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revision 614 by elspeth, Wed Mar 22 01:37:07 2006 UTC revision 1819 by artak, Tue Sep 30 05:58:06 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
465       @cvar GS: Gauss-Seidel solver
466    
467     """     """
468     DEFAULT= 0     DEFAULT= 0
# Line 441  class LinearPDE(object): Line 489  class LinearPDE(object):
489     PASO= 21     PASO= 21
490     AMG= 22     AMG= 22
491     RILU = 23     RILU = 23
492       TRILINOS = 24
493       NONLINEAR_GMRES = 25
494       TFQMR = 26
495       MINRES = 27
496       GS=28
497    
498     SMALL_TOLERANCE=1.e-13     SMALL_TOLERANCE=1.e-13
499     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
# Line 478  class LinearPDE(object): Line 531  class LinearPDE(object):
531         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
532         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
534           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
535           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
537           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
539           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
540           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
541           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
542           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
543           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
544         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
545         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
546    
# Line 663  class LinearPDE(object): Line 726  class LinearPDE(object):
726       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
727       """       """
728       if u==None:       if u==None:
729            return self.getOperator()*self.getSolution()          return self.getOperator()*self.getSolution()
730       else:       else:
731          self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())          return self.getOperator()*escript.Data(u,self.getFunctionSpaceForSolution())
732    
733     def getResidual(self,u=None):     def getResidual(self,u=None):
734       """       """
# Line 759  class LinearPDE(object): Line 822  class LinearPDE(object):
822                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
823                        if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)                        if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
824                        out=False                        out=False
825             # and now the reduced coefficients
826             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
827             if not A_reduced.isEmpty():
828                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
829                if self.getNumSolutions()>1:
830                   for i in range(self.getNumEquations()):
831                      for j in range(self.getDim()):
832                         for k in range(self.getNumSolutions()):
833                            for l in range(self.getDim()):
834                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
835                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
836                                   out=False
837                else:
838                   for j in range(self.getDim()):
839                      for l in range(self.getDim()):
840                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
841                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
842                            out=False
843             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
844             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
845             if B_reduced.isEmpty() and not C_reduced.isEmpty():
846                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
847                out=False
848             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
849                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
850                out=False
851             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
852                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
853                if self.getNumSolutions()>1:
854                   for i in range(self.getNumEquations()):
855                       for j in range(self.getDim()):
856                          for k in range(self.getNumSolutions()):
857                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
858                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
859                                  out=False
860                else:
861                   for j in range(self.getDim()):
862                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
863                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
864                         out=False
865             if self.getNumSolutions()>1:
866               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
867               if not D_reduced.isEmpty():
868                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
869                 for i in range(self.getNumEquations()):
870                    for k in range(self.getNumSolutions()):
871                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
872                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
873                          out=False
874               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
875               if not d_reduced.isEmpty():
876                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
877                 for i in range(self.getNumEquations()):
878                    for k in range(self.getNumSolutions()):
879                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
880                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
881                          out=False
882               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
883               if not d_contact_reduced.isEmpty():
884                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
885                 for i in range(self.getNumEquations()):
886                    for k in range(self.getNumSolutions()):
887                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
888                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
889                          out=False
890        return out        return out
891    
892     def getSolution(self,**options):     def getSolution(self,**options):
# Line 798  class LinearPDE(object): Line 926  class LinearPDE(object):
926       """       """
927       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
928    
929       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}       M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
930    
931       or       or
932    
933       M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}       M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
934    
935       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
936       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 810  class LinearPDE(object): Line 938  class LinearPDE(object):
938       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
939       """       """
940       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
941       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
942               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
943               -util.self.getCoefficientOfGeneralPDE("X") \
944               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
945               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
946               -util.self.getCoefficientOfGeneralPDE("X_reduced")
947     # =============================================================================     # =============================================================================
948     #   solver settings:     #   solver settings:
949     # =============================================================================     # =============================================================================
# Line 819  class LinearPDE(object): Line 952  class LinearPDE(object):
952         sets a new solver         sets a new solver
953    
954         @param solver: sets a new solver method.         @param solver: sets a new solver method.
955         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, 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}
956         @param preconditioner: sets a new solver method.         @param preconditioner: sets a new solver method.
957         @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},  L{GS}
958         """         """
959         if solver==None: solve=self.DEFAULT         if solver==None: solver=self.__solver_method
960           if preconditioner==None: preconditioner=self.__preconditioner
961           if solver==None: solver=self.DEFAULT
962         if preconditioner==None: preconditioner=self.DEFAULT         if preconditioner==None: preconditioner=self.DEFAULT
963         if not (solver,preconditioner)==self.getSolverMethod():         if not (solver,preconditioner)==self.getSolverMethod():
964             self.__solver_method=solver             self.__solver_method=solver
# Line 847  class LinearPDE(object): Line 982  class LinearPDE(object):
982         elif m[0]==self.ITERATIVE: method= "ITERATIVE"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
983         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
984         elif m[0]==self.PCG: method= "PCG"         elif m[0]==self.PCG: method= "PCG"
985           elif m[0]==self.TFQMR: method= "TFQMR"
986           elif m[0]==self.MINRES: method= "MINRES"
987         elif m[0]==self.CR: method= "CR"         elif m[0]==self.CR: method= "CR"
988         elif m[0]==self.CGS: method= "CGS"         elif m[0]==self.CGS: method= "CGS"
989         elif m[0]==self.BICGSTAB: method= "BICGSTAB"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
# Line 862  class LinearPDE(object): Line 999  class LinearPDE(object):
999         elif m[1]==self.SSOR: method+= "+SSOR"         elif m[1]==self.SSOR: method+= "+SSOR"
1000         elif m[1]==self.AMG: method+= "+AMG"         elif m[1]==self.AMG: method+= "+AMG"
1001         elif m[1]==self.RILU: method+= "+RILU"         elif m[1]==self.RILU: method+= "+RILU"
1002           elif m[1]==self.GS: method+= "+GS"
1003         if p==self.DEFAULT: package="DEFAULT"         if p==self.DEFAULT: package="DEFAULT"
1004         elif p==self.PASO: package= "PASO"         elif p==self.PASO: package= "PASO"
1005         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
1006         elif p==self.SCSL: package= "SCSL"         elif p==self.SCSL: package= "SCSL"
1007         elif p==self.UMFPACK: package= "UMFPACK"         elif p==self.UMFPACK: package= "UMFPACK"
1008           elif p==self.TRILINOS: package= "TRILINOS"
1009         else : method="unknown"         else : method="unknown"
1010         return "%s solver of %s package"%(method,package)         return "%s solver of %s package"%(method,package)
1011    
# Line 884  class LinearPDE(object): Line 1023  class LinearPDE(object):
1023         """         """
1024         sets a new solver package         sets a new solver package
1025    
1026         @param solver: sets a new solver method.         @param package: sets a new solver method.
1027         @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}         @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1028         """         """
1029         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1030         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
1031             self.__solver_method=solver             self.__solver_package=package
1032             self.__checkMatrixType()             self.__checkMatrixType()
1033             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
1034    
# Line 922  class LinearPDE(object): Line 1061  class LinearPDE(object):
1061         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1062                     the system will be resolved.                     the system will be resolved.
1063         @type tol: positive C{float}         @type tol: positive C{float}
1064         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1065         """         """
1066         if not tol>0:         if not tol>0:
1067             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1068         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1069         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1070         self.__tolerance=tol         self.__tolerance=tol
# Line 1206  class LinearPDE(object): Line 1345  class LinearPDE(object):
1345         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1346             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1347         else:         else:
1348             self.__righthandside*=0             self.__righthandside.setToZero()
1349             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1350         return self.__righthandside         return self.__righthandside
1351    
# Line 1256  class LinearPDE(object): Line 1395  class LinearPDE(object):
1395       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1396       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1397       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1398                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1399                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1400       """       """
1401       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1402          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1284  class LinearPDE(object): Line 1424  class LinearPDE(object):
1424       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1425       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1426       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1427                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1428                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1429       """       """
1430       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1431          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1300  class LinearPDE(object): Line 1441  class LinearPDE(object):
1441       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1442       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1443       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1444                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1445                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1446       """       """
1447       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1448          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1316  class LinearPDE(object): Line 1458  class LinearPDE(object):
1458       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1459       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1460       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1461                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1462                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1463       """       """
1464       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1465          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
# Line 1446  class LinearPDE(object): Line 1589  class LinearPDE(object):
1589        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1590        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1591        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1592          @keyword A_reduced: value for coefficient A_reduced.
1593          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1594        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1595        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1596          @keyword B_reduced: value for coefficient B_reduced
1597          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1598        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1599        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1600          @keyword C_reduced: value for coefficient C_reduced
1601          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1602        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1603        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1604          @keyword D_reduced: value for coefficient D_reduced
1605          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1606        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1607        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1608          @keyword X_reduced: value for coefficient X_reduced
1609          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1610        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1611        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1612          @keyword Y_reduced: value for coefficient Y_reduced
1613          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1614        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1615        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1616          @keyword d_reduced: value for coefficient d_reduced
1617          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1618        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1619        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1620        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1621        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1622                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1623          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1624        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1625        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1626                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1627          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1628        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1629        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1630                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1500  class LinearPDE(object): Line 1659  class LinearPDE(object):
1659        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1660        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1661          try:          try:
1662             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1663                                             self.getNumEquations(),self.getNumSolutions(),
1664                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1665               self.alteredCoefficient(i)
1666            except IllegalCoefficientFunctionSpace,m:
1667                # if the function space is wrong then we try the reduced version:
1668                i_red=i+"_reduced"
1669                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1670                    try:
1671                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1672                                                          self.getNumEquations(),self.getNumSolutions(),
1673                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1674                        self.alteredCoefficient(i_red)
1675                    except IllegalCoefficientValue,m:
1676                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1677                    except IllegalCoefficientFunctionSpace,m:
1678                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1679                else:
1680                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1681          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1682             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1683        self.__altered_coefficients=True        self.__altered_coefficients=True
1684        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1685        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1512  class LinearPDE(object): Line 1687  class LinearPDE(object):
1687           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1688           homogeneous_constraint=True           homogeneous_constraint=True
1689           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1690               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1691                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1692                 self.__invalidateSystem()                 self.__invalidateSystem()
1693    
# Line 1531  class LinearPDE(object): Line 1706  class LinearPDE(object):
1706                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1707                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient A in lumped matrix may not be present."
1708                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1709                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient B in lumped matrix may not be present."
1710                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1711                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient C in lumped matrix may not be present."
1712                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1713                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1714                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1715                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1716                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1717                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1718                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1719                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1720                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1721                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1722                   D=self.getCoefficientOfGeneralPDE("D")                   D=self.getCoefficientOfGeneralPDE("D")
1723                     d=self.getCoefficientOfGeneralPDE("d")
1724                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1725                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1726                   if not D.isEmpty():                   if not D.isEmpty():
1727                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1728                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1729                       else:                       else:
1730                          D_times_e=D                          D_times_e=D
1731                   else:                   else:
1732                      D_times_e=escript.Data()                      D_times_e=escript.Data()
                  d=self.getCoefficientOfGeneralPDE("d")  
1733                   if not d.isEmpty():                   if not d.isEmpty():
1734                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1735                          d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1736                       else:                       else:
1737                          d_times_e=d                          d_times_e=d
1738                   else:                   else:
1739                      d_times_e=escript.Data()                      d_times_e=escript.Data()
1740                   d_contact=self.getCoefficientOfGeneralPDE("d_contact")        
1741                   if not d_contact.isEmpty():                   if not D_reduced.isEmpty():
1742                         if self.getNumSolutions()>1:
1743                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1744                         else:
1745                            D_reduced_times_e=D_reduced
1746                     else:
1747                        D_reduced_times_e=escript.Data()
1748                     if not d_reduced.isEmpty():
1749                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1750                          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(),)))
1751                       else:                       else:
1752                          d_contact_times_e=d_contact                          d_reduced_times_e=d_reduced
1753                   else:                   else:
1754                      d_contact_times_e=escript.Data()                      d_reduced_times_e=escript.Data()
1755        
1756                   self.__operator=self.__getNewRightHandSide()                   self.__operator=self.__getNewRightHandSide()
1757                   self.getDomain().addPDEToRHS(self.__operator, \                   if False and hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1758                                                escript.Data(), \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1759                                                D_times_e, \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1760                                                d_times_e,\                   else:
1761                                                d_contact_times_e)                      self.getDomain().addPDEToRHS(self.__operator, \
1762                                                     escript.Data(), \
1763                                                     D_times_e, \
1764                                                     d_times_e,\
1765                                                     escript.Data())
1766                        self.getDomain().addPDEToRHS(self.__operator, \
1767                                                     escript.Data(), \
1768                                                     D_reduced_times_e, \
1769                                                     d_reduced_times_e,\
1770                                                     escript.Data())
1771                   self.__operator=1./self.__operator                   self.__operator=1./self.__operator
1772                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1773                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1574  class LinearPDE(object): Line 1777  class LinearPDE(object):
1777                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1778                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1779                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1780                     self.getDomain().addPDEToRHS(self.__righthandside, \
1781                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1782                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1783                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1784                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1785                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1786                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1787            else:            else:
# Line 1589  class LinearPDE(object): Line 1797  class LinearPDE(object):
1797                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1798                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1799                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1800                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1801                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1803                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1804                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1805                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1806                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1807                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1808                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1809                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1810                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1811                   self.__applyConstraint()                   self.__applyConstraint()
1812                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1813                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1600  class LinearPDE(object): Line 1819  class LinearPDE(object):
1819                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1820                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1821                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1822                     self.getDomain().addPDEToRHS(self.__righthandside, \
1823                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1824                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1825                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1826                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1827                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1828                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1829                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1615  class LinearPDE(object): Line 1839  class LinearPDE(object):
1839                              escript.Data(),\                              escript.Data(),\
1840                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1841                              escript.Data())                              escript.Data())
1842                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1843                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1844                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1845                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1846                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1847                                escript.Data(), \
1848                                escript.Data(), \
1849                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1850                                escript.Data(),\
1851                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1852                                escript.Data())
1853                   self.__applyConstraint()                   self.__applyConstraint()
1854                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1855                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1648  class Poisson(LinearPDE): Line 1883  class Poisson(LinearPDE):
1883       """       """
1884       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1885       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1886                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1887                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1888       self.setSymmetryOn()       self.setSymmetryOn()
1889    
1890     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1696  class Poisson(LinearPDE): Line 1932  class Poisson(LinearPDE):
1932           return escript.Data()           return escript.Data()
1933       elif name == "y_contact" :       elif name == "y_contact" :
1934           return escript.Data()           return escript.Data()
1935         elif name == "A_reduced" :
1936             return escript.Data()
1937         elif name == "B_reduced" :
1938             return escript.Data()
1939         elif name == "C_reduced" :
1940             return escript.Data()
1941         elif name == "D_reduced" :
1942             return escript.Data()
1943         elif name == "X_reduced" :
1944             return escript.Data()
1945         elif name == "Y_reduced" :
1946             return self.getCoefficient("f_reduced")
1947         elif name == "d_reduced" :
1948             return escript.Data()
1949         elif name == "y_reduced" :
1950             return escript.Data()
1951         elif name == "d_contact_reduced" :
1952             return escript.Data()
1953         elif name == "y_contact_reduced" :
1954             return escript.Data()
1955       elif name == "r" :       elif name == "r" :
1956           return escript.Data()           return escript.Data()
1957       elif name == "q" :       elif name == "q" :
# Line 1732  class Helmholtz(LinearPDE): Line 1988  class Helmholtz(LinearPDE):
1988       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1989                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1990                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1991                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1992                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1993                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1994                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1995                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1996                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1997       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1795  class Helmholtz(LinearPDE): Line 2053  class Helmholtz(LinearPDE):
2053           return escript.Data()           return escript.Data()
2054       elif name == "y_contact" :       elif name == "y_contact" :
2055           return escript.Data()           return escript.Data()
2056         elif name == "A_reduced" :
2057             return escript.Data()
2058         elif name == "B_reduced" :
2059             return escript.Data()
2060         elif name == "C_reduced" :
2061             return escript.Data()
2062         elif name == "D_reduced" :
2063             return escript.Data()
2064         elif name == "X_reduced" :
2065             return escript.Data()
2066         elif name == "Y_reduced" :
2067             return self.getCoefficient("f_reduced")
2068         elif name == "d_reduced" :
2069             return escript.Data()
2070         elif name == "y_reduced" :
2071            return self.getCoefficient("g_reduced")
2072         elif name == "d_contact_reduced" :
2073             return escript.Data()
2074         elif name == "y_contact_reduced" :
2075             return escript.Data()
2076       elif name == "r" :       elif name == "r" :
2077           return self.getCoefficient("r")           return self.getCoefficient("r")
2078       elif name == "q" :       elif name == "q" :
# Line 1806  class LameEquation(LinearPDE): Line 2084  class LameEquation(LinearPDE):
2084     """     """
2085     Class to define a Lame equation problem:     Class to define a Lame equation problem:
2086    
2087     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[j])[i])[j] = F_i -grad(S{sigma}[i,j])[j] }     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[k])[k])[j] = F_i -grad(S{sigma}[ij])[j] }
2088    
2089     with natural boundary conditons:     with natural boundary conditons:
2090    
2091     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) - S{lambda}*grad(u[j])[i]) = f_i -n[j]*S{sigma}[i,j] }     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
2092    
2093     and constraints:     and constraints:
2094    
# Line 1893  class LameEquation(LinearPDE): Line 2171  class LameEquation(LinearPDE):
2171           return escript.Data()           return escript.Data()
2172       elif name == "y_contact" :       elif name == "y_contact" :
2173           return escript.Data()           return escript.Data()
2174         elif name == "A_reduced" :
2175             return escript.Data()
2176         elif name == "B_reduced" :
2177             return escript.Data()
2178         elif name == "C_reduced" :
2179             return escript.Data()
2180         elif name == "D_reduced" :
2181             return escript.Data()
2182         elif name == "X_reduced" :
2183             return escript.Data()
2184         elif name == "Y_reduced" :
2185             return escript.Data()
2186         elif name == "d_reduced" :
2187             return escript.Data()
2188         elif name == "y_reduced" :
2189             return escript.Data()
2190         elif name == "d_contact_reduced" :
2191             return escript.Data()
2192         elif name == "y_contact_reduced" :
2193             return escript.Data()
2194       elif name == "r" :       elif name == "r" :
2195           return self.getCoefficient("r")           return self.getCoefficient("r")
2196       elif name == "q" :       elif name == "q" :
# Line 1900  class LameEquation(LinearPDE): Line 2198  class LameEquation(LinearPDE):
2198       else:       else:
2199          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2200    
2201  class AdvectivePDE(LinearPDE):  def LinearSinglePDE(domain,debug=False):
2202     """     """
2203     In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}     defines a single linear PDEs
    up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.  
   
    In the following we set  
   
    M{Z[j]=C[j]-B[j]}  
   
    or  
   
    M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}  
   
    To measure the dominance of the advective terms over the diffusive term M{A} the  
    X{Pelclet number} M{P} is used. It is defined as  
   
    M{P=h|Z|/(2|A|)}  
   
    where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size  
    from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.  
   
    From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:  
   
    M{S{Xi}=S{xi}(P) h/|Z|}  
   
    where M{S{xi}} is a suitable function of the Peclet number.  
   
    In the case of a single PDE the coefficient are up-dated in the following way:  
          - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}  
          - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}  
          - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}  
          - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}  
   
    Similar for the case of a systems of PDEs:  
          - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}  
          - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}  
          - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}  
          - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}  
   
    where M{S{delta}} is L{kronecker}.  
    Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}  
    but with the intension to stabilize the solution.  
2204    
2205       @param domain: domain of the PDE
2206       @type domain: L{Domain<escript.Domain>}
2207       @param debug: if True debug informations are printed.
2208       @rtype: L{LinearPDE}
2209     """     """
2210     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):     return LinearPDE(domain,numEquations=1,numSolutions=1,debug=debug)
       """  
       creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}  
   
       @param domain: domain of the PDE  
       @type domain: L{Domain<escript.Domain>}  
       @param numEquations: number of equations. If numEquations==None the number of equations  
                            is exracted from the PDE coefficients.  
       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components  
                            is exracted from the PDE coefficients.  
       @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the  
                  M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.  
       @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.  
       @param debug: if True debug informations are printed.  
       """  
       super(AdvectivePDE, self).__init__(domain,\  
                                          numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def setValue(self,**coefficients):  
       """  
       sets new values to coefficients  
2211    
2212        @param coefficients: new values assigned to coefficients  def LinearPDESystem(domain,debug=False):
2213        @keyword A: value for coefficient A.     """
2214        @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.  
2215    
2216        """     @param domain: domain of the PDE
2217        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>}
2218        super(AdvectivePDE, self).setValue(**coefficients)     @param debug: if True debug informations are printed.
2219       @rtype: L{LinearPDE}
2220       """
2221       return LinearPDE(domain,numEquations=domain.getDim(),numSolutions=domain.getDim(),debug=debug)
2222    
2223     def ELMAN_RAMAGE(self,P):  class TransportPDE(object):
2224       """       """
2225       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  
2226    
2227         Mu_{,t} =-(A_{ij}u_{,j})_j-(B_{j}u)_{,j} + C_{j} u_{,j} + Y_i + X_{i,i}
2228        
2229         u=r where q>0
2230        
2231         all coefficients are constant over time.
2232    
2233         typical usage:
2234    
2235             p=TransportPDE(dom)
2236             p.setValue(M=Scalar(1.,Function(dom),C=Scalar(1.,Function(dom)*[-1.,0.])
2237             p.setInitialSolution(u=exp(-length(dom.getX()-[0.1,0.1])**2)
2238             t=0
2239             dt=0.1
2240             while (t<1.):
2241                  u=p.solve(dt)
2242    
2243         """
2244         def __init__(self,domain,num_equations=1,theta=0.5,useSUPG=False,trace=True):
2245            self.__domain=domain
2246            self.__num_equations=num_equations
2247            self.__useSUPG=useSUPG
2248            self.__trace=trace
2249            self.__theta=theta
2250            self.__matrix_type=0
2251            self.__reduced=True
2252            self.__reassemble=True
2253            if self.__useSUPG:
2254               self.__pde=LinearPDE(domain,numEquations=num_equations,numSolutions=num_equations,debug=trace)
2255               self.__pde.setSymmetryOn()
2256               self.__pde.setReducedOrderOn()
2257            else:
2258               self.__transport_problem=self.__getNewTransportProblem()
2259            self.setTolerance()
2260            self.__M=escript.Data()
2261            self.__A=escript.Data()
2262            self.__B=escript.Data()
2263            self.__C=escript.Data()
2264            self.__D=escript.Data()
2265            self.__X=escript.Data()
2266            self.__Y=escript.Data()
2267            self.__d=escript.Data()
2268            self.__y=escript.Data()
2269            self.__d_contact=escript.Data()
2270            self.__y_contact=escript.Data()
2271            self.__r=escript.Data()
2272            self.__q=escript.Data()
2273    
2274         def trace(self,text):
2275                 if self.__trace: print text
2276         def getSafeTimeStepSize(self):
2277            if self.__useSUPG:
2278                if self.__reassemble:
2279                   h=self.__domain.getSize()
2280                   dt=None
2281                   if not self.__A.isEmpty():
2282                      dt2=util.inf(h**2*self.__M/util.length(self.__A))
2283                      if dt == None:
2284                         dt = dt2
2285                      else:
2286                         dt=1./(1./dt+1./dt2)
2287                   if not self.__B.isEmpty():
2288                      dt2=util.inf(h*self.__M/util.length(self.__B))
2289                      if dt == None:
2290                         dt = dt2
2291                      else:
2292                         dt=1./(1./dt+1./dt2)
2293                   if not  self.__C.isEmpty():
2294                      dt2=util.inf(h*self.__M/util.length(self.__C))
2295                      if dt == None:
2296                         dt = dt2
2297                      else:
2298                         dt=1./(1./dt+1./dt2)
2299                   if not self.__D.isEmpty():
2300                      dt2=util.inf(self.__M/util.length(self.__D))
2301                      if dt == None:
2302                         dt = dt2
2303                      else:
2304                         dt=1./(1./dt+1./dt2)
2305                   self.__dt = dt/2
2306                return self.__dt
2307            else:
2308                return self.__getTransportProblem().getSafeTimeStepSize()
2309         def getDomain(self):
2310            return self.__domain
2311         def getTheta(self):
2312            return self.__theta
2313         def getNumEquations(self):
2314            return self.__num_equations
2315         def setReducedOn(self):
2316              if not self.reduced():
2317                  if self.__useSUPG:
2318                     self.__pde.setReducedOrderOn()
2319                  else:
2320                     self.__transport_problem=self.__getNewTransportProblem()
2321              self.__reduced=True
2322         def setReducedOff(self):
2323              if self.reduced():
2324                  if self.__useSUPG:
2325                     self.__pde.setReducedOrderOff()
2326                  else:
2327                     self.__transport_problem=self.__getNewTransportProblem()
2328              self.__reduced=False
2329         def reduced(self):
2330             return self.__reduced
2331         def getFunctionSpace(self):
2332            if self.reduced():
2333               return escript.ReducedSolution(self.getDomain())
2334            else:
2335               return escript.Solution(self.getDomain())
2336    
2337     def getCoefficientOfGeneralPDE(self,name):       def setTolerance(self,tol=1.e-8):
2338       """          self.__tolerance=tol
2339       return the value of the coefficient name of the general PDE          if self.__useSUPG:
2340                  self.__pde.setTolerance(self.__tolerance)
2341    
2342       @param name: name of the coefficient requested.       def __getNewTransportProblem(self):
2343       @type name: C{string}         """
2344       @return: the value of the coefficient name         returns an instance of a new operator
2345       @rtype: L{Data<escript.Data>}         """
2346       @raise IllegalCoefficient: if name is not one of coefficients         self.trace("New Transport problem is allocated.")
2347                    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( \
2348       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.                                 self.getTheta(),
2349       """                                 self.getNumEquations(), \
2350       if not self.getNumEquations() == self.getNumSolutions():                                 self.getFunctionSpace(), \
2351            raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."                                 self.__matrix_type)
2352              
2353       if name == "A" :       def __getNewSolutionVector(self):
2354           A=self.getCoefficient("A")           if self.getNumEquations() ==1 :
2355           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  
2356           else:           else:
2357              if X.isEmpty():                  out=escript.Data(0.0,(self.getNumEquations(),),self.getFunctionSpace())
2358                  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  
2359    
2360  # $Log$       def __getTransportProblem(self):
2361  # Revision 1.14  2005/09/22 01:54:57  jgs         if self.__reassemble:
2362  # Merge of development branch dev-02 back to main trunk on 2005-09-22               self.__source=self.__getNewSolutionVector()
2363  #               self.__transport_problem.reset()
2364  # Revision 1.13  2005/09/15 03:44:19  jgs               self.getDomain().addPDEToTransportProblem(
2365  # Merge of development branch dev-02 back to main trunk on 2005-09-15                           self.__transport_problem,
2366  #                           self.__source,
2367  # Revision 1.12  2005/09/01 03:31:28  jgs                           self.__M,
2368  # Merge of development branch dev-02 back to main trunk on 2005-09-01                           self.__A,
2369  #                           self.__B,
2370  # Revision 1.11  2005/08/23 01:24:28  jgs                           self.__C,
2371  # Merge of development branch dev-02 back to main trunk on 2005-08-23                           self.__D,
2372  #                           self.__X,
2373  # Revision 1.10  2005/08/12 01:45:36  jgs                           self.__Y,
2374  # erge of development branch dev-02 back to main trunk on 2005-08-12                           self.__d,
2375  #                           self.__y,
2376  # Revision 1.9.2.17  2005/09/21 07:03:33  matt                           self.__d_contact,
2377  # PDECoefficient and LinearPDE are now new style classes (introduced in Python                           self.__y_contact)
2378  # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been               self.__transport_problem.insertConstraint(self.__source,self.__q,self.__r)
2379  # modified to instead use portable/cooperative "super" calls to extend base               self.__reassemble=False
2380  # class methods.         return self.__transport_problem
2381  #       def setValue(self,M=None, A=None, B=None, C=None, D=None, X=None, Y=None,
2382  # 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):
2383  # Removed redundant if-loop.               if not M==None:
2384  #                    self.__reassemble=True
2385  # Revision 1.9.2.15  2005/09/14 08:09:18  matt                    self.__M=M
2386  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.               if not A==None:
2387  #                    self.__reassemble=True
2388  # Revision 1.9.2.14  2005/09/07 06:26:16  gross                    self.__A=A
2389  # the solver from finley are put into the standalone package paso now               if not B==None:
2390  #                    self.__reassemble=True
2391  # Revision 1.9.2.13  2005/08/31 08:45:03  gross                    self.__B=B
2392  # in the case of lumping no new system is allocated if the constraint is changed.               if not C==None:
2393  #                    self.__reassemble=True
2394  # Revision 1.9.2.12  2005/08/31 07:10:23  gross                    self.__C=C
2395  # test for Lumping added               if not D==None:
2396  #                    self.__reassemble=True
2397  # Revision 1.9.2.11  2005/08/30 01:53:45  gross                    self.__D=D
2398  # bug in format fixed.               if not X==None:
2399  #                    self.__reassemble=True
2400  # Revision 1.9.2.10  2005/08/26 07:14:17  gross                    self.__X=X
2401  # a few more bugs in linearPDE fixed. remaining problem are finley problems               if not Y==None:
2402  #                    self.__reassemble=True
2403  # Revision 1.9.2.9  2005/08/26 06:30:45  gross                    self.__Y=Y
2404  # fix for reported bug  0000004. test_linearPDE passes a few more tests               if not d==None:
2405  #                    self.__reassemble=True
2406  # Revision 1.9.2.8  2005/08/26 04:30:13  gross                    self.__d=d
2407  # gneric unit testing for linearPDE               if not y==None:
2408  #                    self.__reassemble=True
2409  # Revision 1.9.2.7  2005/08/25 07:06:50  gross                    self.__y=y
2410  # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so               if not d_contact==None:
2411  #                    self.__reassemble=True
2412  # Revision 1.9.2.6  2005/08/24 05:01:24  gross                    self.__d_contact=d_contact
2413  # problem with resetting the matrix in case of resetting its values to 0 fixed.               if not y_contact==None:
2414  #                    self.__reassemble=True
2415  # Revision 1.9.2.5  2005/08/24 02:03:28  gross                    self.__y_contact=y_contact
2416  # epydoc mark up partially fixed               if not q==None:
2417  #                    self.__reassemble=True
2418  # Revision 1.9.2.4  2005/08/22 07:11:09  gross                    self.__q=q
2419  # some problems with LinearPDEs fixed.               if not r==None:
2420  #                    self.__reassemble=True
2421  # Revision 1.9.2.3  2005/08/18 04:48:48  gross                    self.__r=r
2422  # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  
2423  #       def setInitialSolution(self,u):
2424  # Revision 1.9.2.2  2005/08/18 04:39:32  gross               if self.__useSUPG:
2425  # 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())
2426  #               else:
2427  # Revision 1.9.2.1  2005/07/29 07:10:27  gross                   self.__transport_problem.setInitialValue(util.interpolate(u,self.getFunctionSpace()))
2428  # new functions in util and a new pde type in linearPDEs  
2429  #       def solve(self,dt,**kwarg):
2430  # Revision 1.1.2.25  2005/07/28 04:21:09  gross             if self.__useSUPG:
2431  # Lame equation: (linear elastic, isotropic) added                  if self.__reassemble:
2432  #                      self.__pde.setValue(D=self.__M,d=self.__d,d_contact=self.__d_contact,q=self.__q) # ,r=self.__r)
2433  # Revision 1.1.2.24  2005/07/22 06:37:11  gross                      self.__reassemble=False
2434  # some extensions to modellib and linearPDEs                  dt2=self.getSafeTimeStepSize()
2435  #                  nn=max(math.ceil(dt/self.getSafeTimeStepSize()),1.)
2436  # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane                  dt2=dt/nn
2437  # Fixed up some docstrings.  Moved module-level functions to top of file so                  nnn=0
2438  # that epydoc and doxygen can pick them up properly.                  u=self.__u
2439  #                  self.trace("number of substeps is %d."%nn)
2440  # Revision 1.1.2.22  2005/05/12 11:41:30  gross                  while nnn<nn :
2441  # some basic Models have been added                      self.__setSUPG(u,u,dt2/2)
2442  #                      u_half=self.__pde.getSolution(verbose=True)
2443  # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane                      self.__setSUPG(u,u_half,dt2)
2444  # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of                      u=self.__pde.getSolution(verbose=True)
2445  # file so that the AdvectivePDE class is picked up by doxygen.  Some                      nnn+=1
2446  # reformatting of docstrings.  Addition of code to make equations come out                  self.__u=u
2447  # as proper LaTeX.                  return self.__u
2448  #             else:
2449  # Revision 1.1.2.20  2005/04/15 07:09:08  gross                 kwarg["tolerance"]=self.__tolerance
2450  # some problems with functionspace and linearPDEs fixed.                 tp=self.__getTransportProblem()
2451  #                 return tp.solve(self.__source,dt,kwarg)
2452  # Revision 1.1.2.19  2005/03/04 05:27:07  gross       def __setSUPG(self,u0,u,dt):
2453  # bug in SystemPattern fixed.              g=util.grad(u)
2454  #              X=0
2455  # Revision 1.1.2.18  2005/02/08 06:16:45  gross              Y=self.__M*u0
2456  # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed              X=0
2457  #              self.__pde.setValue(r=u0)
2458  # Revision 1.1.2.17  2005/02/08 05:56:19  gross              if not self.__A.isEmpty():
2459  # Reference Number handling added                 X=X+dt*util.matrixmult(self.__A,g)
2460  #              if not self.__B.isEmpty():
2461  # Revision 1.1.2.16  2005/02/07 04:41:28  gross                 X=X+dt*self.__B*u
2462  # some function exposed to python to make mesh merging running              if not  self.__C.isEmpty():
2463  #                 Y=Y+dt*util.inner(self.__C,g)
2464  # Revision 1.1.2.15  2005/02/03 00:14:44  gross              if not self.__D.isEmpty():
2465  # timeseries add and ESySParameter.py renames esysXML.py for consistence                 Y=Y+dt*self.__D*u
2466  #              if not self.__X.isEmpty():
2467  # Revision 1.1.2.14  2005/02/01 06:44:10  gross                 X=X+dt*self.__X
2468  # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working              if not self.__Y.isEmpty():
2469  #                 Y=Y+dt*self.__Y
2470  # Revision 1.1.2.13  2005/01/25 00:47:07  gross              self.__pde.setValue(X=X,Y=Y)
2471  # updates in the documentation              if not self.__y.isEmpty():
2472  #                 self.__pde.setValue(y=dt*self.__y)
2473  # Revision 1.1.2.12  2005/01/12 01:28:04  matt              if not self.__y_contact.isEmpty():
2474  # Added createCoefficient method for linearPDEs.                 self.__pde.setValue(y=dt*self.__y_contact)
2475  #              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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