/[escript]/trunk/escript/py_src/linearPDEs.py
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revision 969 by ksteube, Tue Feb 13 23:02:23 2007 UTC revision 1118 by gross, Tue Apr 24 08:55:04 2007 UTC
# Line 38  class IllegalCoefficient(ValueError): Line 38  class IllegalCoefficient(ValueError):
38     """     """
39     raised if an illegal coefficient of the general ar particular PDE is requested.     raised if an illegal coefficient of the general ar particular PDE is requested.
40     """     """
41       pass
42    
43  class IllegalCoefficientValue(ValueError):  class IllegalCoefficientValue(ValueError):
44     """     """
45     raised if an incorrect value for a coefficient is used.     raised if an incorrect value for a coefficient is used.
46     """     """
47       pass
48    
49    class IllegalCoefficientFunctionSpace(ValueError):
50       """
51       raised if an incorrect function space for a coefficient is used.
52       """
53    
54  class UndefinedPDEError(ValueError):  class UndefinedPDEError(ValueError):
55     """     """
56     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
57     """     """
58       pass
59    
60  class PDECoefficient(object):  class PDECoefficient(object):
61      """      """
# Line 56  class PDECoefficient(object): Line 64  class PDECoefficient(object):
64      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain      @cvar INTERIOR: indicator that coefficient is defined on the interior of the PDE domain
65      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain      @cvar BOUNDARY: indicator that coefficient is defined on the boundary of the PDE domain
66      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain      @cvar CONTACT: indicator that coefficient is defined on the contact region within the PDE domain
67        @cvar INTERIOR_REDUCED: indicator that coefficient is defined on the interior of the PDE domain using a reduced integration order
68        @cvar BOUNDARY_REDUCED: indicator that coefficient is defined on the boundary of the PDE domain using a reduced integration order
69        @cvar CONTACT_REDUCED: indicator that coefficient is defined on the contact region within the PDE domain using a reduced integration order
70      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE      @cvar SOLUTION: indicator that coefficient is defined trough a solution of the PDE
71      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE      @cvar REDUCED: indicator that coefficient is defined trough a reduced solution of the PDE
72      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations      @cvar BY_EQUATION: indicator that the dimension of the coefficient shape is defined by the number PDE equations
# Line 77  class PDECoefficient(object): Line 88  class PDECoefficient(object):
88      OPERATOR=10      OPERATOR=10
89      RIGHTHANDSIDE=11      RIGHTHANDSIDE=11
90      BOTH=12      BOTH=12
91        INTERIOR_REDUCED=13
92        BOUNDARY_REDUCED=14
93        CONTACT_REDUCED=15
94    
95      def __init__(self,where,pattern,altering):      def __init__(self, where, pattern, altering):
96         """         """
97         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
98    
99         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
100         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED}         @type where: one of L{INTERIOR}, L{BOUNDARY}, L{CONTACT}, L{SOLUTION}, L{REDUCED},
101                               L{INTERIOR_REDUCED}, L{BOUNDARY_REDUCED}, L{CONTACT_REDUCED}.
102         @param pattern: describes the shape of the coefficient and how the shape is build for a given         @param pattern: describes the shape of the coefficient and how the shape is build for a given
103                spatial dimension and numbers of equation and solution in then PDE. For instance,                spatial dimension and numbers of equation and solution in then PDE. For instance,
104                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which                (L{BY_EQUATION},L{BY_SOLUTION},L{BY_DIM}) descrbes a rank 3 coefficient which
# Line 94  class PDECoefficient(object): Line 109  class PDECoefficient(object):
109         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}         @type pattern: C{tuple} of L{BY_EQUATION}, L{BY_SOLUTION}, L{BY_DIM}
110         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered         @param altering: indicates what part of the PDE is altered if the coefficiennt is altered
111         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
112           @param reduced: indicates if reduced
113           @type reduced: C{bool}
114         """         """
115         super(PDECoefficient, self).__init__()         super(PDECoefficient, self).__init__()
116         self.what=where         self.what=where
# Line 123  class PDECoefficient(object): Line 139  class PDECoefficient(object):
139         """         """
140         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
141              return escript.Function(domain)              return escript.Function(domain)
142           elif self.what==self.INTERIOR_REDUCED:
143                return escript.ReducedFunction(domain)
144         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
145              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
146           elif self.what==self.BOUNDARY_REDUCED:
147                return escript.ReducedFunctionOnBoundary(domain)
148         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
149              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
150           elif self.what==self.CONTACT_REDUCED:
151                return escript.ReducedFunctionOnContactZero(domain)
152         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
153              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
154                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
# Line 161  class PDECoefficient(object): Line 183  class PDECoefficient(object):
183         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
184         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}         @type newValue: any object that can be converted into a L{Data<escript.Data>} object with the appropriate shape and L{FunctionSpace<escript.FunctionSpace>}
185         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient         @raise IllegalCoefficientValue: if the shape of the assigned value does not match the shape of the coefficient
186           @raise IllegalCoefficientFunctionSpace: if unable to interploate value to appropriate function space
187         """         """
188         if newValue==None:         if newValue==None:
189             newValue=escript.Data()             newValue=escript.Data()
190         elif isinstance(newValue,escript.Data):         elif isinstance(newValue,escript.Data):
191             if not newValue.isEmpty():             if not newValue.isEmpty():
192                try:                if not newValue.getFunctionSpace() == self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder):
193                   newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))                  try:
194                except:                    newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
195                   raise IllegalCoefficientValue,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)                  except:
196                      raise IllegalCoefficientFunctionSpace,"Unable to interpolate coefficient to function space %s"%self.getFunctionSpace(domain)
197         else:         else:
198             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))             newValue=escript.Data(newValue,self.getFunctionSpace(domain,reducedEquationOrder,reducedSolutionOrder))
199         if not newValue.isEmpty():         if not newValue.isEmpty():
# Line 313  class LinearPDE(object): Line 337  class LinearPDE(object):
337    
338     For a single PDE with a solution with a single component the linear PDE is defined in the following form:     For a single PDE with a solution with a single component the linear PDE is defined in the following form:
339    
340     M{-grad(A[j,l]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}     M{-(grad(A[j,l]+A_reduced[j,l])*grad(u)[l]+(B[j]+B_reduced[j])u)[j]+(C[l]+C_reduced[l])*grad(u)[l]+(D+D_reduced)=-grad(X+X_reduced)[j,j]+(Y+Y_reduced)}
341    
342    
343     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,     where M{grad(F)} denotes the spatial derivative of M{F}. Einstein's summation convention,
344     ie. summation over indexes appearing twice in a term of a sum is performed, is used.     ie. summation over indexes appearing twice in a term of a sum is performed, is used.
345     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the     The coefficients M{A}, M{B}, M{C}, M{D}, M{X} and M{Y} have to be specified through L{Data<escript.Data>} objects in the
346     L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.     L{Function<escript.Function>} and the coefficients M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced} and M{Y_reduced} have to be specified through L{Data<escript.Data>} objects in the
347     M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.     L{ReducedFunction<escript.ReducedFunction>}. It is also allowd to use objects that can be converted into
348       such L{Data<escript.Data>} objects. M{A} and M{A_reduced} are rank two, M{B_reduced}, M{C_reduced}, M{X_reduced}
349       M{B_reduced}, M{C_reduced} and M{X_reduced} are rank one and M{D}, M{D_reduced} and M{Y_reduced} are scalar.
350    
351     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
352    
353     M{n[j]*(A[i,j]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}     M{n[j]*((A[i,j]+A_reduced[i,j])*grad(u)[l]+(B+B_reduced)[j]*u)+(d+d_reduced)*u=n[j]*(X[j]+X_reduced[j])+y}
354    
355     where M{n} is the outer normal field calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.     where M{n} is the outer normal field. Notice that the coefficients M{A}, M{A_reduced}, M{B}, M{B_reduced}, M{X} and M{X_reduced} are defined in the PDE. The coefficients M{d} and M{y} and are each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>} and the coefficients M{d_reduced} and M{y_reduced} and are each a scalar in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
    Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are  
    each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.  
356    
357    
358     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form     Constraints for the solution prescribing the value of the solution at certain locations in the domain. They have the form
# Line 339  class LinearPDE(object): Line 364  class LinearPDE(object):
364    
365     The PDE is symmetrical if     The PDE is symmetrical if
366    
367     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]}     M{A[i,j]=A[j,i]}  and M{B[j]=C[j]} and M{A_reduced[i,j]=A_reduced[j,i]}  and M{B_reduced[j]=C_reduced[j]
368    
369     For a system of PDEs and a solution with several components the PDE has the form     For a system of PDEs and a solution with several components the PDE has the form
370    
371     M{-grad(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])[j]+C[i,k,l]*grad(u[k])[l]+D[i,k]*u[k] =-grad(X[i,j])[j]+Y[i] }     M{-grad((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])[j]+(C[i,k,l]+C_reduced[i,k,l])*grad(u[k])[l]+(D[i,k]+D_reduced[i,k]*u[k] =-grad(X[i,j]+X_reduced[i,j])[j]+Y[i]+Y_reduced[i] }
372    
373     M{A} is a ramk four, M{B} and M{C} are each a rank three, M{D} and M{X} are each a rank two and M{Y} is a rank one.     M{A} and M{A_reduced} are of rank four, M{B}, M{B_reduced}, M{C} and M{C_reduced} are each of rank three, M{D}, M{D_reduced}, M{X_reduced} and M{X} are each a rank two and M{Y} and M{Y_reduced} are of rank one.
374     The natural boundary conditions take the form:     The natural boundary conditions take the form:
375    
376     M{n[j]*(A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}     M{n[j]*((A[i,j,k,l]+A_reduced[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k])+(d[i,k]+d_reduced[i,k])*u[k]=n[j]*(X[i,j]+X_reduced[i,j])+y[i]+y_reduced[i]}
377    
378    
379     The coefficient M{d} is a rank two and M{y} is a  rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form     The coefficient M{d} is a rank two and M{y} is a rank one both in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}. Constraints take the form and the coefficients M{d_reduced} is a rank two and M{y_reduced} is a rank one both in the L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
380    
381       Constraints take the form
382    
383     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
384    
# Line 361  class LinearPDE(object): Line 387  class LinearPDE(object):
387     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
388    
389          - M{A[i,j,k,l]=A[k,l,i,j]}          - M{A[i,j,k,l]=A[k,l,i,j]}
390            - M{A_reduced[i,j,k,l]=A_reduced[k,l,i,j]}
391          - M{B[i,j,k]=C[k,i,j]}          - M{B[i,j,k]=C[k,i,j]}
392            - M{B_reduced[i,j,k]=C_reduced[k,i,j]}
393          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
394            - M{D_reduced[i,k]=D_reduced[i,k]}
395          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
396            - M{d_reduced[i,k]=d_reduced[k,i]}
397    
398     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the     L{LinearPDE} also supports solution discontinuities over a contact region in the domain. To specify the conditions across the
399     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution     discontinuity we are using the generalised flux M{J} which is in the case of a systems of PDEs and several components of the solution
400     defined as     defined as
401    
402     M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}     M{J[i,j]=(A[i,j,k,l]+A_reduced[[i,j,k,l])*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])*u[k]-X[i,j]-X_reduced[i,j]}
403    
404     For the case of single solution component and single PDE M{J} is defined     For the case of single solution component and single PDE M{J} is defined
405    
406     M{J_{j}=A[i,j]*grad(u)[j]+B[i]*u-X[i]}     M{J_{j}=(A[i,j]+A_reduced[i,j])*grad(u)[j]+(B[i]+B_reduced[i])*u-X[i]-X_reduced[i]}
407    
408     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1     In the context of discontinuities M{n} denotes the normal on the discontinuity pointing from side 0 towards side 1
409     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs     calculated from L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnContactZero<escript.FunctionOnContactZero>}. For a system of PDEs
410     the contact condition takes the form     the contact condition takes the form
411    
412     M{n[j]*J0[i,j]=n[j]*J1[i,j]=y_contact[i]- d_contact[i,k]*jump(u)[k]}     M{n[j]*J0[i,j]=n[j]*J1[i,j]=(y_contact[i]+y_contact_reduced[i])- (d_contact[i,k]+d_contact_reduced[i,k])*jump(u)[k]}
413    
414     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference     where M{J0} and M{J1} are the fluxes on side 0 and side 1 of the discontinuity, respectively. M{jump(u)}, which is the difference
415     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by     of the solution at side 1 and at side 0, denotes the jump of M{u} across discontinuity along the normal calcualted by
416     L{jump<util.jump>}.     L{jump<util.jump>}.
417     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.     The coefficient M{d_contact} is a rank two and M{y_contact} is a rank one both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.
418        The coefficient M{d_contact_reduced} is a rank two and M{y_contact_reduced} is a rank one both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}.
419     In case of a single PDE and a single component solution the contact condition takes the form     In case of a single PDE and a single component solution the contact condition takes the form
420    
421     M{n[j]*J0_{j}=n[j]*J1_{j}=y_contact-d_contact*jump(u)}     M{n[j]*J0_{j}=n[j]*J1_{j}=(y_contact+y_contact_reduced)-(d_contact+y_contact_reduced)*jump(u)}
422    
423     In this case the the coefficient M{d_contact} and M{y_contact} are eaach scalar     In this case the coefficient M{d_contact} and M{y_contact} are each scalar both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>} and the coefficient M{d_contact_reduced} and M{y_contact_reduced} are each scalar both in the L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>} or L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>}
    both in the L{FunctionOnContactZero<escript.FunctionOnContactZero>} or L{FunctionOnContactOne<escript.FunctionOnContactOne>}.  
424    
425     @cvar DEFAULT: The default method used to solve the system of linear equations     @cvar DEFAULT: The default method used to solve the system of linear equations
426     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
# Line 413  class LinearPDE(object): Line 443  class LinearPDE(object):
443     @cvar SCSL: SGI SCSL solver library     @cvar SCSL: SGI SCSL solver library
444     @cvar MKL: Intel's MKL solver library     @cvar MKL: Intel's MKL solver library
445     @cvar UMFPACK: the UMFPACK library     @cvar UMFPACK: the UMFPACK library
    @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs  
446     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
447     @cvar AMG: algebraic multi grid     @cvar AMG: algebraic multi grid
448     @cvar RILU: recursive ILU     @cvar RILU: recursive ILU
# Line 443  class LinearPDE(object): Line 472  class LinearPDE(object):
472     PASO= 21     PASO= 21
473     AMG= 22     AMG= 22
474     RILU = 23     RILU = 23
    TRILINOS = 24  
475    
476     SMALL_TOLERANCE=1.e-13     SMALL_TOLERANCE=1.e-13
477     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
# Line 481  class LinearPDE(object): Line 509  class LinearPDE(object):
509         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
510         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),         "d_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
511         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
512           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
513           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
514           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
515           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
516           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
517           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
518           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
519           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
520           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
521           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
522         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
523         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
524    
# Line 762  class LinearPDE(object): Line 800  class LinearPDE(object):
800                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
801                        if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)                        if verbose: print "non-symmetric PDE because d_contact[%d,%d]!=d_contact[%d,%d]"%(i,k,k,i)
802                        out=False                        out=False
803             # and now the reduced coefficients
804             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
805             if not A_reduced.isEmpty():
806                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
807                if self.getNumSolutions()>1:
808                   for i in range(self.getNumEquations()):
809                      for j in range(self.getDim()):
810                         for k in range(self.getNumSolutions()):
811                            for l in range(self.getDim()):
812                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
813                                   if verbose: print "non-symmetric PDE because A_reduced[%d,%d,%d,%d]!=A_reduced[%d,%d,%d,%d]"%(i,j,k,l,k,l,i,j)
814                                   out=False
815                else:
816                   for j in range(self.getDim()):
817                      for l in range(self.getDim()):
818                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
819                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
820                            out=False
821             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
822             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
823             if B_reduced.isEmpty() and not C_reduced.isEmpty():
824                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
825                out=False
826             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
827                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
828                out=False
829             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
830                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
831                if self.getNumSolutions()>1:
832                   for i in range(self.getNumEquations()):
833                       for j in range(self.getDim()):
834                          for k in range(self.getNumSolutions()):
835                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
836                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
837                                  out=False
838                else:
839                   for j in range(self.getDim()):
840                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
841                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
842                         out=False
843             if self.getNumSolutions()>1:
844               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
845               if not D_reduced.isEmpty():
846                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
847                 for i in range(self.getNumEquations()):
848                    for k in range(self.getNumSolutions()):
849                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
850                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
851                          out=False
852               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
853               if not d_reduced.isEmpty():
854                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
855                 for i in range(self.getNumEquations()):
856                    for k in range(self.getNumSolutions()):
857                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
858                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
859                          out=False
860               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
861               if not d_contact_reduced.isEmpty():
862                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
863                 for i in range(self.getNumEquations()):
864                    for k in range(self.getNumSolutions()):
865                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
866                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
867                          out=False
868        return out        return out
869    
870     def getSolution(self,**options):     def getSolution(self,**options):
# Line 801  class LinearPDE(object): Line 904  class LinearPDE(object):
904       """       """
905       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
906    
907       M{J[i,j]=A[i,j,k,l]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}       M{J[i,j]=(A[i,j,k,l]+A_reduced[A[i,j,k,l]]*grad(u[k])[l]+(B[i,j,k]+B_reduced[i,j,k])u[k]-X[i,j]-X_reduced[i,j]}
908    
909       or       or
910    
911       M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}       M{J[j]=(A[i,j]+A_reduced[i,j])*grad(u)[l]+(B[j]+B_reduced[j])u-X[j]-X_reduced[j]}
912    
913       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.       @param u: argument in the flux. If u is not present or equals L{None} the current solution is used.
914       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 813  class LinearPDE(object): Line 916  class LinearPDE(object):
916       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
917       """       """
918       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
919       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u))+util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u)-util.self.getCoefficientOfGeneralPDE("X")       return util.tensormult(self.getCoefficientOfGeneralPDE("A"),util.grad(u,Funtion(self.getDomain))) \
920               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
921               -util.self.getCoefficientOfGeneralPDE("X") \
922               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
923               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
924               -util.self.getCoefficientOfGeneralPDE("X_reduced")
925     # =============================================================================     # =============================================================================
926     #   solver settings:     #   solver settings:
927     # =============================================================================     # =============================================================================
# Line 870  class LinearPDE(object): Line 978  class LinearPDE(object):
978         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
979         elif p==self.SCSL: package= "SCSL"         elif p==self.SCSL: package= "SCSL"
980         elif p==self.UMFPACK: package= "UMFPACK"         elif p==self.UMFPACK: package= "UMFPACK"
        elif p==self.TRILINOS: package= "TRILINOS"  
981         else : method="unknown"         else : method="unknown"
982         return "%s solver of %s package"%(method,package)         return "%s solver of %s package"%(method,package)
983    
# Line 889  class LinearPDE(object): Line 996  class LinearPDE(object):
996         sets a new solver package         sets a new solver package
997    
998         @param package: sets a new solver method.         @param package: sets a new solver method.
999         @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}         @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
1000         """         """
1001         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1002         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
# Line 1210  class LinearPDE(object): Line 1317  class LinearPDE(object):
1317         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1318             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1319         else:         else:
1320             self.__righthandside*=0             self.__righthandside.setToZero()
1321             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1322         return self.__righthandside         return self.__righthandside
1323    
# Line 1260  class LinearPDE(object): Line 1367  class LinearPDE(object):
1367       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1368       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1369       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1370                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1371                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1372       """       """
1373       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1374          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1288  class LinearPDE(object): Line 1396  class LinearPDE(object):
1396       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1397       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1398       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1399                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1400                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1401       """       """
1402       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1403          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1304  class LinearPDE(object): Line 1413  class LinearPDE(object):
1413       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1414       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1415       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1416                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1417                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1418       """       """
1419       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1420          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1320  class LinearPDE(object): Line 1430  class LinearPDE(object):
1430       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1431       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1432       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1433                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact}, M{r} or M{q}.                    M{A}, M{B}, M{C}, M{D}, M{X}, M{Y}, M{d}, M{y}, M{d_contact}, M{y_contact},
1434                      M{A_reduced}, M{B_reduced}, M{C_reduced}, M{D_reduced}, M{X_reduced}, M{Y_reduced}, M{d_reduced}, M{y_reduced}, M{d_contact_reduced}, M{y_contact_reduced}, M{r} or M{q}.
1435       """       """
1436       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1437          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getShape(self.getDomain(),self.getNumEquations(),self.getNumSolutions())
# Line 1450  class LinearPDE(object): Line 1561  class LinearPDE(object):
1561        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1562        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1563        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type A: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1564          @keyword A_reduced: value for coefficient A_reduced.
1565          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1566        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1567        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type B: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1568          @keyword B_reduced: value for coefficient B_reduced
1569          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1570        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1571        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type C: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1572          @keyword C_reduced: value for coefficient C_reduced
1573          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1574        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1575        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type D: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1576          @keyword D_reduced: value for coefficient D_reduced
1577          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1578        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1579        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type X: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1580          @keyword X_reduced: value for coefficient X_reduced
1581          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1582        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1583        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.        @type Y: any type that can be casted to L{Data<escript.Data>} object on L{Function<escript.Function>}.
1584          @keyword Y_reduced: value for coefficient Y_reduced
1585          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1586        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1587        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type d: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1588          @keyword d_reduced: value for coefficient d_reduced
1589          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1590        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1591        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.        @type y: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
1592        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1593        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.        @type d_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1594                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1595          @type d_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.ReducedFunctionOnContactOne>} or  L{ReducedFunctionOnContactZero<escript.ReducedFunctionOnContactZero>}.
1596        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1597        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>}.        @type y_contact: any type that can be casted to L{Data<escript.Data>} object on L{FunctionOnContactOne<escript.FunctionOnContactOne>} or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.
1598                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1599          @type y_contact_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnContactOne<escript.FunctionOnContactOne>} or L{ReducedFunctionOnContactZero<escript.FunctionOnContactZero>}.
1600        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1601        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}        @type r: any type that can be casted to L{Data<escript.Data>} object on L{Solution<escript.Solution>} or L{ReducedSolution<escript.ReducedSolution>}
1602                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1504  class LinearPDE(object): Line 1631  class LinearPDE(object):
1631        # now we check the shape of the coefficient if numEquations and numSolutions are set:        # now we check the shape of the coefficient if numEquations and numSolutions are set:
1632        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1633          try:          try:
1634             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1635                                             self.getNumEquations(),self.getNumSolutions(),
1636                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1637               self.alteredCoefficient(i)
1638            except IllegalCoefficientFunctionSpace,m:
1639                # if the function space is wrong then we try the reduced version:
1640                i_red=i+"_reduced"
1641                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1642                    try:
1643                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1644                                                          self.getNumEquations(),self.getNumSolutions(),
1645                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1646                        self.alteredCoefficient(i_red)
1647                    except IllegalCoefficientValue,m:
1648                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1649                    except IllegalCoefficientFunctionSpace,m:
1650                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1651                else:
1652                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1653          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1654             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1655        self.__altered_coefficients=True        self.__altered_coefficients=True
1656        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1657        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1535  class LinearPDE(object): Line 1678  class LinearPDE(object):
1678                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1679                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient A in lumped matrix may not be present."
1680                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1681                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient B in lumped matrix may not be present."
1682                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1683                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient C in lumped matrix may not be present."
1684                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1685                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1686                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1687                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1688                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1689                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1690                   D=self.getCoefficientOfGeneralPDE("D")                   D=self.getCoefficientOfGeneralPDE("D")
1691                   if not D.isEmpty():                   if not D.isEmpty():
1692                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
                         #D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))  
1693                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1694                       else:                       else:
1695                          D_times_e=D                          D_times_e=D
# Line 1550  class LinearPDE(object): Line 1698  class LinearPDE(object):
1698                   d=self.getCoefficientOfGeneralPDE("d")                   d=self.getCoefficientOfGeneralPDE("d")
1699                   if not d.isEmpty():                   if not d.isEmpty():
1700                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
                         #d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))  
1701                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1702                       else:                       else:
1703                          d_times_e=d                          d_times_e=d
# Line 1571  class LinearPDE(object): Line 1718  class LinearPDE(object):
1718                                                D_times_e, \                                                D_times_e, \
1719                                                d_times_e,\                                                d_times_e,\
1720                                                d_contact_times_e)                                                d_contact_times_e)
1721                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1722                     if not D_reduced.isEmpty():
1723                         if self.getNumSolutions()>1:
1724                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1725                         else:
1726                            D_reduced_times_e=D_reduced
1727                     else:
1728                        D_reduced_times_e=escript.Data()
1729                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1730                     if not d_reduced.isEmpty():
1731                         if self.getNumSolutions()>1:
1732                            d_reduced_times_e=util.matrix_mult(d_reduced,numarray.ones((self.getNumSolutions(),)))
1733                         else:
1734                            d_reduced_times_e=d_reduced
1735                     else:
1736                        d_reduced_times_e=escript.Data()
1737                     d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
1738                     if not d_contact_reduced.isEmpty():
1739                         if self.getNumSolutions()>1:
1740                            d_contact_reduced_times_e=util.matrixmult(d_contact_reduced,numarray.ones((self.getNumSolutions(),)))
1741                         else:
1742                            d_contact_reduced_times_e=d_contact_reduced
1743                     else:
1744                        d_contact_reduced_times_e=escript.Data()
1745        
1746                     self.__operator=self.__getNewRightHandSide()
1747                     self.getDomain().addPDEToRHS(self.__operator, \
1748                                                  escript.Data(), \
1749                                                  D_times_e, \
1750                                                  d_times_e,\
1751                                                  d_contact_times_e)
1752                     self.getDomain().addPDEToRHS(self.__operator, \
1753                                                  escript.Data(), \
1754                                                  D_reduced_times_e, \
1755                                                  d_reduced_times_e,\
1756                                                  d_contact_reduced_times_e)
1757                   self.__operator=1./self.__operator                   self.__operator=1./self.__operator
1758                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1759                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1580  class LinearPDE(object): Line 1763  class LinearPDE(object):
1763                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1764                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1765                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1766                     self.getDomain().addPDEToRHS(self.__righthandside, \
1767                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1768                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1769                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1770                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1771                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1772                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1773            else:            else:
# Line 1595  class LinearPDE(object): Line 1783  class LinearPDE(object):
1783                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1784                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1785                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1786                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1787                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1788                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1789                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1790                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1791                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1792                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1793                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1794                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1795                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1796                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1797                   self.__applyConstraint()                   self.__applyConstraint()
1798                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1799                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1606  class LinearPDE(object): Line 1805  class LinearPDE(object):
1805                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1806                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1807                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1808                     self.getDomain().addPDEToRHS(self.__righthandside, \
1809                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1810                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1811                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1812                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1813                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1814                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1815                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1621  class LinearPDE(object): Line 1825  class LinearPDE(object):
1825                              escript.Data(),\                              escript.Data(),\
1826                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1827                              escript.Data())                              escript.Data())
1828                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1829                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1830                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1831                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1832                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1833                                escript.Data(), \
1834                                escript.Data(), \
1835                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1836                                escript.Data(),\
1837                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1838                                escript.Data())
1839                   self.__applyConstraint()                   self.__applyConstraint()
1840                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1841                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1654  class Poisson(LinearPDE): Line 1869  class Poisson(LinearPDE):
1869       """       """
1870       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1871       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1872                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1873                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1874       self.setSymmetryOn()       self.setSymmetryOn()
1875    
1876     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1702  class Poisson(LinearPDE): Line 1918  class Poisson(LinearPDE):
1918           return escript.Data()           return escript.Data()
1919       elif name == "y_contact" :       elif name == "y_contact" :
1920           return escript.Data()           return escript.Data()
1921         elif name == "A_reduced" :
1922             return escript.Data()
1923         elif name == "B_reduced" :
1924             return escript.Data()
1925         elif name == "C_reduced" :
1926             return escript.Data()
1927         elif name == "D_reduced" :
1928             return escript.Data()
1929         elif name == "X_reduced" :
1930             return escript.Data()
1931         elif name == "Y_reduced" :
1932             return self.getCoefficient("f_reduced")
1933         elif name == "d_reduced" :
1934             return escript.Data()
1935         elif name == "y_reduced" :
1936             return escript.Data()
1937         elif name == "d_contact_reduced" :
1938             return escript.Data()
1939         elif name == "y_contact_reduced" :
1940             return escript.Data()
1941       elif name == "r" :       elif name == "r" :
1942           return escript.Data()           return escript.Data()
1943       elif name == "q" :       elif name == "q" :
# Line 1738  class Helmholtz(LinearPDE): Line 1974  class Helmholtz(LinearPDE):
1974       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1975                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1976                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1977                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1978                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1979                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1980                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1981                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1982                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1983       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1801  class Helmholtz(LinearPDE): Line 2039  class Helmholtz(LinearPDE):
2039           return escript.Data()           return escript.Data()
2040       elif name == "y_contact" :       elif name == "y_contact" :
2041           return escript.Data()           return escript.Data()
2042         elif name == "A_reduced" :
2043             return escript.Data()
2044         elif name == "B_reduced" :
2045             return escript.Data()
2046         elif name == "C_reduced" :
2047             return escript.Data()
2048         elif name == "D_reduced" :
2049             return escript.Data()
2050         elif name == "X_reduced" :
2051             return escript.Data()
2052         elif name == "Y_reduced" :
2053             return self.getCoefficient("f_reduced")
2054         elif name == "d_reduced" :
2055             return escript.Data()
2056         elif name == "y_reduced" :
2057            return self.getCoefficient("g_reduced")
2058         elif name == "d_contact_reduced" :
2059             return escript.Data()
2060         elif name == "y_contact_reduced" :
2061             return escript.Data()
2062       elif name == "r" :       elif name == "r" :
2063           return self.getCoefficient("r")           return self.getCoefficient("r")
2064       elif name == "q" :       elif name == "q" :
# Line 1899  class LameEquation(LinearPDE): Line 2157  class LameEquation(LinearPDE):
2157           return escript.Data()           return escript.Data()
2158       elif name == "y_contact" :       elif name == "y_contact" :
2159           return escript.Data()           return escript.Data()
2160         elif name == "A_reduced" :
2161             return escript.Data()
2162         elif name == "B_reduced" :
2163             return escript.Data()
2164         elif name == "C_reduced" :
2165             return escript.Data()
2166         elif name == "D_reduced" :
2167             return escript.Data()
2168         elif name == "X_reduced" :
2169             return escript.Data()
2170         elif name == "Y_reduced" :
2171             return escript.Data()
2172         elif name == "d_reduced" :
2173             return escript.Data()
2174         elif name == "y_reduced" :
2175             return escript.Data()
2176         elif name == "d_contact_reduced" :
2177             return escript.Data()
2178         elif name == "y_contact_reduced" :
2179             return escript.Data()
2180       elif name == "r" :       elif name == "r" :
2181           return self.getCoefficient("r")           return self.getCoefficient("r")
2182       elif name == "q" :       elif name == "q" :
# Line 1906  class LameEquation(LinearPDE): Line 2184  class LameEquation(LinearPDE):
2184       else:       else:
2185          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2186    
 class AdvectivePDE(LinearPDE):  
    """  
    In cases of PDEs dominated by the advection terms M{B} and M{C} against the adevctive terms M{A}  
    up-winding has been used.  The L{AdvectivePDE} class applies SUPG upwinding to the advective terms.  
   
    In the following we set  
   
    M{Z[j]=C[j]-B[j]}  
   
    or  
   
    M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}  
   
    To measure the dominance of the advective terms over the diffusive term M{A} the  
    X{Pelclet number} M{P} is used. It is defined as  
   
    M{P=h|Z|/(2|A|)}  
   
    where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size  
    from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.  
   
    From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:  
   
    M{S{Xi}=S{xi}(P) h/|Z|}  
   
    where M{S{xi}} is a suitable function of the Peclet number.  
   
    In the case of a single PDE the coefficient are up-dated in the following way:  
          - M{A[i,j] S{<-} A[i,j] + S{Xi} * Z[j] * Z[l]}  
          - M{B[j] S{<-} B[j] + S{Xi} * C[j] * D}  
          - M{C[j] S{<-} C[j] + S{Xi} * B[j] * D}  
          - M{X[j] S{<-} X[j] + S{Xi} * Z[j] * Y}  
   
    Similar for the case of a systems of PDEs:  
          - M{A[i,j,k,l] S{<-} A[i,j,k,l]+ S{delta}[p,m] * S{Xi} * Z[p,i,j] * Z[m,k,l]}  
          - M{B[i,j,k] S{<-} B[i,j,k] +  S{delta}[p,m] * S{Xi} * D[p,k] * C[m,i,j]}  
          - M{C[i,k,l] S{<-} C[i,k,l] +  S{delta}[p,m] * S{Xi} * D[p,k] * B[m,l,i]}  
          - M{X[i,j] S{<-} X[i,j] + S{delta}[p,m] * S{Xi}  * Y[p] * Z[m,i,j]}  
   
    where M{S{delta}} is L{kronecker}.  
    Using upwinding in this form, introduces an additonal error which is proprtional to the cell size M{h}  
    but with the intension to stabilize the solution.  
   
    """  
    def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):  
       """  
       creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}  
   
       @param domain: domain of the PDE  
       @type domain: L{Domain<escript.Domain>}  
       @param numEquations: number of equations. If numEquations==None the number of equations  
                            is exracted from the PDE coefficients.  
       @param numSolutions: number of solution components. If  numSolutions==None the number of solution components  
                            is exracted from the PDE coefficients.  
       @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the  
                  M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.  
       @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.  
       @param debug: if True debug informations are printed.  
       """  
       super(AdvectivePDE, self).__init__(domain,\  
                                          numEquations,numSolutions,debug)  
       if xi==None:  
          self.__xi=AdvectivePDE.ELMAN_RAMAGE  
       else:  
          self.__xi=xi  
       self.__Xi=escript.Data()  
   
    def setValue(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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