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revision 614 by elspeth, Wed Mar 22 01:37:07 2006 UTC revision 1809 by ksteube, Thu Sep 25 06:43:44 2008 UTC
# Line 1  Line 1 
1  # $Id$  
2    ########################################################
3    #
4    # Copyright (c) 2003-2008 by University of Queensland
5    # Earth Systems Science Computational Center (ESSCC)
6    # http://www.uq.edu.au/esscc
7    #
8    # Primary Business: Queensland, Australia
9    # Licensed under the Open Software License version 3.0
10    # http://www.opensource.org/licenses/osl-3.0.php
11    #
12    ########################################################
13    
14    __copyright__="""Copyright (c) 2003-2008 by University of Queensland
15    Earth Systems Science Computational Center (ESSCC)
16    http://www.uq.edu.au/esscc
17    Primary Business: Queensland, Australia"""
18    __license__="""Licensed under the Open Software License version 3.0
19    http://www.opensource.org/licenses/osl-3.0.php"""
20    __url__="http://www.uq.edu.au/esscc/escript-finley"
21    
22  """  """
23  The module provides an interface to define and solve linear partial  The module provides an interface to define and solve linear partial
24  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
# Line 7  the PDE solver library defined through t Line 27  the PDE solver library defined through t
27  The general interface is provided through the L{LinearPDE} class. The  The general interface is provided through the L{LinearPDE} class. The
28  L{AdvectivePDE} which is derived from the L{LinearPDE} class  L{AdvectivePDE} which is derived from the L{LinearPDE} class
29  provides an interface to PDE dominated by its advective terms. The L{Poisson},  provides an interface to PDE dominated by its advective terms. The L{Poisson},
30  L{Helmholtz}, L{LameEquation}, L{AdvectionDiffusion}  L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
31  classs which are also derived form the L{LinearPDE} class should be used  classs which are also derived form the L{LinearPDE} class should be used
32  to define of solve these sepecial PDEs.  to define of solve these sepecial PDEs.
33    
34  @var __author__: name of author  @var __author__: name of author
35    @var __copyright__: copyrights
36  @var __license__: licence agreement  @var __license__: licence agreement
37  @var __url__: url entry point on documentation  @var __url__: url entry point on documentation
38  @var __version__: version  @var __version__: version
39  @var __date__: date of the version  @var __date__: date of the version
40  """  """
41    
42    import math
43  import escript  import escript
44  import util  import util
45  import numarray  import numarray
46    
47  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
 __copyright__="""  Copyright (c) 2006 by ACcESS MNRF  
                     http://www.access.edu.au  
                 Primary Business: Queensland, Australia"""  
 __license__="""Licensed under the Open Software License version 3.0  
              http://www.opensource.org/licenses/osl-3.0.php"""  
 __url__="http://www.iservo.edu.au/esys/escript"  
 __version__="$Revision$"  
 __date__="$Date$"  
48    
49    
50  class IllegalCoefficient(ValueError):  class IllegalCoefficient(ValueError):
51     """     """
52     raised if an illegal coefficient of the general ar particular PDE is requested.     raised if an illegal coefficient of the general ar particular PDE is requested.
53     """     """
54       pass
55    
56  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
57     """     """
58     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
59     """     """
60       pass
61    
62    class IllegalCoefficientFunctionSpace(ValueError):
63       """
64       raised if an incorrect function space for a coefficient is used.
65       """
66    
67  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
68     """     """
69     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
70     """     """
71       pass
72    
73  class PDECoefficient(object):  class PDECoefficient(object):
74      """      """
# Line 55  class PDECoefficient(object): Line 77  class PDECoefficient(object):
77      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
78      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
79      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
80        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
81        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
82        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
83      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
84      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
85      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
# Line 76  class PDECoefficient(object): Line 101  class PDECoefficient(object):
101      OPERATOR=10      OPERATOR=10
102      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
103      BOTH=12      BOTH=12
104        INTERIOR_REDUCED=13
105        BOUNDARY_REDUCED=14
106        CONTACT_REDUCED=15
107    
108      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
109         """         """
110         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
111    
112         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
113         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
114                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
115         @param pattern: describes the shape of the coefficient and how the shape is build for a given         @param pattern: describes the shape of the coefficient and how the shape is build for a given
116                spatial dimension and numbers of equation and solution in then PDE. For instance,                spatial dimension and numbers of equation and solution in then PDE. For instance,
117                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
# Line 93  class PDECoefficient(object): Line 122  class PDECoefficient(object):
122         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
123         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
124         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
125           @param reduced: indicates if reduced
126           @type reduced: C{bool}
127         """         """
128         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
129         self.what=where         self.what=where
# Line 114  class PDECoefficient(object): Line 144  class PDECoefficient(object):
144         @param domain: domain on which the PDE uses the coefficient         @param domain: domain on which the PDE uses the coefficient
145         @type domain: L{Domain<escript.Domain>}         @type domain: L{Domain<escript.Domain>}
146         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
147         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
148         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
149         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
150         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
151         @rtype:  L{FunctionSpace<escript.FunctionSpace>}         @rtype:  L{FunctionSpace<escript.FunctionSpace>}
152         """         """
153         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
154              return escript.Function(domain)              return escript.Function(domain)
155           elif self.what==self.INTERIOR_REDUCED:
156                return escript.ReducedFunction(domain)
157         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
158              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
159           elif self.what==self.BOUNDARY_REDUCED:
160                return escript.ReducedFunctionOnBoundary(domain)
161         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
162              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
163           elif self.what==self.CONTACT_REDUCED:
164                return escript.ReducedFunctionOnContactZero(domain)
165         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
166              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
167                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 154  class PDECoefficient(object): Line 190  class PDECoefficient(object):
190         @param numSolutions: number of components of the PDE solution         @param numSolutions: number of components of the PDE solution
191         @type numSolutions: C{int}         @type numSolutions: C{int}
192         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
193         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
194         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
195         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
196         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
197         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
198         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
199           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
200         """         """
201         if newValue==None:         if newValue==None:
202             newValue=escript.Data()             newValue=escript.Data()
203         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
204             if not newValue.isEmpty():             if not newValue.isEmpty():
205                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
206                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
207                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
208                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
209                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
210         else:         else:
211             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
212         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 312  class LinearPDE(object): Line 350  class LinearPDE(object):
350    
351     For a single PDE with a solution with a single component the linear PDE is defined in the following form:     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
352    
353     M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
354    
355    
356     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
357     ie. summation over indexes appearing twice in a term of a sum is performed, is used.     ie. summation over indexes appearing twice in a term of a sum is performed, is used.
358     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
359     L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.     L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
360     M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.     L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
361       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
362       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
363    
364     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
365    
366     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
367    
368     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.     where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
    Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are  
    each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
369    
370    
371     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
# Line 338  class LinearPDE(object): Line 377  class LinearPDE(object):
377    
378     The PDE is symmetrical if     The PDE is symmetrical if
379    
380     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]}
381    
382     For a system of PDEs and a solution with several components the PDE has the form     For a system of PDEs and a solution with several components the PDE has the form
383    
384     M{-grad(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])[j]+C[i,k,l]*grad(u[k])[l]+D[i,k]*u[k] =-grad(X[i,j])[j]+Y[i] }     M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
385    
386     M{A} is a ramk four, M{B} and M{C} are each a rank three, M{D} and M{X} are each a rank two and M{Y} is a rank one.     M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
387     The natural boundary conditions take the form:     The natural boundary conditions take the form:
388    
389     M{n[j]*(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}     M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
390    
391    
392     The coefficient M{d} is a rank two and M{y} is a  rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form     The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
393    
394       Constraints take the form
395    
396     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
397    
# Line 360  class LinearPDE(object): Line 400  class LinearPDE(object):
400     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
401    
402          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
403            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
404          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
405            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
406          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
407            - M{D_reduced[i,k]=D_reduced[i,k]}
408          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
409            - M{d_reduced[i,k]=d_reduced[k,i]}
410    
411     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
412     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
413     defined as     defined as
414    
415     M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}     M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
416    
417     For the case of single solution component and single PDE M{J} is defined     For the case of single solution component and single PDE M{J} is defined
418    
419     M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}     M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
420    
421     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
422     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
423     the contact condition takes the form     the contact condition takes the form
424    
425     M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}     M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
426    
427     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
428     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
429     L{jump<util.jump>}.     L{jump<util.jump>}.
430     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
431       The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
432     In case of a single PDE and a single component solution the contact condition takes the form     In case of a single PDE and a single component solution the contact condition takes the form
433    
434     M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}     M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
435    
436     In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar     In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
    both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
437    
438     @cvar DEFAULT: The default method used to solve the system of linear equations     @cvar DEFAULT: The default method used to solve the system of linear equations
439     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 398  class LinearPDE(object): Line 442  class LinearPDE(object):
442     @cvar CR: The conjugate residual method     @cvar CR: The conjugate residual method
443     @cvar CGS: The conjugate gardient square method     @cvar CGS: The conjugate gardient square method
444     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
445       @cvar TFQMR: Transport Free Quasi Minimal Residual method.
446       @cvar MINRES: Minimum residual method.
447     @cvar SSOR: The symmetric overrealaxtion method     @cvar SSOR: The symmetric overrealaxtion method
448     @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in     @cvar ILU0: The incomplete LU factorization preconditioner  with no fill in
449     @cvar ILUT: The incomplete LU factorization preconditioner with will in     @cvar ILUT: The incomplete LU factorization preconditioner with will in
# Line 412  class LinearPDE(object): Line 458  class LinearPDE(object):
458     @cvar SCSL: SGI SCSL solver library     @cvar SCSL: SGI SCSL solver library
459     @cvar MKL: Intel's MKL solver library     @cvar MKL: Intel's MKL solver library
460     @cvar UMFPACK: the UMFPACK library     @cvar UMFPACK: the UMFPACK library
461       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
462     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
463     @cvar AMG: algebraic multi grid     @cvar AMG: algebraic multi grid
464     @cvar RILU: recursive ILU     @cvar RILU: recursive ILU
# Line 441  class LinearPDE(object): Line 488  class LinearPDE(object):
488     PASO= 21     PASO= 21
489     AMG= 22     AMG= 22
490     RILU = 23     RILU = 23
491       TRILINOS = 24
492       NONLINEAR_GMRES = 25
493       TFQMR = 26
494       MINRES = 27
495    
496     SMALL_TOLERANCE=1.e-13     SMALL_TOLERANCE=1.e-13
497     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
# Line 478  class LinearPDE(object): Line 529  class LinearPDE(object):
529         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
530         "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),
531         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
532           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
533           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
534           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
535           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
537           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
538           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
539           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
541           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
542         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
543         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
544    
# Line 663  class LinearPDE(object): Line 724  class LinearPDE(object):
724       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
725       """       """
726       if u==None:       if u==None:
727            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
728       else:       else:
729          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
730    
731     def getResidual(self,u=None):     def getResidual(self,u=None):
732       """       """
# Line 759  class LinearPDE(object): Line 820  class LinearPDE(object):
820                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
821                        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)
822                        out=False                        out=False
823             # and now the reduced coefficients
824             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
825             if not A_reduced.isEmpty():
826                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
827                if self.getNumSolutions()>1:
828                   for i in range(self.getNumEquations()):
829                      for j in range(self.getDim()):
830                         for k in range(self.getNumSolutions()):
831                            for l in range(self.getDim()):
832                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
833                                   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)
834                                   out=False
835                else:
836                   for j in range(self.getDim()):
837                      for l in range(self.getDim()):
838                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
839                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
840                            out=False
841             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
842             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
843             if B_reduced.isEmpty() and not C_reduced.isEmpty():
844                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
845                out=False
846             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
847                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
848                out=False
849             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
850                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
851                if self.getNumSolutions()>1:
852                   for i in range(self.getNumEquations()):
853                       for j in range(self.getDim()):
854                          for k in range(self.getNumSolutions()):
855                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
856                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
857                                  out=False
858                else:
859                   for j in range(self.getDim()):
860                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
861                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
862                         out=False
863             if self.getNumSolutions()>1:
864               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
865               if not D_reduced.isEmpty():
866                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
867                 for i in range(self.getNumEquations()):
868                    for k in range(self.getNumSolutions()):
869                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
870                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
871                          out=False
872               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
873               if not d_reduced.isEmpty():
874                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
875                 for i in range(self.getNumEquations()):
876                    for k in range(self.getNumSolutions()):
877                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
878                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
879                          out=False
880               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
881               if not d_contact_reduced.isEmpty():
882                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
883                 for i in range(self.getNumEquations()):
884                    for k in range(self.getNumSolutions()):
885                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
886                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
887                          out=False
888        return out        return out
889    
890     def getSolution(self,**options):     def getSolution(self,**options):
# Line 798  class LinearPDE(object): Line 924  class LinearPDE(object):
924       """       """
925       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
926    
927       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]}
928    
929       or       or
930    
931       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]}
932    
933       @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.
934       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 810  class LinearPDE(object): Line 936  class LinearPDE(object):
936       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
937       """       """
938       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
939       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))) \
940               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
941               -util.self.getCoefficientOfGeneralPDE("X") \
942               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
943               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
944               -util.self.getCoefficientOfGeneralPDE("X_reduced")
945     # =============================================================================     # =============================================================================
946     #   solver settings:     #   solver settings:
947     # =============================================================================     # =============================================================================
# Line 819  class LinearPDE(object): Line 950  class LinearPDE(object):
950         sets a new solver         sets a new solver
951    
952         @param solver: sets a new solver method.         @param solver: sets a new solver method.
953         @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}         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{TFQMR}, L{MINRES}, L{PRES20}, L{LUMPING}, L{AMG}
954         @param preconditioner: sets a new solver method.         @param preconditioner: sets a new solver method.
955         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}         @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
956         """         """
957         if solver==None: solve=self.DEFAULT         if solver==None: solver=self.__solver_method
958           if preconditioner==None: preconditioner=self.__preconditioner
959           if solver==None: solver=self.DEFAULT
960         if preconditioner==None: preconditioner=self.DEFAULT         if preconditioner==None: preconditioner=self.DEFAULT
961         if not (solver,preconditioner)==self.getSolverMethod():         if not (solver,preconditioner)==self.getSolverMethod():
962             self.__solver_method=solver             self.__solver_method=solver
# Line 847  class LinearPDE(object): Line 980  class LinearPDE(object):
980         elif m[0]==self.ITERATIVE: method= "ITERATIVE"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
981         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
982         elif m[0]==self.PCG: method= "PCG"         elif m[0]==self.PCG: method= "PCG"
983           elif m[0]==self.TFQMR: method= "TFQMR"
984           elif m[0]==self.MINRES: method= "MINRES"
985         elif m[0]==self.CR: method= "CR"         elif m[0]==self.CR: method= "CR"
986         elif m[0]==self.CGS: method= "CGS"         elif m[0]==self.CGS: method= "CGS"
987         elif m[0]==self.BICGSTAB: method= "BICGSTAB"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
# Line 867  class LinearPDE(object): Line 1002  class LinearPDE(object):
1002         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
1003         elif p==self.SCSL: package= "SCSL"         elif p==self.SCSL: package= "SCSL"
1004         elif p==self.UMFPACK: package= "UMFPACK"         elif p==self.UMFPACK: package= "UMFPACK"
1005           elif p==self.TRILINOS: package= "TRILINOS"
1006         else : method="unknown"         else : method="unknown"
1007         return "%s solver of %s package"%(method,package)         return "%s solver of %s package"%(method,package)
1008    
# Line 884  class LinearPDE(object): Line 1020  class LinearPDE(object):
1020         """         """
1021         sets a new solver package         sets a new solver package
1022    
1023         @param solver: sets a new solver method.         @param package: sets a new solver method.
1024         @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}         @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1025         """         """
1026         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1027         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
1028             self.__solver_method=solver             self.__solver_package=package
1029             self.__checkMatrixType()             self.__checkMatrixType()
1030             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
1031    
# Line 922  class LinearPDE(object): Line 1058  class LinearPDE(object):
1058         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1059                     the system will be resolved.                     the system will be resolved.
1060         @type tol: positive C{float}         @type tol: positive C{float}
1061         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1062         """         """
1063         if not tol>0:         if not tol>0:
1064             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1065         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1066         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1067         self.__tolerance=tol         self.__tolerance=tol
# Line 1206  class LinearPDE(object): Line 1342  class LinearPDE(object):
1342         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1343             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1344         else:         else:
1345             self.__righthandside*=0             self.__righthandside.setToZero()
1346             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1347         return self.__righthandside         return self.__righthandside
1348    
# Line 1256  class LinearPDE(object): Line 1392  class LinearPDE(object):
1392       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1393       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1394       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1395                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1396                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1397       """       """
1398       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1399          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1284  class LinearPDE(object): Line 1421  class LinearPDE(object):
1421       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1422       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1423       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1424                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1425                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1426       """       """
1427       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1428          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1300  class LinearPDE(object): Line 1438  class LinearPDE(object):
1438       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1439       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1440       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1441                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1442                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1443       """       """
1444       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1445          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1316  class LinearPDE(object): Line 1455  class LinearPDE(object):
1455       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1456       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1457       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1458                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1459                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1460       """       """
1461       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1462          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
# Line 1446  class LinearPDE(object): Line 1586  class LinearPDE(object):
1586        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1587        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1588        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1589          @keyword A_reduced: value for coefficient A_reduced.
1590          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1591        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1592        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1593          @keyword B_reduced: value for coefficient B_reduced
1594          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1595        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1596        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1597          @keyword C_reduced: value for coefficient C_reduced
1598          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1599        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1600        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1601          @keyword D_reduced: value for coefficient D_reduced
1602          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1603        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1604        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1605          @keyword X_reduced: value for coefficient X_reduced
1606          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1607        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1608        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1609          @keyword Y_reduced: value for coefficient Y_reduced
1610          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1611        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1612        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1613          @keyword d_reduced: value for coefficient d_reduced
1614          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1615        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1616        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1617        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1618        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1619                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1620          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1621        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1622        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1623                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1624          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1625        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1626        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1627                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1500  class LinearPDE(object): Line 1656  class LinearPDE(object):
1656        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1657        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1658          try:          try:
1659             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1660                                             self.getNumEquations(),self.getNumSolutions(),
1661                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1662               self.alteredCoefficient(i)
1663            except IllegalCoefficientFunctionSpace,m:
1664                # if the function space is wrong then we try the reduced version:
1665                i_red=i+"_reduced"
1666                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1667                    try:
1668                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1669                                                          self.getNumEquations(),self.getNumSolutions(),
1670                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1671                        self.alteredCoefficient(i_red)
1672                    except IllegalCoefficientValue,m:
1673                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1674                    except IllegalCoefficientFunctionSpace,m:
1675                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1676                else:
1677                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1678          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1679             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1680        self.__altered_coefficients=True        self.__altered_coefficients=True
1681        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1682        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1512  class LinearPDE(object): Line 1684  class LinearPDE(object):
1684           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1685           homogeneous_constraint=True           homogeneous_constraint=True
1686           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1687               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1688                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1689                 self.__invalidateSystem()                 self.__invalidateSystem()
1690    
# Line 1531  class LinearPDE(object): Line 1703  class LinearPDE(object):
1703                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1704                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient A in lumped matrix may not be present."
1705                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1706                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient B in lumped matrix may not be present."
1707                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1708                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient C in lumped matrix may not be present."
1709                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1710                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1711                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1712                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1713                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1714                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1715                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1716                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1717                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1718                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1719                   D=self.getCoefficientOfGeneralPDE("D")                   D=self.getCoefficientOfGeneralPDE("D")
1720                     d=self.getCoefficientOfGeneralPDE("d")
1721                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1723                   if not D.isEmpty():                   if not D.isEmpty():
1724                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1725                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1726                       else:                       else:
1727                          D_times_e=D                          D_times_e=D
1728                   else:                   else:
1729                      D_times_e=escript.Data()                      D_times_e=escript.Data()
                  d=self.getCoefficientOfGeneralPDE("d")  
1730                   if not d.isEmpty():                   if not d.isEmpty():
1731                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1732                          d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1733                       else:                       else:
1734                          d_times_e=d                          d_times_e=d
1735                   else:                   else:
1736                      d_times_e=escript.Data()                      d_times_e=escript.Data()
1737                   d_contact=self.getCoefficientOfGeneralPDE("d_contact")        
1738                   if not d_contact.isEmpty():                   if not D_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            D_reduced_times_e=D_reduced
1743                     else:
1744                        D_reduced_times_e=escript.Data()
1745                     if not d_reduced.isEmpty():
1746                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1747                          d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))                          d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1748                       else:                       else:
1749                          d_contact_times_e=d_contact                          d_reduced_times_e=d_reduced
1750                   else:                   else:
1751                      d_contact_times_e=escript.Data()                      d_reduced_times_e=escript.Data()
1752        
1753                   self.__operator=self.__getNewRightHandSide()                   self.__operator=self.__getNewRightHandSide()
1754                   self.getDomain().addPDEToRHS(self.__operator, \                   if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1755                                                escript.Data(), \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1756                                                D_times_e, \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1757                                                d_times_e,\                   else:
1758                                                d_contact_times_e)                      self.getDomain().addPDEToRHS(self.__operator, \
1759                                                     escript.Data(), \
1760                                                     D_times_e, \
1761                                                     d_times_e,\
1762                                                     escript.Data())
1763                        self.getDomain().addPDEToRHS(self.__operator, \
1764                                                     escript.Data(), \
1765                                                     D_reduced_times_e, \
1766                                                     d_reduced_times_e,\
1767                                                     escript.Data())
1768                   self.__operator=1./self.__operator                   self.__operator=1./self.__operator
1769                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1770                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1574  class LinearPDE(object): Line 1774  class LinearPDE(object):
1774                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1775                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1776                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1777                     self.getDomain().addPDEToRHS(self.__righthandside, \
1778                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1779                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1780                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1781                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1782                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1783                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1784            else:            else:
# Line 1589  class LinearPDE(object): Line 1794  class LinearPDE(object):
1794                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1795                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1796                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1797                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1798                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1806                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1808                   self.__applyConstraint()                   self.__applyConstraint()
1809                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1810                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1600  class LinearPDE(object): Line 1816  class LinearPDE(object):
1816                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1817                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1818                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1819                     self.getDomain().addPDEToRHS(self.__righthandside, \
1820                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1821                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1822                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1823                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1824                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1825                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1826                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1615  class LinearPDE(object): Line 1836  class LinearPDE(object):
1836                              escript.Data(),\                              escript.Data(),\
1837                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1838                              escript.Data())                              escript.Data())
1839                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1840                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1841                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1842                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1843                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1844                                escript.Data(), \
1845                                escript.Data(), \
1846                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1847                                escript.Data(),\
1848                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1849                                escript.Data())
1850                   self.__applyConstraint()                   self.__applyConstraint()
1851                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1852                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1648  class Poisson(LinearPDE): Line 1880  class Poisson(LinearPDE):
1880       """       """
1881       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1882       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1883                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1884                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1885       self.setSymmetryOn()       self.setSymmetryOn()
1886    
1887     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1696  class Poisson(LinearPDE): Line 1929  class Poisson(LinearPDE):
1929           return escript.Data()           return escript.Data()
1930       elif name == "y_contact" :       elif name == "y_contact" :
1931           return escript.Data()           return escript.Data()
1932         elif name == "A_reduced" :
1933             return escript.Data()
1934         elif name == "B_reduced" :
1935             return escript.Data()
1936         elif name == "C_reduced" :
1937             return escript.Data()
1938         elif name == "D_reduced" :
1939             return escript.Data()
1940         elif name == "X_reduced" :
1941             return escript.Data()
1942         elif name == "Y_reduced" :
1943             return self.getCoefficient("f_reduced")
1944         elif name == "d_reduced" :
1945             return escript.Data()
1946         elif name == "y_reduced" :
1947             return escript.Data()
1948         elif name == "d_contact_reduced" :
1949             return escript.Data()
1950         elif name == "y_contact_reduced" :
1951             return escript.Data()
1952       elif name == "r" :       elif name == "r" :
1953           return escript.Data()           return escript.Data()
1954       elif name == "q" :       elif name == "q" :
# Line 1732  class Helmholtz(LinearPDE): Line 1985  class Helmholtz(LinearPDE):
1985       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1986                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1987                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1988                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1989                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1993                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1994       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1795  class Helmholtz(LinearPDE): Line 2050  class Helmholtz(LinearPDE):
2050           return escript.Data()           return escript.Data()
2051       elif name == "y_contact" :       elif name == "y_contact" :
2052           return escript.Data()           return escript.Data()
2053         elif name == "A_reduced" :
2054             return escript.Data()
2055         elif name == "B_reduced" :
2056             return escript.Data()
2057         elif name == "C_reduced" :
2058             return escript.Data()
2059         elif name == "D_reduced" :
2060             return escript.Data()
2061         elif name == "X_reduced" :
2062             return escript.Data()
2063         elif name == "Y_reduced" :
2064             return self.getCoefficient("f_reduced")
2065         elif name == "d_reduced" :
2066             return escript.Data()
2067         elif name == "y_reduced" :
2068            return self.getCoefficient("g_reduced")
2069         elif name == "d_contact_reduced" :
2070             return escript.Data()
2071         elif name == "y_contact_reduced" :
2072             return escript.Data()
2073       elif name == "r" :       elif name == "r" :
2074           return self.getCoefficient("r")           return self.getCoefficient("r")
2075       elif name == "q" :       elif name == "q" :
# Line 1806  class LameEquation(LinearPDE): Line 2081  class LameEquation(LinearPDE):
2081     """     """
2082     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2083    
2084     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[j])[i])[j] = F_i -grad(S{sigma}[i,j])[j] }     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[k])[k])[j] = F_i -grad(S{sigma}[ij])[j] }
2085    
2086     with natural boundary conditons:     with natural boundary conditons:
2087    
2088     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) - S{lambda}*grad(u[j])[i]) = f_i -n[j]*S{sigma}[i,j] }     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
2089    
2090     and constraints:     and constraints:
2091    
# Line 1893  class LameEquation(LinearPDE): Line 2168  class LameEquation(LinearPDE):
2168           return escript.Data()           return escript.Data()
2169       elif name == "y_contact" :       elif name == "y_contact" :
2170           return escript.Data()           return escript.Data()
2171         elif name == "A_reduced" :
2172             return escript.Data()
2173         elif name == "B_reduced" :
2174             return escript.Data()
2175         elif name == "C_reduced" :
2176             return escript.Data()
2177         elif name == "D_reduced" :
2178             return escript.Data()
2179         elif name == "X_reduced" :
2180             return escript.Data()
2181         elif name == "Y_reduced" :
2182             return escript.Data()
2183         elif name == "d_reduced" :
2184             return escript.Data()
2185         elif name == "y_reduced" :
2186             return escript.Data()
2187         elif name == "d_contact_reduced" :
2188             return escript.Data()
2189         elif name == "y_contact_reduced" :
2190             return escript.Data()
2191       elif name == "r" :       elif name == "r" :
2192           return self.getCoefficient("r")           return self.getCoefficient("r")
2193       elif name == "q" :       elif name == "q" :
# Line 1900  class LameEquation(LinearPDE): Line 2195  class LameEquation(LinearPDE):
2195       else:       else:
2196          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2197    
2198  class AdvectivePDE(LinearPDE):  def LinearSinglePDE(domain,debug=False):
2199     """     """
2200     In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}     defines a single linear PDEs
    up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.  
   
    In the following we set  
   
    M{Z[j]=C[j]-B[j]}  
   
    or  
   
    M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}  
   
    To measure the dominance of the advective terms over the diffusive term M{A} the  
    X{Pelclet number} M{P} is used. It is defined as  
   
    M{P=h|Z|/(2|A|)}  
   
    where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size  
    from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.  
   
    From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:  
   
    M{S{Xi}=S{xi}(P) h/|Z|}  
   
    where M{S{xi}} is a suitable function of the Peclet number.  
   
    In the case of a single PDE the coefficient are up-dated in the following way:  
          - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}  
          - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}  
          - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}  
          - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}  
   
    Similar for the case of a systems of PDEs:  
          - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}  
          - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}  
          - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}  
          - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}  
   
    where M{S{delta}} is L{kronecker}.  
    Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}  
    but with the intension to stabilize the solution.  
2201    
2202       @param domain: domain of the PDE
2203       @type domain: L{Domain<escript.Domain>}
2204       @param debug: if True debug informations are printed.
2205       @rtype: L{LinearPDE}
2206     """     """
2207     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
       """  
       creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}  
   
       @param domain: domain of the PDE  
       @type domain: L{Domain<escript.Domain>}  
       @param numEquations: number of equations. If numEquations==None the number of equations  
                            is exracted from the PDE coefficients.  
       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components  
                            is exracted from the PDE coefficients.  
       @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the  
                  M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.  
       @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.  
       @param debug: if True debug informations are printed.  
       """  
       super(AdvectivePDE, self).__init__(domain,\  
                                          numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def setValue(self,**coefficients):  
       """  
       sets new values to coefficients  
2208    
2209        @param coefficients: new values assigned to coefficients  def LinearPDESystem(domain,debug=False):
2210        @keyword A: value for coefficient A.     """
2211        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.     defines a system of linear PDEs
       @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.  
2212    
2213        """     @param domain: domain of the PDE
2214        if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()     @type domain: L{Domain<escript.Domain>}
2215        super(AdvectivePDE, self).setValue(**coefficients)     @param debug: if True debug informations are printed.
2216       @rtype: L{LinearPDE}
2217       """
2218       return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2219    
2220     def ELMAN_RAMAGE(self,P):  class TransportPDE(object):
2221       """       """
2222       Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.       Warning: This is still a very experimental. The class is still changing!
      This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)  
           - M{S{xi}(P)=0} for M{P<1}  
           - M{S{xi}(P)=(1-1/P)/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))  
   
    def SIMPLIFIED_BROOK_HUGHES(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      The original methods is  
   
      M{S{xi}(P)=coth(P)-1/P}  
   
      As the evaluation of M{coth} is expensive we are using the approximation:  
   
          - M{S{xi}(P)=P/3} where M{P<3}  
          - M{S{xi}(P)=1/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      c=util.whereNegative(P-3.)  
      return P/6.*c+1./2.*(1.-c)  
   
    def HALF(self,P):  
      """  
      Predefined function to set value M{1/2} for M{S{xi}}  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return escript.Scalar(0.5,P.getFunctionSpace())  
   
    def __getXi(self):  
       if self.__Xi.isEmpty():  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          A=self.getCoefficient("A")  
          h=self.getDomain().getSize()  
          self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))  
          if not C.isEmpty() or not B.isEmpty():  
             if not C.isEmpty() and not B.isEmpty():  
                 if self.getNumEquations()>1:  
                    if self.getNumSolutions()>1:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for i in range(self.getNumEquations()):  
                          for k in range(self.getNumSolutions()):  
                             for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2  
                       length_of_flux=util.sqrt(flux2)  
                       # flux=C-util.reorderComponents(B,[0,2,1])  
                    else:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for i in range(self.getNumEquations()):  
                          for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2  
                       length_of_flux=util.sqrt(flux2)  
                       # flux=C-B  
                 else:  
                    if self.getNumSolutions()>1:  
                       flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2  
                       # flux=C-util.reorderComponents(B,[1,0])  
                       length_of_flux=util.sqrt(flux2)  
                    else:  
                       length_of_flux=util.length(C-B)  
             elif C.isEmpty():  
               length_of_flux=util.length(B)  
             else:  
               length_of_flux=util.length(C)  
             flux_max=util.Lsup(length_of_flux)  
             if flux_max>0.:  
               if A.isEmpty():  
                   inv_A=1./self.SMALL_TOLERANCE  
                   peclet_number=escript.Scalar(inv_A,length_of_flux.getFunctionSpace())  
                   xi=self.__xi(self,peclet_number)  
               else:  
                   # length_of_A=util.inner(flux,util.tensormutiply(A,flux))  
                   length_of_A=util.length(A)  
                   A_max=util.Lsup(length_of_A)  
                   if A_max>0:  
                        inv_A=1./(length_of_A+A_max*self.SMALL_TOLERANCE)  
                   else:  
                        inv_A=1./self.SMALL_TOLERANCE  
                   peclet_number=length_of_flux*h/2*inv_A  
                   xi=self.__xi(self,peclet_number)  
               self.__Xi=h*xi/(length_of_flux+flux_max*self.SMALL_TOLERANCE)  
               self.trace("preclet number = %e"%util.Lsup(peclet_number))  
             else:  
               self.__Xi=escript.Scalar(0.,length_of_flux.getFunctionSpace())  
       return self.__Xi  
2223    
2224         Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2225        
2226         u=r where q>0
2227        
2228         all coefficients are constant over time.
2229    
2230         typical usage:
2231    
2232             p=TransportPDE(dom)
2233             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2234             p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2235             t=0
2236             dt=0.1
2237             while (t<1.):
2238                  u=p.solve(dt)
2239    
2240         """
2241         def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2242            self.__domain=domain
2243            self.__num_equations=num_equations
2244            self.__useSUPG=useSUPG
2245            self.__trace=trace
2246            self.__theta=theta
2247            self.__matrix_type=0
2248            self.__reduced=True
2249            self.__reassemble=True
2250            if self.__useSUPG:
2251               self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2252               self.__pde.setSymmetryOn()
2253               self.__pde.setReducedOrderOn()
2254            else:
2255               self.__transport_problem=self.__getNewTransportProblem()
2256            self.setTolerance()
2257            self.__M=escript.Data()
2258            self.__A=escript.Data()
2259            self.__B=escript.Data()
2260            self.__C=escript.Data()
2261            self.__D=escript.Data()
2262            self.__X=escript.Data()
2263            self.__Y=escript.Data()
2264            self.__d=escript.Data()
2265            self.__y=escript.Data()
2266            self.__d_contact=escript.Data()
2267            self.__y_contact=escript.Data()
2268            self.__r=escript.Data()
2269            self.__q=escript.Data()
2270    
2271         def trace(self,text):
2272                 if self.__trace: print text
2273         def getSafeTimeStepSize(self):
2274            if self.__useSUPG:
2275                if self.__reassemble:
2276                   h=self.__domain.getSize()
2277                   dt=None
2278                   if not self.__A.isEmpty():
2279                      dt2=util.inf(h**2*self.__M/util.length(self.__A))
2280                      if dt == None:
2281                         dt = dt2
2282                      else:
2283                         dt=1./(1./dt+1./dt2)
2284                   if not self.__B.isEmpty():
2285                      dt2=util.inf(h*self.__M/util.length(self.__B))
2286                      if dt == None:
2287                         dt = dt2
2288                      else:
2289                         dt=1./(1./dt+1./dt2)
2290                   if not  self.__C.isEmpty():
2291                      dt2=util.inf(h*self.__M/util.length(self.__C))
2292                      if dt == None:
2293                         dt = dt2
2294                      else:
2295                         dt=1./(1./dt+1./dt2)
2296                   if not self.__D.isEmpty():
2297                      dt2=util.inf(self.__M/util.length(self.__D))
2298                      if dt == None:
2299                         dt = dt2
2300                      else:
2301                         dt=1./(1./dt+1./dt2)
2302                   self.__dt = dt/2
2303                return self.__dt
2304            else:
2305                return self.__getTransportProblem().getSafeTimeStepSize()
2306         def getDomain(self):
2307            return self.__domain
2308         def getTheta(self):
2309            return self.__theta
2310         def getNumEquations(self):
2311            return self.__num_equations
2312         def setReducedOn(self):
2313              if not self.reduced():
2314                  if self.__useSUPG:
2315                     self.__pde.setReducedOrderOn()
2316                  else:
2317                     self.__transport_problem=self.__getNewTransportProblem()
2318              self.__reduced=True
2319         def setReducedOff(self):
2320              if self.reduced():
2321                  if self.__useSUPG:
2322                     self.__pde.setReducedOrderOff()
2323                  else:
2324                     self.__transport_problem=self.__getNewTransportProblem()
2325              self.__reduced=False
2326         def reduced(self):
2327             return self.__reduced
2328         def getFunctionSpace(self):
2329            if self.reduced():
2330               return escript.ReducedSolution(self.getDomain())
2331            else:
2332               return escript.Solution(self.getDomain())
2333    
2334     def getCoefficientOfGeneralPDE(self,name):       def setTolerance(self,tol=1.e-8):
2335       """          self.__tolerance=tol
2336       return the value of the coefficient name of the general PDE          if self.__useSUPG:
2337                  self.__pde.setTolerance(self.__tolerance)
2338    
2339       @param name: name of the coefficient requested.       def __getNewTransportProblem(self):
2340       @type name: C{string}         """
2341       @return: the value of the coefficient name         returns an instance of a new operator
2342       @rtype: L{Data<escript.Data>}         """
2343       @raise IllegalCoefficient: if name is not one of coefficients         self.trace("New Transport problem is allocated.")
2344                    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}.         return self.getDomain().newTransportProblem( \
2345       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.                                 self.getTheta(),
2346       """                                 self.getNumEquations(), \
2347       if not self.getNumEquations() == self.getNumSolutions():                                 self.getFunctionSpace(), \
2348            raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."                                 self.__matrix_type)
2349              
2350       if name == "A" :       def __getNewSolutionVector(self):
2351           A=self.getCoefficient("A")           if self.getNumEquations() ==1 :
2352           B=self.getCoefficient("B")                  out=escript.Data(0.0,(),self.getFunctionSpace())
          C=self.getCoefficient("C")  
          if B.isEmpty() and C.isEmpty():  
             Aout=A  
          else:  
             if A.isEmpty():  
                Aout=self.createCoefficientOfGeneralPDE("A")  
             else:  
                Aout=A[:]  
             Xi=self.__getXi()  
             if self.getNumEquations()>1:  
                 for i in range(self.getNumEquations()):  
                    for j in range(self.getDim()):  
                       for k in range(self.getNumSolutions()):  
                          for l in range(self.getDim()):  
                             if not C.isEmpty() and not B.isEmpty():  
                                # tmp=C-util.reorderComponents(B,[0,2,1])  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*(C[p,i,j]-B[p,j,i])*(C[p,k,l]-B[p,l,k])  
                             elif C.isEmpty():  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)  
                             else:  
                                for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]  
                                # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)  
             else:  
                if not C.isEmpty() and not B.isEmpty():  
                    delta=(C-B)  
                    Aout+=util.outer(Xi*delta,delta)  
                elif not B.isEmpty():  
                    Aout+=util.outer(Xi*B,B)  
                elif not C.isEmpty():  
                    Aout+=util.outer(Xi*C,C)  
          return Aout  
      elif name == "B" :  
          # return self.getCoefficient("B")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if C.isEmpty() or D.isEmpty():  
             Bout=B  
          else:  
             Xi=self.__getXi()  
             if B.isEmpty():  
                 Bout=self.createCoefficientOfGeneralPDE("B")  
             else:  
                 Bout=B[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                   for p in range(self.getNumEquations()):  
                      tmp=Xi*D[p,k]  
                      for i in range(self.getNumEquations()):  
                         for j in range(self.getDim()):  
                            Bout[i,j,k]+=tmp*C[p,i,j]  
                            # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)  
             else:  
                Bout+=(Xi*D)*C  
          return Bout  
      elif name == "C" :  
          # return self.getCoefficient("C")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          D=self.getCoefficient("D")  
          if B.isEmpty() or D.isEmpty():  
             Cout=C  
          else:  
             Xi=self.__getXi()  
             if C.isEmpty():  
                 Cout=self.createCoefficientOfGeneralPDE("C")  
             else:  
                 Cout=C[:]  
             if self.getNumEquations()>1:  
                for k in range(self.getNumSolutions()):  
                    for p in range(self.getNumEquations()):  
                       tmp=Xi*D[p,k]  
                       for i in range(self.getNumEquations()):  
                         for l in range(self.getDim()):  
                                  Cout[i,k,l]+=tmp*B[p,l,i]  
                                  # Cout=Cout+Xi*B[p,l,i]*D[p,k]  
             else:  
                Cout+=(Xi*D)*B  
          return Cout  
      elif name == "D" :  
          return self.getCoefficient("D")  
      elif name == "X" :  
          # return self.getCoefficient("X")  
          X=self.getCoefficient("X")  
          Y=self.getCoefficient("Y")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if Y.isEmpty() or (B.isEmpty() and C.isEmpty()):  
             Xout=X  
2353           else:           else:
2354              if X.isEmpty():                  out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2355                  Xout=self.createCoefficientOfGeneralPDE("X")           return out
             else:  
                 Xout=X[:]  
             Xi=self.__getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                              # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                              # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
                              # Xout=X_out+Xi*util.inner(Y,C,offset=1)  
             else:  
               if not C.isEmpty() and not B.isEmpty():  
                 Xout+=(Xi*Y)*(C-B)  
               elif C.isEmpty():  
                 Xout-=(Xi*Y)*B  
               else:  
                 Xout+=(Xi*Y)*C  
          return Xout  
      elif name == "Y" :  
          return self.getCoefficient("Y")  
      elif name == "d" :  
          return self.getCoefficient("d")  
      elif name == "y" :  
          return self.getCoefficient("y")  
      elif name == "d_contact" :  
          return self.getCoefficient("d_contact")  
      elif name == "y_contact" :  
          return self.getCoefficient("y_contact")  
      elif name == "r" :  
          return self.getCoefficient("r")  
      elif name == "q" :  
          return self.getCoefficient("q")  
      else:  
         raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name  
2356    
2357  # $Log$       def __getTransportProblem(self):
2358  # Revision 1.14  2005/09/22 01:54:57  jgs         if self.__reassemble:
2359  # Merge of development branch dev-02 back to main trunk on 2005-09-22               self.__source=self.__getNewSolutionVector()
2360  #               self.__transport_problem.reset()
2361  # Revision 1.13  2005/09/15 03:44:19  jgs               self.getDomain().addPDEToTransportProblem(
2362  # Merge of development branch dev-02 back to main trunk on 2005-09-15                           self.__transport_problem,
2363  #                           self.__source,
2364  # Revision 1.12  2005/09/01 03:31:28  jgs                           self.__M,
2365  # Merge of development branch dev-02 back to main trunk on 2005-09-01                           self.__A,
2366  #                           self.__B,
2367  # Revision 1.11  2005/08/23 01:24:28  jgs                           self.__C,
2368  # Merge of development branch dev-02 back to main trunk on 2005-08-23                           self.__D,
2369  #                           self.__X,
2370  # Revision 1.10  2005/08/12 01:45:36  jgs                           self.__Y,
2371  # erge of development branch dev-02 back to main trunk on 2005-08-12                           self.__d,
2372  #                           self.__y,
2373  # Revision 1.9.2.17  2005/09/21 07:03:33  matt                           self.__d_contact,
2374  # PDECoefficient and LinearPDE are now new style classes (introduced in Python                           self.__y_contact)
2375  # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been               self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2376  # modified to instead use portable/cooperative "super" calls to extend base               self.__reassemble=False
2377  # class methods.         return self.__transport_problem
2378  #       def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2379  # Revision 1.9.2.16  2005/09/16 01:54:37  matt                    d=None, y=None, d_contact=None, y_contact=None, q=None, r=None):
2380  # Removed redundant if-loop.               if not M==None:
2381  #                    self.__reassemble=True
2382  # Revision 1.9.2.15  2005/09/14 08:09:18  matt                    self.__M=M
2383  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.               if not A==None:
2384  #                    self.__reassemble=True
2385  # Revision 1.9.2.14  2005/09/07 06:26:16  gross                    self.__A=A
2386  # the solver from finley are put into the standalone package paso now               if not B==None:
2387  #                    self.__reassemble=True
2388  # Revision 1.9.2.13  2005/08/31 08:45:03  gross                    self.__B=B
2389  # in the case of lumping no new system is allocated if the constraint is changed.               if not C==None:
2390  #                    self.__reassemble=True
2391  # Revision 1.9.2.12  2005/08/31 07:10:23  gross                    self.__C=C
2392  # test for Lumping added               if not D==None:
2393  #                    self.__reassemble=True
2394  # Revision 1.9.2.11  2005/08/30 01:53:45  gross                    self.__D=D
2395  # bug in format fixed.               if not X==None:
2396  #                    self.__reassemble=True
2397  # Revision 1.9.2.10  2005/08/26 07:14:17  gross                    self.__X=X
2398  # a few more bugs in linearPDE fixed. remaining problem are finley problems               if not Y==None:
2399  #                    self.__reassemble=True
2400  # Revision 1.9.2.9  2005/08/26 06:30:45  gross                    self.__Y=Y
2401  # fix for reported bug  0000004. test_linearPDE passes a few more tests               if not d==None:
2402  #                    self.__reassemble=True
2403  # Revision 1.9.2.8  2005/08/26 04:30:13  gross                    self.__d=d
2404  # gneric unit testing for linearPDE               if not y==None:
2405  #                    self.__reassemble=True
2406  # Revision 1.9.2.7  2005/08/25 07:06:50  gross                    self.__y=y
2407  # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so               if not d_contact==None:
2408  #                    self.__reassemble=True
2409  # Revision 1.9.2.6  2005/08/24 05:01:24  gross                    self.__d_contact=d_contact
2410  # problem with resetting the matrix in case of resetting its values to 0 fixed.               if not y_contact==None:
2411  #                    self.__reassemble=True
2412  # Revision 1.9.2.5  2005/08/24 02:03:28  gross                    self.__y_contact=y_contact
2413  # epydoc mark up partially fixed               if not q==None:
2414  #                    self.__reassemble=True
2415  # Revision 1.9.2.4  2005/08/22 07:11:09  gross                    self.__q=q
2416  # some problems with LinearPDEs fixed.               if not r==None:
2417  #                    self.__reassemble=True
2418  # Revision 1.9.2.3  2005/08/18 04:48:48  gross                    self.__r=r
2419  # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  
2420  #       def setInitialSolution(self,u):
2421  # Revision 1.9.2.2  2005/08/18 04:39:32  gross               if self.__useSUPG:
2422  # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now                   self.__u=util.interpolate(u,self.getFunctionSpace())
2423  #               else:
2424  # Revision 1.9.2.1  2005/07/29 07:10:27  gross                   self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2425  # new functions in util and a new pde type in linearPDEs  
2426  #       def solve(self,dt,**kwarg):
2427  # Revision 1.1.2.25  2005/07/28 04:21:09  gross             if self.__useSUPG:
2428  # Lame equation: (linear elastic, isotropic) added                  if self.__reassemble:
2429  #                      self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2430  # Revision 1.1.2.24  2005/07/22 06:37:11  gross                      self.__reassemble=False
2431  # some extensions to modellib and linearPDEs                  dt2=self.getSafeTimeStepSize()
2432  #                  nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2433  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane                  dt2=dt/nn
2434  # Fixed up some docstrings.  Moved module-level functions to top of file so                  nnn=0
2435  # that epydoc and doxygen can pick them up properly.                  u=self.__u
2436  #                  self.trace("number of substeps is %d."%nn)
2437  # Revision 1.1.2.22  2005/05/12 11:41:30  gross                  while nnn<nn :
2438  # some basic Models have been added                      self.__setSUPG(u,u,dt2/2)
2439  #                      u_half=self.__pde.getSolution(verbose=True)
2440  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane                      self.__setSUPG(u,u_half,dt2)
2441  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of                      u=self.__pde.getSolution(verbose=True)
2442  # file so that the AdvectivePDE class is picked up by doxygen.  Some                      nnn+=1
2443  # reformatting of docstrings.  Addition of code to make equations come out                  self.__u=u
2444  # as proper LaTeX.                  return self.__u
2445  #             else:
2446  # Revision 1.1.2.20  2005/04/15 07:09:08  gross                 kwarg["tolerance"]=self.__tolerance
2447  # some problems with functionspace and linearPDEs fixed.                 tp=self.__getTransportProblem()
2448  #                 return tp.solve(self.__source,dt,kwarg)
2449  # Revision 1.1.2.19  2005/03/04 05:27:07  gross       def __setSUPG(self,u0,u,dt):
2450  # bug in SystemPattern fixed.              g=util.grad(u)
2451  #              X=0
2452  # Revision 1.1.2.18  2005/02/08 06:16:45  gross              Y=self.__M*u0
2453  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed              X=0
2454  #              self.__pde.setValue(r=u0)
2455  # Revision 1.1.2.17  2005/02/08 05:56:19  gross              if not self.__A.isEmpty():
2456  # Reference Number handling added                 X=X+dt*util.matrixmult(self.__A,g)
2457  #              if not self.__B.isEmpty():
2458  # Revision 1.1.2.16  2005/02/07 04:41:28  gross                 X=X+dt*self.__B*u
2459  # some function exposed to python to make mesh merging running              if not  self.__C.isEmpty():
2460  #                 Y=Y+dt*util.inner(self.__C,g)
2461  # Revision 1.1.2.15  2005/02/03 00:14:44  gross              if not self.__D.isEmpty():
2462  # timeseries add and ESySParameter.py renames esysXML.py for consistence                 Y=Y+dt*self.__D*u
2463  #              if not self.__X.isEmpty():
2464  # Revision 1.1.2.14  2005/02/01 06:44:10  gross                 X=X+dt*self.__X
2465  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working              if not self.__Y.isEmpty():
2466  #                 Y=Y+dt*self.__Y
2467  # Revision 1.1.2.13  2005/01/25 00:47:07  gross              self.__pde.setValue(X=X,Y=Y)
2468  # updates in the documentation              if not self.__y.isEmpty():
2469  #                 self.__pde.setValue(y=dt*self.__y)
2470  # Revision 1.1.2.12  2005/01/12 01:28:04  matt              if not self.__y_contact.isEmpty():
2471  # Added createCoefficient method for linearPDEs.                 self.__pde.setValue(y=dt*self.__y_contact)
2472  #              self.__pde.setValue(r=u0)
 # Revision 1.1.2.11  2005/01/11 01:55:34  gross  
 # a problem in linearPDE class fixed  
 #  
 # Revision 1.1.2.10  2005/01/07 01:13:29  gross  
 # some bugs in linearPDE fixed  
 #  
 # Revision 1.1.2.9  2005/01/06 06:24:58  gross  
 # some bugs in slicing fixed  
 #  
 # Revision 1.1.2.8  2005/01/05 04:21:40  gross  
 # FunctionSpace checking/matchig in slicing added  
 #  
 # Revision 1.1.2.7  2004/12/29 10:03:41  gross  
 # bug in setValue fixed  
 #  
 # Revision 1.1.2.6  2004/12/29 05:29:59  gross  
 # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()  
 #  
 # Revision 1.1.2.5  2004/12/29 00:18:41  gross  
 # AdvectivePDE added  
 #  
 # Revision 1.1.2.4  2004/12/24 06:05:41  gross  
 # some changes in linearPDEs to add AdevectivePDE  
 #  
 # Revision 1.1.2.3  2004/12/16 00:12:34  gross  
 # __init__ of LinearPDE does not accept any coefficient anymore  
 #  
 # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  
 # *** empty log message ***  
 #  
 # Revision 1.1.2.1  2004/12/12 22:53:47  gross  
 # linearPDE has been renamed LinearPDE  
 #  
 # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross  
 # GMRES added  
 #  
 # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross  
 # options for GMRES and PRES20 added  
 #  
 # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross  
 # some small changes  
 #  
 # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross  
 # Finley solves 4M unknowns now  
 #  
 # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross  
 # poisson solver added  
 #  
 # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross  
 # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry  
 #  
 # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross  
 # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed  
 #  
 # Revision 1.1.1.1  2004/10/26 06:53:56  jgs  
 # initial import of project esys2  
 #  
 # Revision 1.3.2.3  2004/10/26 06:43:48  jgs  
 # committing Lutz's and Paul's changes to brach jgs  
 #  
 # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane  
 # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.  
 #  
 # Revision 1.3  2004/09/23 00:53:23  jgs  
 # minor fixes  
 #  
 # Revision 1.1  2004/08/28 12:58:06  gross  
 # SimpleSolve is not running yet: problem with == of functionsspace  
 #  

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