPDEToRHS(self.__operator, \
1717                                                  escript.Data(), \
1718                                                  D_times_e, \
1719                                                  d_times_e,\
1720                                                  d_contact_times_e)
1721                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                     if not D_reduced.isEmpty():
1723                         if self.getNumSolutions()>1:
1724                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1725                         else:
1726                            D_reduced_times_e=D_reduced
1727                     else:
1728                        D_reduced_times_e=escript.Data()
1729                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1730                     if not d_reduced.isEmpty():
1731                         if self.getNumSolutions()>1:
1732                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1733                         else:
1734                            d_reduced_times_e=d_reduced
1735                     else:
1736                        d_reduced_times_e=escript.Data()
1737                     d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
1738                     if not d_contact_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            d_contact_reduced_times_e=util.matrixmult(d_contact_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            d_contact_reduced_times_e=d_contact_reduced
1743                     else:
1744                        d_contact_reduced_times_e=escript.Data()
1745        
1746                     self.__operator=self.__getNewRightHandSide()
1747                     self.getDomain().addPDEToRHS(self.__operator, \
1748                                                  escript.Data(), \
1749                                                  D_times_e, \
1750                                                  d_times_e,\
1751                                                  d_contact_times_e)
1752                     self.getDomain().addPDEToRHS(self.__operator, \
1753                                                  escript.Data(), \
1754                                                  D_reduced_times_e, \
1755                                                  d_reduced_times_e,\
1756                                                  d_contact_reduced_times_e)
1757                     self.__operator=1./self.__operator
1758                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1759                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
1760                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
# Line 1541  class LinearPDE(object): Line 1763  class LinearPDE(object):
1763                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1764                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1765                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1766                     self.getDomain().addPDEToRHS(self.__righthandside, \
1767                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1768                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1769                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1770                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1771                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1772                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1773            else:            else:
# Line 1556  class LinearPDE(object): Line 1783  class LinearPDE(object):
1783                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1784                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1785                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1786                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1787                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1788                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1789                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1790                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1791                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1792                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1793                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1794                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1797                   self.__applyConstraint()                   self.__applyConstraint()
1798                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1799                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1567  class LinearPDE(object): Line 1805  class LinearPDE(object):
1805                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1806                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1807                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1808                     self.getDomain().addPDEToRHS(self.__righthandside, \
1809                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1810                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1811                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1812                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1813                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1814                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1815                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1582  class LinearPDE(object): Line 1825  class LinearPDE(object):
1825                              escript.Data(),\                              escript.Data(),\
1826                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1827                              escript.Data())                              escript.Data())
1828                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1829                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1830                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1831                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1832                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1833                                escript.Data(), \
1834                                escript.Data(), \
1835                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1836                                escript.Data(),\
1837                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1838                                escript.Data())
1839                   self.__applyConstraint()                   self.__applyConstraint()
1840                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1841                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1615  class Poisson(LinearPDE): Line 1869  class Poisson(LinearPDE):
1869       """       """
1870       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1871       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1872                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1873                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1874       self.setSymmetryOn()       self.setSymmetryOn()
1875    
1876     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1663  class Poisson(LinearPDE): Line 1918  class Poisson(LinearPDE):
1918           return escript.Data()           return escript.Data()
1919       elif name == "y_contact" :       elif name == "y_contact" :
1920           return escript.Data()           return escript.Data()
1921         elif name == "A_reduced" :
1922             return escript.Data()
1923         elif name == "B_reduced" :
1924             return escript.Data()
1925         elif name == "C_reduced" :
1926             return escript.Data()
1927         elif name == "D_reduced" :
1928             return escript.Data()
1929         elif name == "X_reduced" :
1930             return escript.Data()
1931         elif name == "Y_reduced" :
1932             return self.getCoefficient("f_reduced")
1933         elif name == "d_reduced" :
1934             return escript.Data()
1935         elif name == "y_reduced" :
1936             return escript.Data()
1937         elif name == "d_contact_reduced" :
1938             return escript.Data()
1939         elif name == "y_contact_reduced" :
1940             return escript.Data()
1941       elif name == "r" :       elif name == "r" :
1942           return escript.Data()           return escript.Data()
1943       elif name == "q" :       elif name == "q" :
# Line 1699  class Helmholtz(LinearPDE): Line 1974  class Helmholtz(LinearPDE):
1974       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1975                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1976                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1977                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1978                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1979                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1980                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1981                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1982                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1983       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1762  class Helmholtz(LinearPDE): Line 2039  class Helmholtz(LinearPDE):
2039           return escript.Data()           return escript.Data()
2040       elif name == "y_contact" :       elif name == "y_contact" :
2041           return escript.Data()           return escript.Data()
2042         elif name == "A_reduced" :
2043             return escript.Data()
2044         elif name == "B_reduced" :
2045             return escript.Data()
2046         elif name == "C_reduced" :
2047             return escript.Data()
2048         elif name == "D_reduced" :
2049             return escript.Data()
2050         elif name == "X_reduced" :
2051             return escript.Data()
2052         elif name == "Y_reduced" :
2053             return self.getCoefficient("f_reduced")
2054         elif name == "d_reduced" :
2055             return escript.Data()
2056         elif name == "y_reduced" :
2057            return self.getCoefficient("g_reduced")
2058         elif name == "d_contact_reduced" :
2059             return escript.Data()
2060         elif name == "y_contact_reduced" :
2061             return escript.Data()
2062       elif name == "r" :       elif name == "r" :
2063           return self.getCoefficient("r")           return self.getCoefficient("r")
2064       elif name == "q" :       elif name == "q" :
# Line 1773  class LameEquation(LinearPDE): Line 2070  class LameEquation(LinearPDE):
2070     """     """
2071     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2072    
2073     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] }
2074    
2075     with natural boundary conditons:     with natural boundary conditons:
2076    
2077     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] }
2078    
2079     and constraints:     and constraints:
2080    
# Line 1797  class LameEquation(LinearPDE): Line 2094  class LameEquation(LinearPDE):
2094                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
2095        self.setSymmetryOn()        self.setSymmetryOn()
2096    
2097     def setValue(self,**coefficients):     def setValues(self,**coefficients):
2098       """       """
2099       sets new values to coefficients       sets new values to coefficients
2100    
# Line 1820  class LameEquation(LinearPDE): Line 2117  class LameEquation(LinearPDE):
2117                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
2118       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
2119       """       """
2120       super(LameEquation, self).setValue(**coefficients)       super(LameEquation, self).setValues(**coefficients)
2121    
2122     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
2123       """       """
# Line 1860  class LameEquation(LinearPDE): Line 2157  class LameEquation(LinearPDE):
2157           return escript.Data()           return escript.Data()
2158       elif name == "y_contact" :       elif name == "y_contact" :
2159           return escript.Data()           return escript.Data()
2160         elif name == "A_reduced" :
2161             return escript.Data()
2162         elif name == "B_reduced" :
2163             return escript.Data()
2164         elif name == "C_reduced" :
2165             return escript.Data()
2166         elif name == "D_reduced" :
2167             return escript.Data()
2168         elif name == "X_reduced" :
2169             return escript.Data()
2170         elif name == "Y_reduced" :
2171             return escript.Data()
2172         elif name == "d_reduced" :
2173             return escript.Data()
2174         elif name == "y_reduced" :
2175             return escript.Data()
2176         elif name == "d_contact_reduced" :
2177             return escript.Data()
2178         elif name == "y_contact_reduced" :
2179             return escript.Data()
2180       elif name == "r" :       elif name == "r" :
2181           return self.getCoefficient("r")           return self.getCoefficient("r")
2182       elif name == "q" :       elif name == "q" :
# Line 1867  class LameEquation(LinearPDE): Line 2184  class LameEquation(LinearPDE):
2184       else:       else:
2185          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2186    
 class AdvectivePDE(LinearPDE):  
    """  
    In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}  
    up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.  
   
    In the following we set  
   
    M{Z[j]=C[j]-B[j]}  
   
    or  
   
    M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}  
   
    To measure the dominance of the advective terms over the diffusive term M{A} the  
    X{Pelclet number} M{P} is used. It is defined as  
   
    M{P=h|Z|/(2|A|)}  
   
    where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size  
    from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.  
   
    From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:  
   
    M{S{Xi}=S{xi}(P) h/|Z|}  
   
    where M{S{xi}} is a suitable function of the Peclet number.  
   
    In the case of a single PDE the coefficient are up-dated in the following way:  
          - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}  
          - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}  
          - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}  
          - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}  
   
    Similar for the case of a systems of PDEs:  
          - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}  
          - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}  
          - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}  
          - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}  
   
    where M{S{delta}} is L{kronecker}.  
    Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}  
    but with the intension to stabilize the solution.  
   
    """  
    def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):  
       """  
       creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}  
   
       @param domain: domain of the PDE  
       @type domain: L{Domain<escript.Domain>}  
       @param numEquations: number of equations. If numEquations==None the number of equations  
                            is exracted from the PDE coefficients.  
       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components  
                            is exracted from the PDE coefficients.  
       @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the  
                  M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.  
       @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.  
       @param debug: if True debug informations are printed.  
       """  
       super(AdvectivePDE, self).__init__(domain,\  
                                          numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def setValue(**coefficients):  
       """  
       sets new values to coefficients  
   
       @param coefficients: new values assigned to coefficients  
       @keyword A: value for coefficient A.  
       @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword B: value for coefficient B  
       @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword C: value for coefficient C  
       @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword D: value for coefficient D  
       @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword X: value for coefficient X  
       @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword Y: value for coefficient Y  
       @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword d: value for coefficient d  
       @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
       @keyword y: value for coefficient y  
       @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
       @keyword d_contact: value for coefficient d_contact  
       @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
                        or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.  
       @keyword y_contact: value for coefficient y_contact  
       @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
                        or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.  
       @keyword r: values prescribed to the solution at the locations of constraints  
       @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}  
                depending of reduced order is used for the solution.  
       @keyword q: mask for location of constraints  
       @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}  
                depending of reduced order is used for the representation of the equation.  
       @raise IllegalCoefficient: if an unknown coefficient keyword is used.  
   
       """  
       if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()  
       super(AdvectivePDE, self).setValue(**coefficients)  
   
    def ELMAN_RAMAGE(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)  
           - M{S{xi}(P)=0} for M{P<1}  
           - M{S{xi}(P)=(1-1/P)/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))  
   
    def SIMPLIFIED_BROOK_HUGHES(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      The original methods is  
   
      M{S{xi}(P)=coth(P)-1/P}  
   
      As the evaluation of M{coth} is expensive we are using the approximation:  
   
          - M{S{xi}(P)=P/3} where M{P<3}  
          - M{S{xi}(P)=1/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      c=util.whereNegative(P-3.)  
      return P/6.*c+1./2.*(1.-c)  
   
    def HALF(self,P):  
      """  
      Predefined function to set value M{1/2} for M{S{xi}}  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return escript.Scalar(0.5,P.getFunctionSpace())  
   
    def __calculateXi(self,peclet_factor,flux,h):  
        flux=util.Lsup(flux)  
        if flux_max>0.:  
           return h*self.__xi(flux*peclet_factor)/(flux+flux_max*self.__TOL)  
        else:  
           return 0.  
   
    def __getXi(self):  
       if self.__Xi.isEmpty():  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          A=self.getCoefficient("A")  
          h=self.getDomain().getSize()  
          self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))  
          if not C.isEmpty() or not B.isEmpty():  
             if not C.isEmpty() and not B.isEmpty():  
                 flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       for i in range(self.getNumEquations()):  
                          for k in range(self.getNumSolutions()):  
                             for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2  
                       # flux=C-util.reorderComponents(B,[0,2,1])  
                    else:  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2  
                       # flux=C-B  
                 else:  
                    if self.getNumSolutions()>1:  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2  
                       # flux=C-util.reorderComponents(B,[1,0])  
                    else:  
                       for l in range(self.getDim()): flux2+=(C[l]-B[l])**2  
                       #flux=C-B  
                 length_of_flux=util.sqrt(flux2)  
             elif C.isEmpty():  
               length_of_flux=util.length(B)  
               #flux=B  
             else:  
               length_of_flux=util.length(C)  
               #flux=C  
   
             #length_of_flux=util.length(flux)  
             flux_max=util.Lsup(length_of_flux)  
             if flux_max>0.:  
                # length_of_A=util.inner(flux,util.tensormutiply(A,flux))  
                length_of_A=util.length(A)  
                A_max=util.Lsup(length_of_A)  
                if A_max>0:  
                     inv_A=1./(length_of_A+A_max*self.__TOL)  
                else:  
                     inv_A=1./self.__TOL  
                peclet_number=length_of_flux*h/2*inv_A  
                xi=self.__xi(peclet_number)  
                self.__Xi=h*xi/(length_of_flux+flux_max*self.__TOL)  
                self.trace("preclet number = %e"%util.Lsup(peclet_number))  
       return self.__Xi  
   
   
    def getCoefficientOfGeneralPDE(self,name):  
      """  
      return the value of the coefficient name of the general PDE  
   
      @param name: name of the coefficient requested.  
      @type name: C{string}  
      @return: the value of the coefficient name  
      @rtype: L{Data<escript.Data>}  
      @raise IllegalCoefficient: if name is not one of coefficients  
                   M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.  
      @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.  
      """  
      if not self.getNumEquations() == self.getNumSolutions():  
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
   
      if name == "A" :  
          A=self.getCoefficient("A")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if B.isEmpty() and C.isEmpty():  
             Aout=A  
          else:  
             if A.isEmpty():  
                Aout=self.createNewCoefficient("A")  
             else:  
                Aout=A[:]  
             Xi=self.__getXi()  
             if self.getNumEquations()>1:  
                 for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()):  
                             if not C.isEmpty() and not B.isEmpty():  
                                # tmp=C-util.reorderComponents(B,[0,2,1])  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k])  
                             elif C.isEmpty():  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)  
                             else:  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)  
             else:  
                 for j in range(self.getDim()):  
                    for l in range(self.getDim()):  
                       if not C.isEmpty() and not B.isEmpty():  
                           Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])  
                       elif C.isEmpty():  
                           Aout[j,l]+=Xi*B[j]*B[l]  
                       else:  
                           Aout[j,l]+=Xi*C[j]*C[l]  
                  # if not C.isEmpty() and not B.isEmpty():  
                  #    tmp=C-B  
                  #    Aout=Aout+Xi*util.outer(tmp,tmp)  
                  # elif C.isEmpty():  
                  #    Aout=Aout+Xi*util.outer(B,B)  
                  # else:  
                  # Aout=Aout+Xi*util.outer(C,C)  
          return Aout  
      elif name == "B" :  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if C.isEmpty() or D.isEmpty():  
             Bout=B  
          else:  
             Xi=self.__getXi()  
             if B.isEmpty():  
                 Bout=self.createNewCoefficient("B")  
             else:  
                 Bout=B[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                   for p in range(self.getNumEquations()):  
                      tmp=Xi*D[p,k]  
                      for i in range(self.getNumEquations()):  
                         for j in range(self.getDim()):  
                            Bout[i,j,k]+=tmp*C[p,i,j]  
                            # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
                # Bout=Bout+Xi*D*C  
          return Bout  
      elif name == "C" :  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if B.isEmpty() or D.isEmpty():  
             Cout=C  
          else:  
             Xi=self.__getXi()  
             if C.isEmpty():  
                 Cout=self.createNewCoefficient("C")  
             else:  
                 Cout=C[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                    for p in range(self.getNumEquations()):  
                       tmp=Xi*D[p,k]  
                       for i in range(self.getNumEquations()):  
                         for l in range(self.getDim()):  
                                  Cout[i,k,l]+=tmp*B[p,l,i]  
                                  # Cout=Cout+Xi*B[p,l,i]*D[p,k]  
             else:  
                tmp=Xi*D  
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
                # Cout=Cout+tmp*D*B  
          return Cout  
      elif name == "D" :  
          return self.getCoefficient("D")  
      elif name == "X" :  
          X=self.getCoefficient("X")  
          Y=self.getCoefficient("Y")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):  
             Xout=X  
          else:  
             if X.isEmpty():  
                 Xout=self.createNewCoefficient("X")  
             else:  
                 Xout=X[:]  
             Xi=self.__getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                              # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                              # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
                              # Xout=X_out+Xi*util.inner(Y,C,offset=1)  
             else:  
                  tmp=Xi*Y  
                  for j in range(self.getDim()):  
                     if not C.isEmpty() and not B.isEmpty():  
                        Xout[j]+=tmp*(C[j]-B[j])  
                        # Xout=Xout+Xi*Y*(C-B)  
                     elif C.isEmpty():  
                        Xout[j]-=tmp*B[j]  
                        # Xout=Xout-Xi*Y*B  
                     else:  
                        Xout[j]+=tmp*C[j]  
                        # Xout=Xout+Xi*Y*C  
          return Xout  
      elif name == "Y" :  
          return self.getCoefficient("Y")  
      elif name == "d" :  
          return self.getCoefficient("d")  
      elif name == "y" :  
          return self.getCoefficient("y")  
      elif name == "d_contact" :  
          return self.getCoefficient("d_contact")  
      elif name == "y_contact" :  
          return self.getCoefficient("y_contact")  
      elif name == "r" :  
          return self.getCoefficient("r")  
      elif name == "q" :  
          return self.getCoefficient("q")  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
   
   
 # $Log$  
 # Revision 1.14  2005/09/22 01:54:57  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-22  
 #  
 # Revision 1.13  2005/09/15 03:44:19  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-15  
 #  
 # Revision 1.12  2005/09/01 03:31:28  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-01  
 #  
 # Revision 1.11  2005/08/23 01:24:28  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-08-23  
 #  
 # Revision 1.10  2005/08/12 01:45:36  jgs  
 # erge of development branch dev-02 back to main trunk on 2005-08-12  
 #  
 # Revision 1.9.2.17  2005/09/21 07:03:33  matt  
 # PDECoefficient and LinearPDE are now new style classes (introduced in Python  
 # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been  
 # modified to instead use portable/cooperative "super" calls to extend base  
 # class methods.  
 #  
 # Revision 1.9.2.16  2005/09/16 01:54:37  matt  
 # Removed redundant if-loop.  
 #  
 # Revision 1.9.2.15  2005/09/14 08:09:18  matt  
 # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.  
 #  
 # Revision 1.9.2.14  2005/09/07 06:26:16  gross  
 # the solver from finley are put into the standalone package paso now  
 #  
 # Revision 1.9.2.13  2005/08/31 08:45:03  gross  
 # in the case of lumping no new system is allocated if the constraint is changed.  
 #  
 # Revision 1.9.2.12  2005/08/31 07:10:23  gross  
 # test for Lumping added  
 #  
 # Revision 1.9.2.11  2005/08/30 01:53:45  gross  
 # bug in format fixed.  
 #  
 # Revision 1.9.2.10  2005/08/26 07:14:17  gross  
 # a few more bugs in linearPDE fixed. remaining problem are finley problems  
 #  
 # Revision 1.9.2.9  2005/08/26 06:30:45  gross  
 # fix for reported bug  0000004. test_linearPDE passes a few more tests  
 #  
 # Revision 1.9.2.8  2005/08/26 04:30:13  gross  
 # gneric unit testing for linearPDE  
 #  
 # Revision 1.9.2.7  2005/08/25 07:06:50  gross  
 # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so  
 #  
 # Revision 1.9.2.6  2005/08/24 05:01:24  gross  
 # problem with resetting the matrix in case of resetting its values to 0 fixed.  
 #  
 # Revision 1.9.2.5  2005/08/24 02:03:28  gross  
 # epydoc mark up partially fixed  
 #  
 # Revision 1.9.2.4  2005/08/22 07:11:09  gross  
 # some problems with LinearPDEs fixed.  
 #  
 # Revision 1.9.2.3  2005/08/18 04:48:48  gross  
 # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  
 #  
 # Revision 1.9.2.2  2005/08/18 04:39:32  gross  
 # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now  
 #  
 # Revision 1.9.2.1  2005/07/29 07:10:27  gross  
 # new functions in util and a new pde type in linearPDEs  
 #  
 # Revision 1.1.2.25  2005/07/28 04:21:09  gross  
 # Lame equation: (linear elastic, isotropic) added  
 #  
 # Revision 1.1.2.24  2005/07/22 06:37:11  gross  
 # some extensions to modellib and linearPDEs  
 #  
 # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  
 # Fixed up some docstrings.  Moved module-level functions to top of file so  
 # that epydoc and doxygen can pick them up properly.  
 #  
 # Revision 1.1.2.22  2005/05/12 11:41:30  gross  
 # some basic Models have been added  
 #  
 # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane  
 # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of  
 # file so that the AdvectivePDE class is picked up by doxygen.  Some  
 # reformatting of docstrings.  Addition of code to make equations come out  
 # as proper LaTeX.  
 #  
 # Revision 1.1.2.20  2005/04/15 07:09:08  gross  
 # some problems with functionspace and linearPDEs fixed.  
 #  
 # Revision 1.1.2.19  2005/03/04 05:27:07  gross  
 # bug in SystemPattern fixed.  
 #  
 # Revision 1.1.2.18  2005/02/08 06:16:45  gross  
 # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed  
 #  
 # Revision 1.1.2.17  2005/02/08 05:56:19  gross  
 # Reference Number handling added  
 #  
 # Revision 1.1.2.16  2005/02/07 04:41:28  gross  
 # some function exposed to python to make mesh merging running  
 #  
 # Revision 1.1.2.15  2005/02/03 00:14:44  gross  
 # timeseries add and ESySParameter.py renames esysXML.py for consistence  
 #  
 # Revision 1.1.2.14  2005/02/01 06:44:10  gross  
 # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working  
 #  
 # Revision 1.1.2.13  2005/01/25 00:47:07  gross  
 # updates in the documentation  
 #  
 # Revision 1.1.2.12  2005/01/12 01:28:04  matt  
 # Added createCoefficient method for linearPDEs.  
 #  
 # Revision 1.1.2.11  2005/01/11 01:55:34  gross  
 # a problem in linearPDE class fixed  
 #  
 # Revision 1.1.2.10  2005/01/07 01:13:29  gross  
 # some bugs in linearPDE fixed  
 #  
 # Revision 1.1.2.9  2005/01/06 06:24:58  gross  
 # some bugs in slicing fixed  
 #  
 # Revision 1.1.2.8  2005/01/05 04:21:40  gross  
 # FunctionSpace checking/matchig in slicing added  
 #  
 # Revision 1.1.2.7  2004/12/29 10:03:41  gross  
 # bug in setValue fixed  
 #  
 # Revision 1.1.2.6  2004/12/29 05:29:59  gross  
 # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()  
 #  
 # Revision 1.1.2.5  2004/12/29 00:18:41  gross  
 # AdvectivePDE added  
 #  
 # Revision 1.1.2.4  2004/12/24 06:05:41  gross  
 # some changes in linearPDEs to add AdevectivePDE  
 #  
 # Revision 1.1.2.3  2004/12/16 00:12:34  gross  
 # __init__ of LinearPDE does not accept any coefficient anymore  
 #  
 # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  
 # *** empty log message ***  
 #  
 # Revision 1.1.2.1  2004/12/12 22:53:47  gross  
 # linearPDE has been renamed LinearPDE  
 #  
 # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross  
 # GMRES added  
 #  
 # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross  
 # options for GMRES and PRES20 added  
 #  
 # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross  
 # some small changes  
 #  
 # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross  
 # Finley solves 4M unknowns now  
 #  
 # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross  
 # poisson solver added  
 #  
 # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross  
 # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry  
 #  
 # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross  
 # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed  
 #  
 # Revision 1.1.1.1  2004/10/26 06:53:56  jgs  
 # initial import of project esys2  
 #  
 # Revision 1.3.2.3  2004/10/26 06:43:48  jgs  
 # committing Lutz's and Paul's changes to brach jgs  
 #  
 # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane  
 # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.  
 #  
 # Revision 1.3  2004/09/23 00:53:23  jgs  
 # minor fixes  
 #  
 # Revision 1.1  2004/08/28 12:58:06  gross  
 # SimpleSolve is not running yet: problem with == of functionsspace  
 #  

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