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trunk/escript/py_src/linearPDEs.py revision 969 by ksteube, Tue Feb 13 23:02:23 2007 UTC temp/escript/py_src/linearPDEs.py revision 1387 by trankine, Fri Jan 11 07:45:26 2008 UTC
# Line 1  Line 1 
1    #
2  # $Id$  # $Id$
3    #
4    #######################################################
5    #
6    #           Copyright 2003-2007 by ACceSS MNRF
7    #       Copyright 2007 by University of Queensland
8    #
9    #                http://esscc.uq.edu.au
10    #        Primary Business: Queensland, Australia
11    #  Licensed under the Open Software License version 3.0
12    #     http://www.opensource.org/licenses/osl-3.0.php
13    #
14    #######################################################
15    #
16    
17  """  """
18  The module provides an interface to define and solve linear partial  The module provides an interface to define and solve linear partial
19  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
# Line 38  class IllegalCoefficient(ValueError): Line 53  class IllegalCoefficient(ValueError):
53     """     """
54     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.
55     """     """
56       pass
57    
58  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
59     """     """
60     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
61     """     """
62       pass
63    
64    class IllegalCoefficientFunctionSpace(ValueError):
65       """
66       raised if an incorrect function space for a coefficient is used.
67       """
68    
69  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
70     """     """
71     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
72     """     """
73       pass
74    
75  class PDECoefficient(object):  class PDECoefficient(object):
76      """      """
# Line 56  class PDECoefficient(object): Line 79  class PDECoefficient(object):
79      @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
80      @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
81      @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
82        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
83        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
84        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
85      @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
86      @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
87      @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 77  class PDECoefficient(object): Line 103  class PDECoefficient(object):
103      OPERATOR=10      OPERATOR=10
104      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
105      BOTH=12      BOTH=12
106        INTERIOR_REDUCED=13
107        BOUNDARY_REDUCED=14
108        CONTACT_REDUCED=15
109    
110      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
111         """         """
112         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
113    
114         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
115         @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},
116                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
117         @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
118                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,
119                (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 94  class PDECoefficient(object): Line 124  class PDECoefficient(object):
124         @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}
125         @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
126         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
127           @param reduced: indicates if reduced
128           @type reduced: C{bool}
129         """         """
130         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
131         self.what=where         self.what=where
# Line 123  class PDECoefficient(object): Line 154  class PDECoefficient(object):
154         """         """
155         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
156              return escript.Function(domain)              return escript.Function(domain)
157           elif self.what==self.INTERIOR_REDUCED:
158                return escript.ReducedFunction(domain)
159         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
160              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
161           elif self.what==self.BOUNDARY_REDUCED:
162                return escript.ReducedFunctionOnBoundary(domain)
163         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
164              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
165           elif self.what==self.CONTACT_REDUCED:
166                return escript.ReducedFunctionOnContactZero(domain)
167         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
168              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
169                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 161  class PDECoefficient(object): Line 198  class PDECoefficient(object):
198         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
199         @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>}
200         @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
201           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
202         """         """
203         if newValue==None:         if newValue==None:
204             newValue=escript.Data()             newValue=escript.Data()
205         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
206             if not newValue.isEmpty():             if not newValue.isEmpty():
207                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
208                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
209                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
210                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
211                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
212         else:         else:
213             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
214         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 313  class LinearPDE(object): Line 352  class LinearPDE(object):
352    
353     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:
354    
355     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)}
356    
357    
358     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,
359     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.
360     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
361     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
362     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
363       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
364       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.
365    
366     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
367    
368     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}
369    
370     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>}.  
371    
372    
373     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 339  class LinearPDE(object): Line 379  class LinearPDE(object):
379    
380     The PDE is symmetrical if     The PDE is symmetrical if
381    
382     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]}
383    
384     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
385    
386     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] }
387    
388     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.
389     The natural boundary conditions take the form:     The natural boundary conditions take the form:
390    
391     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]}
392    
393    
394     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>}.
395    
396       Constraints take the form
397    
398     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
399    
# Line 361  class LinearPDE(object): Line 402  class LinearPDE(object):
402     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
403    
404          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
405            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
406          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
407            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
408          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
409            - M{D_reduced[i,k]=D_reduced[i,k]}
410          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
411            - M{d_reduced[i,k]=d_reduced[k,i]}
412    
413     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
414     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
415     defined as     defined as
416    
417     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]}
418    
419     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
420    
421     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]}
422    
423     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
424     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
425     the contact condition takes the form     the contact condition takes the form
426    
427     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]}
428    
429     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
430     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
431     L{jump<util.jump>}.     L{jump<util.jump>}.
432     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>}.
433       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>}.
434     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
435    
436     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)}
437    
438     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>}.  
439    
440     @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
441     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 481  class LinearPDE(object): Line 526  class LinearPDE(object):
526         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
527         "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),
528         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
529           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
530           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
531           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
532           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
533           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
534           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
535           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
536           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
537           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
538           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
539         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
540         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
541    
# Line 762  class LinearPDE(object): Line 817  class LinearPDE(object):
817                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
818                        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)
819                        out=False                        out=False
820             # and now the reduced coefficients
821             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
822             if not A_reduced.isEmpty():
823                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
824                if self.getNumSolutions()>1:
825                   for i in range(self.getNumEquations()):
826                      for j in range(self.getDim()):
827                         for k in range(self.getNumSolutions()):
828                            for l in range(self.getDim()):
829                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
830                                   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)
831                                   out=False
832                else:
833                   for j in range(self.getDim()):
834                      for l in range(self.getDim()):
835                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
836                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
837                            out=False
838             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
839             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
840             if B_reduced.isEmpty() and not C_reduced.isEmpty():
841                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
842                out=False
843             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
844                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
845                out=False
846             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
847                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
848                if self.getNumSolutions()>1:
849                   for i in range(self.getNumEquations()):
850                       for j in range(self.getDim()):
851                          for k in range(self.getNumSolutions()):
852                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
853                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
854                                  out=False
855                else:
856                   for j in range(self.getDim()):
857                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
858                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
859                         out=False
860             if self.getNumSolutions()>1:
861               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
862               if not D_reduced.isEmpty():
863                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
864                 for i in range(self.getNumEquations()):
865                    for k in range(self.getNumSolutions()):
866                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
867                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
868                          out=False
869               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
870               if not d_reduced.isEmpty():
871                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
872                 for i in range(self.getNumEquations()):
873                    for k in range(self.getNumSolutions()):
874                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
875                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
876                          out=False
877               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
878               if not d_contact_reduced.isEmpty():
879                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
880                 for i in range(self.getNumEquations()):
881                    for k in range(self.getNumSolutions()):
882                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
883                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
884                          out=False
885        return out        return out
886    
887     def getSolution(self,**options):     def getSolution(self,**options):
# Line 801  class LinearPDE(object): Line 921  class LinearPDE(object):
921       """       """
922       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
923    
924       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]}
925    
926       or       or
927    
928       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]}
929    
930       @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.
931       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 813  class LinearPDE(object): Line 933  class LinearPDE(object):
933       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
934       """       """
935       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
936       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))) \
937               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
938               -util.self.getCoefficientOfGeneralPDE("X") \
939               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
940               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
941               -util.self.getCoefficientOfGeneralPDE("X_reduced")
942     # =============================================================================     # =============================================================================
943     #   solver settings:     #   solver settings:
944     # =============================================================================     # =============================================================================
# Line 826  class LinearPDE(object): Line 951  class LinearPDE(object):
951         @param preconditioner: sets a new solver method.         @param preconditioner: sets a new solver method.
952         @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}
953         """         """
954         if solver==None: solve=self.DEFAULT         if solver==None: solver=self.__solver_method
955           if preconditioner==None: preconditioner=self.__preconditioner
956           if solver==None: solver=self.DEFAULT
957         if preconditioner==None: preconditioner=self.DEFAULT         if preconditioner==None: preconditioner=self.DEFAULT
958         if not (solver,preconditioner)==self.getSolverMethod():         if not (solver,preconditioner)==self.getSolverMethod():
959             self.__solver_method=solver             self.__solver_method=solver
# Line 1210  class LinearPDE(object): Line 1337  class LinearPDE(object):
1337         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1338             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1339         else:         else:
1340             self.__righthandside*=0             self.__righthandside.setToZero()
1341             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1342         return self.__righthandside         return self.__righthandside
1343    
# Line 1260  class LinearPDE(object): Line 1387  class LinearPDE(object):
1387       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1388       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1389       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1390                    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},
1391                      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}.
1392       """       """
1393       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1394          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1288  class LinearPDE(object): Line 1416  class LinearPDE(object):
1416       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1417       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1418       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1419                    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},
1420                      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}.
1421       """       """
1422       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1423          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1304  class LinearPDE(object): Line 1433  class LinearPDE(object):
1433       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1434       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1435       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1436                    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},
1437                      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}.
1438       """       """
1439       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1440          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1320  class LinearPDE(object): Line 1450  class LinearPDE(object):
1450       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1451       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1452       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1453                    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},
1454                      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}.
1455       """       """
1456       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1457          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 1450  class LinearPDE(object): Line 1581  class LinearPDE(object):
1581        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1582        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1583        @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>}.
1584          @keyword A_reduced: value for coefficient A_reduced.
1585          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1586        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1587        @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>}.
1588          @keyword B_reduced: value for coefficient B_reduced
1589          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1590        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1591        @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>}.
1592          @keyword C_reduced: value for coefficient C_reduced
1593          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1594        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1595        @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>}.
1596          @keyword D_reduced: value for coefficient D_reduced
1597          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1598        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1599        @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>}.
1600          @keyword X_reduced: value for coefficient X_reduced
1601          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1602        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1603        @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>}.
1604          @keyword Y_reduced: value for coefficient Y_reduced
1605          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1606        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1607        @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>}.
1608          @keyword d_reduced: value for coefficient d_reduced
1609          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
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{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1612        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1613        @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>}.
1614                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1615          @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>}.
1616        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1617        @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>}.
1618                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1619          @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>}.
1620        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1621        @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>}
1622                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1504  class LinearPDE(object): Line 1651  class LinearPDE(object):
1651        # 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:
1652        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1653          try:          try:
1654             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1655                                             self.getNumEquations(),self.getNumSolutions(),
1656                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1657               self.alteredCoefficient(i)
1658            except IllegalCoefficientFunctionSpace,m:
1659                # if the function space is wrong then we try the reduced version:
1660                i_red=i+"_reduced"
1661                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1662                    try:
1663                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1664                                                          self.getNumEquations(),self.getNumSolutions(),
1665                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1666                        self.alteredCoefficient(i_red)
1667                    except IllegalCoefficientValue,m:
1668                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1669                    except IllegalCoefficientFunctionSpace,m:
1670                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1671                else:
1672                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1673          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1674             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1675        self.__altered_coefficients=True        self.__altered_coefficients=True
1676        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1677        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1535  class LinearPDE(object): Line 1698  class LinearPDE(object):
1698                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1699                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient A in lumped matrix may not be present."
1700                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1701                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient B in lumped matrix may not be present."
1702                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1703                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient C in lumped matrix may not be present."
1704                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1705                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1706                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1707                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1708                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1709                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1710                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1711                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1712                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1713                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1714                   D=self.getCoefficientOfGeneralPDE("D")                   D=self.getCoefficientOfGeneralPDE("D")
1715                     d=self.getCoefficientOfGeneralPDE("d")
1716                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1717                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1718                   if not D.isEmpty():                   if not D.isEmpty():
1719                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
                         #D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))  
1720                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1721                       else:                       else:
1722                          D_times_e=D                          D_times_e=D
1723                   else:                   else:
1724                      D_times_e=escript.Data()                      D_times_e=escript.Data()
                  d=self.getCoefficientOfGeneralPDE("d")  
1725                   if not d.isEmpty():                   if not d.isEmpty():
1726                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
                         #d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))  
1727                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1728                       else:                       else:
1729                          d_times_e=d                          d_times_e=d
1730                   else:                   else:
1731                      d_times_e=escript.Data()                      d_times_e=escript.Data()
1732                   d_contact=self.getCoefficientOfGeneralPDE("d_contact")        
1733                   if not d_contact.isEmpty():                   if not D_reduced.isEmpty():
1734                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1735                          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(),)))
1736                       else:                       else:
1737                          d_contact_times_e=d_contact                          D_reduced_times_e=D_reduced
1738                   else:                   else:
1739                      d_contact_times_e=escript.Data()                      D_reduced_times_e=escript.Data()
1740                         if not d_reduced.isEmpty():
1741                         if self.getNumSolutions()>1:
1742                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1743                         else:
1744                            d_reduced_times_e=d_reduced
1745                     else:
1746                        d_reduced_times_e=escript.Data()
1747    
1748                   self.__operator=self.__getNewRightHandSide()                   self.__operator=self.__getNewRightHandSide()
1749                   self.getDomain().addPDEToRHS(self.__operator, \                   if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1750                                                escript.Data(), \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1751                                                D_times_e, \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1752                                                d_times_e,\                   else:
1753                                                d_contact_times_e)                      self.getDomain().addPDEToRHS(self.__operator, \
1754                                                     escript.Data(), \
1755                                                     D_times_e, \
1756                                                     d_times_e,\
1757                                                     escript.Data())
1758                        self.getDomain().addPDEToRHS(self.__operator, \
1759                                                     escript.Data(), \
1760                                                     D_reduced_times_e, \
1761                                                     d_reduced_times_e,\
1762                                                     escript.Data())
1763                   self.__operator=1./self.__operator                   self.__operator=1./self.__operator
1764                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1765                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1580  class LinearPDE(object): Line 1769  class LinearPDE(object):
1769                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1770                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1771                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1772                     self.getDomain().addPDEToRHS(self.__righthandside, \
1773                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1774                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1775                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1776                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1777                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1778                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1779            else:            else:
# Line 1595  class LinearPDE(object): Line 1789  class LinearPDE(object):
1789                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1790                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1791                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1792                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1793                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1794                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1797                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1798                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1799                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1800                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1802                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1803                   self.__applyConstraint()                   self.__applyConstraint()
1804                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1805                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1606  class LinearPDE(object): Line 1811  class LinearPDE(object):
1811                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1812                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1813                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1814                     self.getDomain().addPDEToRHS(self.__righthandside, \
1815                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1816                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1817                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1818                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1819                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1820                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1821                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1621  class LinearPDE(object): Line 1831  class LinearPDE(object):
1831                              escript.Data(),\                              escript.Data(),\
1832                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1833                              escript.Data())                              escript.Data())
1834                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1835                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1836                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1837                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1838                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1839                                escript.Data(), \
1840                                escript.Data(), \
1841                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1842                                escript.Data(),\
1843                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1844                                escript.Data())
1845                   self.__applyConstraint()                   self.__applyConstraint()
1846                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1847                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1654  class Poisson(LinearPDE): Line 1875  class Poisson(LinearPDE):
1875       """       """
1876       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1877       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1878                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1879                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1880       self.setSymmetryOn()       self.setSymmetryOn()
1881    
1882     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1702  class Poisson(LinearPDE): Line 1924  class Poisson(LinearPDE):
1924           return escript.Data()           return escript.Data()
1925       elif name == "y_contact" :       elif name == "y_contact" :
1926           return escript.Data()           return escript.Data()
1927         elif name == "A_reduced" :
1928             return escript.Data()
1929         elif name == "B_reduced" :
1930             return escript.Data()
1931         elif name == "C_reduced" :
1932             return escript.Data()
1933         elif name == "D_reduced" :
1934             return escript.Data()
1935         elif name == "X_reduced" :
1936             return escript.Data()
1937         elif name == "Y_reduced" :
1938             return self.getCoefficient("f_reduced")
1939         elif name == "d_reduced" :
1940             return escript.Data()
1941         elif name == "y_reduced" :
1942             return escript.Data()
1943         elif name == "d_contact_reduced" :
1944             return escript.Data()
1945         elif name == "y_contact_reduced" :
1946             return escript.Data()
1947       elif name == "r" :       elif name == "r" :
1948           return escript.Data()           return escript.Data()
1949       elif name == "q" :       elif name == "q" :
# Line 1738  class Helmholtz(LinearPDE): Line 1980  class Helmholtz(LinearPDE):
1980       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1981                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1982                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1983                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1984                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1985                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1986                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1987                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1988                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1989       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1801  class Helmholtz(LinearPDE): Line 2045  class Helmholtz(LinearPDE):
2045           return escript.Data()           return escript.Data()
2046       elif name == "y_contact" :       elif name == "y_contact" :
2047           return escript.Data()           return escript.Data()
2048         elif name == "A_reduced" :
2049             return escript.Data()
2050         elif name == "B_reduced" :
2051             return escript.Data()
2052         elif name == "C_reduced" :
2053             return escript.Data()
2054         elif name == "D_reduced" :
2055             return escript.Data()
2056         elif name == "X_reduced" :
2057             return escript.Data()
2058         elif name == "Y_reduced" :
2059             return self.getCoefficient("f_reduced")
2060         elif name == "d_reduced" :
2061             return escript.Data()
2062         elif name == "y_reduced" :
2063            return self.getCoefficient("g_reduced")
2064         elif name == "d_contact_reduced" :
2065             return escript.Data()
2066         elif name == "y_contact_reduced" :
2067             return escript.Data()
2068       elif name == "r" :       elif name == "r" :
2069           return self.getCoefficient("r")           return self.getCoefficient("r")
2070       elif name == "q" :       elif name == "q" :
# Line 1899  class LameEquation(LinearPDE): Line 2163  class LameEquation(LinearPDE):
2163           return escript.Data()           return escript.Data()
2164       elif name == "y_contact" :       elif name == "y_contact" :
2165           return escript.Data()           return escript.Data()
2166         elif name == "A_reduced" :
2167             return escript.Data()
2168         elif name == "B_reduced" :
2169             return escript.Data()
2170         elif name == "C_reduced" :
2171             return escript.Data()
2172         elif name == "D_reduced" :
2173             return escript.Data()
2174         elif name == "X_reduced" :
2175             return escript.Data()
2176         elif name == "Y_reduced" :
2177             return escript.Data()
2178         elif name == "d_reduced" :
2179             return escript.Data()
2180         elif name == "y_reduced" :
2181             return escript.Data()
2182         elif name == "d_contact_reduced" :
2183             return escript.Data()
2184         elif name == "y_contact_reduced" :
2185             return escript.Data()
2186       elif name == "r" :       elif name == "r" :
2187           return self.getCoefficient("r")           return self.getCoefficient("r")
2188       elif name == "q" :       elif name == "q" :
# Line 1906  class LameEquation(LinearPDE): Line 2190  class LameEquation(LinearPDE):
2190       else:       else:
2191          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2192    
 class AdvectivePDE(LinearPDE):  
    """  
    In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}  
    up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.  
   
    In the following we set  
   
    M{Z[j]=C[j]-B[j]}  
   
    or  
   
    M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}  
   
    To measure the dominance of the advective terms over the diffusive term M{A} the  
    X{Pelclet number} M{P} is used. It is defined as  
   
    M{P=h|Z|/(2|A|)}  
   
    where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size  
    from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.  
   
    From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:  
   
    M{S{Xi}=S{xi}(P) h/|Z|}  
   
    where M{S{xi}} is a suitable function of the Peclet number.  
   
    In the case of a single PDE the coefficient are up-dated in the following way:  
          - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}  
          - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}  
          - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}  
          - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}  
   
    Similar for the case of a systems of PDEs:  
          - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}  
          - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}  
          - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}  
          - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}  
   
    where M{S{delta}} is L{kronecker}.  
    Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}  
    but with the intension to stabilize the solution.  
   
    """  
    def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):  
       """  
       creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}  
   
       @param domain: domain of the PDE  
       @type domain: L{Domain<escript.Domain>}  
       @param numEquations: number of equations. If numEquations==None the number of equations  
                            is exracted from the PDE coefficients.  
       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components  
                            is exracted from the PDE coefficients.  
       @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the  
                  M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.  
       @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.  
       @param debug: if True debug informations are printed.  
       """  
       super(AdvectivePDE, self).__init__(domain,\  
                                          numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def setValue(self,**coefficients):  
       """  
       sets new values to coefficients  
   
       @param coefficients: new values assigned to coefficients  
       @keyword A: value for coefficient A.  
       @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword B: value for coefficient B  
       @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword C: value for coefficient C  
       @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword D: value for coefficient D  
       @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword X: value for coefficient X  
       @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword Y: value for coefficient Y  
       @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.  
       @keyword d: value for coefficient d  
       @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
       @keyword y: value for coefficient y  
       @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
       @keyword d_contact: value for coefficient d_contact  
       @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
                        or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.  
       @keyword y_contact: value for coefficient y_contact  
       @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
                        or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.  
       @keyword r: values prescribed to the solution at the locations of constraints  
       @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}  
                depending of reduced order is used for the solution.  
       @keyword q: mask for location of constraints  
       @type q: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}  
                depending of reduced order is used for the representation of the equation.  
       @raise IllegalCoefficient: if an unknown coefficient keyword is used.  
   
       """  
       if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()  
       super(AdvectivePDE, self).setValue(**coefficients)  
   
    def ELMAN_RAMAGE(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)  
           - M{S{xi}(P)=0} for M{P<1}  
           - M{S{xi}(P)=(1-1/P)/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))  
   
    def SIMPLIFIED_BROOK_HUGHES(self,P):  
      """  
      Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.  
      The original methods is  
   
      M{S{xi}(P)=coth(P)-1/P}  
   
      As the evaluation of M{coth} is expensive we are using the approximation:  
   
          - M{S{xi}(P)=P/3} where M{P<3}  
          - M{S{xi}(P)=1/2} otherwise  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      c=util.whereNegative(P-3.)  
      return P/6.*c+1./2.*(1.-c)  
   
    def HALF(self,P):  
      """  
      Predefined function to set value M{1/2} for M{S{xi}}  
   
      @param P: Preclet number  
      @type P: L{Scalar<escript.Scalar>}  
      @return: up-wind weightimg factor  
      @rtype: L{Scalar<escript.Scalar>}  
      """  
      return escript.Scalar(0.5,P.getFunctionSpace())  
   
    def __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  
   
   
    def getCoefficientOfGeneralPDE(self,name):  
      """  
      return the value of the coefficient name of the general PDE  
   
      @param name: name of the coefficient requested.  
      @type name: C{string}  
      @return: the value of the coefficient name  
      @rtype: L{Data<escript.Data>}  
      @raise IllegalCoefficient: if name is not one of coefficients  
                   M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.  
      @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.  
      """  
      if not self.getNumEquations() == self.getNumSolutions():  
           raise ValueError,"AdvectivePDE expects the number of solution componets and the number of equations to be equal."  
   
      if name == "A" :  
          A=self.getCoefficient("A")  
          B=self.getCoefficient("B")  
          C=self.getCoefficient("C")  
          if B.isEmpty() and C.isEmpty():  
             Aout=A  
          else:  
             if A.isEmpty():  
                Aout=self.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  
          else:  
             if X.isEmpty():  
                 Xout=self.createCoefficientOfGeneralPDE("X")  
             else:  
                 Xout=X[:]  
             Xi=self.__getXi()  
             if self.getNumEquations()>1:  
                  for p in range(self.getNumEquations()):  
                     tmp=Xi*Y[p]  
                     for i in range(self.getNumEquations()):  
                        for j in range(self.getDim()):  
                           if not C.isEmpty() and not B.isEmpty():  
                              Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])  
                              # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)  
                           elif C.isEmpty():  
                              Xout[i,j]-=tmp*B[p,j,i]  
                              # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)  
                           else:  
                              Xout[i,j]+=tmp*C[p,i,j]  
                              # Xout=X_out+Xi*util.inner(Y,C,offset=1)  
             else:  
               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  
   
 # $Log$  
 # Revision 1.14  2005/09/22 01:54:57  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-22  
 #  
 # Revision 1.13  2005/09/15 03:44:19  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-15  
 #  
 # Revision 1.12  2005/09/01 03:31:28  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-09-01  
 #  
 # Revision 1.11  2005/08/23 01:24:28  jgs  
 # Merge of development branch dev-02 back to main trunk on 2005-08-23  
 #  
 # Revision 1.10  2005/08/12 01:45:36  jgs  
 # erge of development branch dev-02 back to main trunk on 2005-08-12  
 #  
 # Revision 1.9.2.17  2005/09/21 07:03:33  matt  
 # PDECoefficient and LinearPDE are now new style classes (introduced in Python  
 # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been  
 # modified to instead use portable/cooperative "super" calls to extend base  
 # class methods.  
 #  
 # Revision 1.9.2.16  2005/09/16 01:54:37  matt  
 # Removed redundant if-loop.  
 #  
 # Revision 1.9.2.15  2005/09/14 08:09:18  matt  
 # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.  
 #  
 # Revision 1.9.2.14  2005/09/07 06:26:16  gross  
 # the solver from finley are put into the standalone package paso now  
 #  
 # Revision 1.9.2.13  2005/08/31 08:45:03  gross  
 # in the case of lumping no new system is allocated if the constraint is changed.  
 #  
 # Revision 1.9.2.12  2005/08/31 07:10:23  gross  
 # test for Lumping added  
 #  
 # Revision 1.9.2.11  2005/08/30 01:53:45  gross  
 # bug in format fixed.  
 #  
 # Revision 1.9.2.10  2005/08/26 07:14:17  gross  
 # a few more bugs in linearPDE fixed. remaining problem are finley problems  
 #  
 # Revision 1.9.2.9  2005/08/26 06:30:45  gross  
 # fix for reported bug  0000004. test_linearPDE passes a few more tests  
 #  
 # Revision 1.9.2.8  2005/08/26 04:30:13  gross  
 # gneric unit testing for linearPDE  
 #  
 # Revision 1.9.2.7  2005/08/25 07:06:50  gross  
 # linearPDE documentation is parsed now by epydoc. there is still a problem with links into escriptcpp.so  
 #  
 # Revision 1.9.2.6  2005/08/24 05:01:24  gross  
 # problem with resetting the matrix in case of resetting its values to 0 fixed.  
 #  
 # Revision 1.9.2.5  2005/08/24 02:03:28  gross  
 # epydoc mark up partially fixed  
 #  
 # Revision 1.9.2.4  2005/08/22 07:11:09  gross  
 # some problems with LinearPDEs fixed.  
 #  
 # Revision 1.9.2.3  2005/08/18 04:48:48  gross  
 # the methods SetLumping*() are removed. Lumping is set trough setSolverMethod(LinearPDE.LUMPING)  
 #  
 # Revision 1.9.2.2  2005/08/18 04:39:32  gross  
 # the constants have been removed from util.py as they not needed anymore. PDE related constants are accessed through LinearPDE attributes now  
 #  
 # Revision 1.9.2.1  2005/07/29 07:10:27  gross  
 # new functions in util and a new pde type in linearPDEs  
 #  
 # Revision 1.1.2.25  2005/07/28 04:21:09  gross  
 # Lame equation: (linear elastic, isotropic) added  
 #  
 # Revision 1.1.2.24  2005/07/22 06:37:11  gross  
 # some extensions to modellib and linearPDEs  
 #  
 # Revision 1.1.2.23  2005/05/13 00:55:20  cochrane  
 # Fixed up some docstrings.  Moved module-level functions to top of file so  
 # that epydoc and doxygen can pick them up properly.  
 #  
 # Revision 1.1.2.22  2005/05/12 11:41:30  gross  
 # some basic Models have been added  
 #  
 # Revision 1.1.2.21  2005/05/12 07:16:12  cochrane  
 # Moved ELMAN_RAMAGE, SIMPLIFIED_BROOK_HUGHES, and HALF functions to bottom of  
 # file so that the AdvectivePDE class is picked up by doxygen.  Some  
 # reformatting of docstrings.  Addition of code to make equations come out  
 # as proper LaTeX.  
 #  
 # Revision 1.1.2.20  2005/04/15 07:09:08  gross  
 # some problems with functionspace and linearPDEs fixed.  
 #  
 # Revision 1.1.2.19  2005/03/04 05:27:07  gross  
 # bug in SystemPattern fixed.  
 #  
 # Revision 1.1.2.18  2005/02/08 06:16:45  gross  
 # Bugs in AdvectivePDE fixed, AdvectiveTest is stable but more testing is needed  
 #  
 # Revision 1.1.2.17  2005/02/08 05:56:19  gross  
 # Reference Number handling added  
 #  
 # Revision 1.1.2.16  2005/02/07 04:41:28  gross  
 # some function exposed to python to make mesh merging running  
 #  
 # Revision 1.1.2.15  2005/02/03 00:14:44  gross  
 # timeseries add and ESySParameter.py renames esysXML.py for consistence  
 #  
 # Revision 1.1.2.14  2005/02/01 06:44:10  gross  
 # new implementation of AdvectivePDE which now also updates right hand side. systems of PDEs are still not working  
 #  
 # Revision 1.1.2.13  2005/01/25 00:47:07  gross  
 # updates in the documentation  
 #  
 # Revision 1.1.2.12  2005/01/12 01:28:04  matt  
 # Added createCoefficient method for linearPDEs.  
 #  
 # Revision 1.1.2.11  2005/01/11 01:55:34  gross  
 # a problem in linearPDE class fixed  
 #  
 # Revision 1.1.2.10  2005/01/07 01:13:29  gross  
 # some bugs in linearPDE fixed  
 #  
 # Revision 1.1.2.9  2005/01/06 06:24:58  gross  
 # some bugs in slicing fixed  
 #  
 # Revision 1.1.2.8  2005/01/05 04:21:40  gross  
 # FunctionSpace checking/matchig in slicing added  
 #  
 # Revision 1.1.2.7  2004/12/29 10:03:41  gross  
 # bug in setValue fixed  
 #  
 # Revision 1.1.2.6  2004/12/29 05:29:59  gross  
 # AdvectivePDE successfully tested for Peclet number 1000000. there is still a problem with setValue and Data()  
 #  
 # Revision 1.1.2.5  2004/12/29 00:18:41  gross  
 # AdvectivePDE added  
 #  
 # Revision 1.1.2.4  2004/12/24 06:05:41  gross  
 # some changes in linearPDEs to add AdevectivePDE  
 #  
 # Revision 1.1.2.3  2004/12/16 00:12:34  gross  
 # __init__ of LinearPDE does not accept any coefficient anymore  
 #  
 # Revision 1.1.2.2  2004/12/14 03:55:01  jgs  
 # *** empty log message ***  
 #  
 # Revision 1.1.2.1  2004/12/12 22:53:47  gross  
 # linearPDE has been renamed LinearPDE  
 #  
 # Revision 1.1.1.1.2.7  2004/12/07 10:13:08  gross  
 # GMRES added  
 #  
 # Revision 1.1.1.1.2.6  2004/12/07 03:19:50  gross  
 # options for GMRES and PRES20 added  
 #  
 # Revision 1.1.1.1.2.5  2004/12/01 06:25:15  gross  
 # some small changes  
 #  
 # Revision 1.1.1.1.2.4  2004/11/24 01:50:21  gross  
 # Finley solves 4M unknowns now  
 #  
 # Revision 1.1.1.1.2.3  2004/11/15 06:05:26  gross  
 # poisson solver added  
 #  
 # Revision 1.1.1.1.2.2  2004/11/12 06:58:15  gross  
 # a lot of changes to get the linearPDE class running: most important change is that there is no matrix format exposed to the user anymore. the format is chosen by the Domain according to the solver and symmetry  
 #  
 # Revision 1.1.1.1.2.1  2004/10/28 22:59:22  gross  
 # finley's RecTest.py is running now: problem in SystemMatrixAdapater fixed  
 #  
 # Revision 1.1.1.1  2004/10/26 06:53:56  jgs  
 # initial import of project esys2  
 #  
 # Revision 1.3.2.3  2004/10/26 06:43:48  jgs  
 # committing Lutz's and Paul's changes to brach jgs  
 #  
 # Revision 1.3.4.1  2004/10/20 05:32:51  cochrane  
 # Added incomplete Doxygen comments to files, or merely put the docstrings that already exist into Doxygen form.  
 #  
 # Revision 1.3  2004/09/23 00:53:23  jgs  
 # minor fixes  
 #  
 # Revision 1.1  2004/08/28 12:58:06  gross  
 # SimpleSolve is not running yet: problem with == of functionsspace  
 #  

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