/[escript]/trunk-mpi-branch/escript/py_src/linearPDEs.py
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trunk/escript/py_src/linearPDEs.py revision 767 by gross, Fri Jun 30 07:29:08 2006 UTC trunk-mpi-branch/escript/py_src/linearPDEs.py revision 1302 by ksteube, Mon Sep 17 06:57:51 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
446       @cvar TRILINOS: the TRILINOS parallel solver class library from Sandia Natl Labs
447     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
448     @cvar AMG: algebraic multi grid     @cvar AMG: algebraic multi grid
449     @cvar RILU: recursive ILU     @cvar RILU: recursive ILU
# Line 442  class LinearPDE(object): Line 473  class LinearPDE(object):
473     PASO= 21     PASO= 21
474     AMG= 22     AMG= 22
475     RILU = 23     RILU = 23
476       TRILINOS = 24
477    
478     SMALL_TOLERANCE=1.e-13     SMALL_TOLERANCE=1.e-13
479     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
# Line 479  class LinearPDE(object): Line 511  class LinearPDE(object):
511         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y"         : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
512         "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),
513         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),         "y_contact" : PDECoefficient(PDECoefficient.CONTACT,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
514           "A_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
515           "B_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
516           "C_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION,PDECoefficient.BY_DIM),PDECoefficient.OPERATOR),
517           "D_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
518           "X_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
519           "Y_reduced"         : PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
520           "d_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
521           "y_reduced"         : PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
522           "d_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_SOLUTION),PDECoefficient.OPERATOR),
523           "y_contact_reduced" : PDECoefficient(PDECoefficient.CONTACT_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
524         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),         "r"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.RIGHTHANDSIDE),
525         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}         "q"         : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_SOLUTION,),PDECoefficient.BOTH)}
526    
# Line 760  class LinearPDE(object): Line 802  class LinearPDE(object):
802                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
803                        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)
804                        out=False                        out=False
805             # and now the reduced coefficients
806             A_reduced=self.getCoefficientOfGeneralPDE("A_reduced")
807             if not A_reduced.isEmpty():
808                tol=util.Lsup(A_reduced)*self.SMALL_TOLERANCE
809                if self.getNumSolutions()>1:
810                   for i in range(self.getNumEquations()):
811                      for j in range(self.getDim()):
812                         for k in range(self.getNumSolutions()):
813                            for l in range(self.getDim()):
814                                if util.Lsup(A_reduced[i,j,k,l]-A_reduced[k,l,i,j])>tol:
815                                   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)
816                                   out=False
817                else:
818                   for j in range(self.getDim()):
819                      for l in range(self.getDim()):
820                         if util.Lsup(A_reduced[j,l]-A_reduced[l,j])>tol:
821                            if verbose: print "non-symmetric PDE because A_reduced[%d,%d]!=A_reduced[%d,%d]"%(j,l,l,j)
822                            out=False
823             B_reduced=self.getCoefficientOfGeneralPDE("B_reduced")
824             C_reduced=self.getCoefficientOfGeneralPDE("C_reduced")
825             if B_reduced.isEmpty() and not C_reduced.isEmpty():
826                if verbose: print "non-symmetric PDE because B_reduced is not present but C_reduced is"
827                out=False
828             elif not B_reduced.isEmpty() and C_reduced.isEmpty():
829                if verbose: print "non-symmetric PDE because C_reduced is not present but B_reduced is"
830                out=False
831             elif not B_reduced.isEmpty() and not C_reduced.isEmpty():
832                tol=(util.Lsup(B_reduced)+util.Lsup(C_reduced))*self.SMALL_TOLERANCE/2.
833                if self.getNumSolutions()>1:
834                   for i in range(self.getNumEquations()):
835                       for j in range(self.getDim()):
836                          for k in range(self.getNumSolutions()):
837                             if util.Lsup(B_reduced[i,j,k]-C_reduced[k,i,j])>tol:
838                                  if verbose: print "non-symmetric PDE because B_reduced[%d,%d,%d]!=C_reduced[%d,%d,%d]"%(i,j,k,k,i,j)
839                                  out=False
840                else:
841                   for j in range(self.getDim()):
842                      if util.Lsup(B_reduced[j]-C_reduced[j])>tol:
843                         if verbose: print "non-symmetric PDE because B_reduced[%d]!=C_reduced[%d]"%(j,j)
844                         out=False
845             if self.getNumSolutions()>1:
846               D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
847               if not D_reduced.isEmpty():
848                 tol=util.Lsup(D_reduced)*self.SMALL_TOLERANCE
849                 for i in range(self.getNumEquations()):
850                    for k in range(self.getNumSolutions()):
851                      if util.Lsup(D_reduced[i,k]-D_reduced[k,i])>tol:
852                          if verbose: print "non-symmetric PDE because D_reduced[%d,%d]!=D_reduced[%d,%d]"%(i,k,k,i)
853                          out=False
854               d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
855               if not d_reduced.isEmpty():
856                 tol=util.Lsup(d_reduced)*self.SMALL_TOLERANCE
857                 for i in range(self.getNumEquations()):
858                    for k in range(self.getNumSolutions()):
859                      if util.Lsup(d_reduced[i,k]-d_reduced[k,i])>tol:
860                          if verbose: print "non-symmetric PDE because d_reduced[%d,%d]!=d_reduced[%d,%d]"%(i,k,k,i)
861                          out=False
862               d_contact_reduced=self.getCoefficientOfGeneralPDE("d_contact_reduced")
863               if not d_contact_reduced.isEmpty():
864                 tol=util.Lsup(d_contact_reduced)*self.SMALL_TOLERANCE
865                 for i in range(self.getNumEquations()):
866                    for k in range(self.getNumSolutions()):
867                      if util.Lsup(d_contact_reduced[i,k]-d_contact_reduced[k,i])>tol:
868                          if verbose: print "non-symmetric PDE because d_contact_reduced[%d,%d]!=d_contact_reduced[%d,%d]"%(i,k,k,i)
869                          out=False
870        return out        return out
871    
872     def getSolution(self,**options):     def getSolution(self,**options):
# Line 799  class LinearPDE(object): Line 906  class LinearPDE(object):
906       """       """
907       returns the flux M{J} for a given M{u}       returns the flux M{J} for a given M{u}
908    
909       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]}
910    
911       or       or
912    
913       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]}
914    
915       @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.
916       @type u: L{Data<escript.Data>} or None       @type u: L{Data<escript.Data>} or None
# Line 811  class LinearPDE(object): Line 918  class LinearPDE(object):
918       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
919       """       """
920       if u==None: u=self.getSolution()       if u==None: u=self.getSolution()
921       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))) \
922               +util.matrixmult(self.getCoefficientOfGeneralPDE("B"),u) \
923               -util.self.getCoefficientOfGeneralPDE("X") \
924               +util.tensormult(self.getCoefficientOfGeneralPDE("A_reduced"),util.grad(u,ReducedFuntion(self.getDomain))) \
925               +util.matrixmult(self.getCoefficientOfGeneralPDE("B_reduced"),u) \
926               -util.self.getCoefficientOfGeneralPDE("X_reduced")
927     # =============================================================================     # =============================================================================
928     #   solver settings:     #   solver settings:
929     # =============================================================================     # =============================================================================
# Line 824  class LinearPDE(object): Line 936  class LinearPDE(object):
936         @param preconditioner: sets a new solver method.         @param preconditioner: sets a new solver method.
937         @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}
938         """         """
939         if solver==None: solve=self.DEFAULT         if solver==None: solver=self.__solver_method
940           if preconditioner==None: preconditioner=self.__preconditioner
941           if solver==None: solver=self.DEFAULT
942         if preconditioner==None: preconditioner=self.DEFAULT         if preconditioner==None: preconditioner=self.DEFAULT
943         if not (solver,preconditioner)==self.getSolverMethod():         if not (solver,preconditioner)==self.getSolverMethod():
944             self.__solver_method=solver             self.__solver_method=solver
# Line 868  class LinearPDE(object): Line 982  class LinearPDE(object):
982         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
983         elif p==self.SCSL: package= "SCSL"         elif p==self.SCSL: package= "SCSL"
984         elif p==self.UMFPACK: package= "UMFPACK"         elif p==self.UMFPACK: package= "UMFPACK"
985           elif p==self.TRILINOS: package= "TRILINOS"
986         else : method="unknown"         else : method="unknown"
987         return "%s solver of %s package"%(method,package)         return "%s solver of %s package"%(method,package)
988    
# Line 886  class LinearPDE(object): Line 1001  class LinearPDE(object):
1001         sets a new solver package         sets a new solver package
1002    
1003         @param package: sets a new solver method.         @param package: sets a new solver method.
1004         @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}         @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}, L{TRILINOS}
1005         """         """
1006         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
1007         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
# Line 923  class LinearPDE(object): Line 1038  class LinearPDE(object):
1038         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence         @param tol: new tolerance for the solver. If the tol is lower then the current tolerence
1039                     the system will be resolved.                     the system will be resolved.
1040         @type tol: positive C{float}         @type tol: positive C{float}
1041         @raise ValueException: if tolerance is not positive.         @raise ValueError: if tolerance is not positive.
1042         """         """
1043         if not tol>0:         if not tol>0:
1044             raise ValueException,"Tolerance as to be positive"             raise ValueError,"Tolerance as to be positive"
1045         if tol<self.getTolerance(): self.__invalidateSolution()         if tol<self.getTolerance(): self.__invalidateSolution()
1046         self.trace("New tolerance %e"%tol)         self.trace("New tolerance %e"%tol)
1047         self.__tolerance=tol         self.__tolerance=tol
# Line 1207  class LinearPDE(object): Line 1322  class LinearPDE(object):
1322         if self.__righthandside.isEmpty():         if self.__righthandside.isEmpty():
1323             self.__righthandside=self.__getNewRightHandSide()             self.__righthandside=self.__getNewRightHandSide()
1324         else:         else:
1325             self.__righthandside*=0             self.__righthandside.setToZero()
1326             self.trace("Right hand side is reset to zero.")             self.trace("Right hand side is reset to zero.")
1327         return self.__righthandside         return self.__righthandside
1328    
# Line 1257  class LinearPDE(object): Line 1372  class LinearPDE(object):
1372       @return: the value of the coefficient  name       @return: the value of the coefficient  name
1373       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1374       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1375                    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},
1376                      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}.
1377       """       """
1378       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1379          return self.getCoefficient(name)          return self.getCoefficient(name)
# Line 1285  class LinearPDE(object): Line 1401  class LinearPDE(object):
1401       @return: a coefficient name initialized to 0.       @return: a coefficient name initialized to 0.
1402       @rtype: L{Data<escript.Data>}       @rtype: L{Data<escript.Data>}
1403       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1404                    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},
1405                      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}.
1406       """       """
1407       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1408          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))          return escript.Data(0,self.getShapeOfCoefficientOfGeneralPDE(name),self.getFunctionSpaceForCoefficientOfGeneralPDE(name))
# Line 1301  class LinearPDE(object): Line 1418  class LinearPDE(object):
1418       @return: the function space to be used for coefficient name       @return: the function space to be used for coefficient name
1419       @rtype: L{FunctionSpace<escript.FunctionSpace>}       @rtype: L{FunctionSpace<escript.FunctionSpace>}
1420       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1421                    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},
1422                      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}.
1423       """       """
1424       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1425          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())          return self.__COEFFICIENTS_OF_GENEARL_PDE[name].getFunctionSpace(self.getDomain())
# Line 1317  class LinearPDE(object): Line 1435  class LinearPDE(object):
1435       @return: the shape of the coefficient name       @return: the shape of the coefficient name
1436       @rtype: C{tuple} of C{int}       @rtype: C{tuple} of C{int}
1437       @raise IllegalCoefficient: if name is not one of coefficients       @raise IllegalCoefficient: if name is not one of coefficients
1438                    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},
1439                      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}.
1440       """       """
1441       if self.hasCoefficientOfGeneralPDE(name):       if self.hasCoefficientOfGeneralPDE(name):
1442          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 1447  class LinearPDE(object): Line 1566  class LinearPDE(object):
1566        @param coefficients: new values assigned to coefficients        @param coefficients: new values assigned to coefficients
1567        @keyword A: value for coefficient A.        @keyword A: value for coefficient A.
1568        @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>}.
1569          @keyword A_reduced: value for coefficient A_reduced.
1570          @type A_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1571        @keyword B: value for coefficient B        @keyword B: value for coefficient B
1572        @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>}.
1573          @keyword B_reduced: value for coefficient B_reduced
1574          @type B_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1575        @keyword C: value for coefficient C        @keyword C: value for coefficient C
1576        @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>}.
1577          @keyword C_reduced: value for coefficient C_reduced
1578          @type C_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1579        @keyword D: value for coefficient D        @keyword D: value for coefficient D
1580        @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>}.
1581          @keyword D_reduced: value for coefficient D_reduced
1582          @type D_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1583        @keyword X: value for coefficient X        @keyword X: value for coefficient X
1584        @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>}.
1585          @keyword X_reduced: value for coefficient X_reduced
1586          @type X_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.ReducedFunction>}.
1587        @keyword Y: value for coefficient Y        @keyword Y: value for coefficient Y
1588        @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>}.
1589          @keyword Y_reduced: value for coefficient Y_reduced
1590          @type Y_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunction<escript.Function>}.
1591        @keyword d: value for coefficient d        @keyword d: value for coefficient d
1592        @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>}.
1593          @keyword d_reduced: value for coefficient d_reduced
1594          @type d_reduced: any type that can be casted to L{Data<escript.Data>} object on L{ReducedFunctionOnBoundary<escript.ReducedFunctionOnBoundary>}.
1595        @keyword y: value for coefficient y        @keyword y: value for coefficient y
1596        @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>}.
1597        @keyword d_contact: value for coefficient d_contact        @keyword d_contact: value for coefficient d_contact
1598        @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>}.
1599                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword d_contact_reduced: value for coefficient d_contact_reduced
1600          @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>}.
1601        @keyword y_contact: value for coefficient y_contact        @keyword y_contact: value for coefficient y_contact
1602        @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>}.
1603                         or  L{FunctionOnContactZero<escript.FunctionOnContactZero>}.        @keyword y_contact_reduced: value for coefficient y_contact_reduced
1604          @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>}.
1605        @keyword r: values prescribed to the solution at the locations of constraints        @keyword r: values prescribed to the solution at the locations of constraints
1606        @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>}
1607                 depending of reduced order is used for the solution.                 depending of reduced order is used for the solution.
# Line 1501  class LinearPDE(object): Line 1636  class LinearPDE(object):
1636        # 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:
1637        for i,d in coefficients.iteritems():        for i,d in coefficients.iteritems():
1638          try:          try:
1639             self.COEFFICIENTS[i].setValue(self.getDomain(),self.getNumEquations(),self.getNumSolutions(),self.reduceEquationOrder(),self.reduceSolutionOrder(),d)             self.COEFFICIENTS[i].setValue(self.getDomain(),
1640                                             self.getNumEquations(),self.getNumSolutions(),
1641                                             self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1642               self.alteredCoefficient(i)
1643            except IllegalCoefficientFunctionSpace,m:
1644                # if the function space is wrong then we try the reduced version:
1645                i_red=i+"_reduced"
1646                if (not i_red in coefficients.keys()) and i_red in self.COEFFICIENTS.keys():
1647                    try:
1648                        self.COEFFICIENTS[i_red].setValue(self.getDomain(),
1649                                                          self.getNumEquations(),self.getNumSolutions(),
1650                                                          self.reduceEquationOrder(),self.reduceSolutionOrder(),d)
1651                        self.alteredCoefficient(i_red)
1652                    except IllegalCoefficientValue,m:
1653                        raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
1654                    except IllegalCoefficientFunctionSpace,m:
1655                        raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1656                else:
1657                    raise IllegalCoefficientFunctionSpace("Coefficient %s:%s"%(i,m))
1658          except IllegalCoefficientValue,m:          except IllegalCoefficientValue,m:
1659             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))             raise IllegalCoefficientValue("Coefficient %s:%s"%(i,m))
         self.alteredCoefficient(i)  
   
1660        self.__altered_coefficients=True        self.__altered_coefficients=True
1661        # check if the systrem is inhomogeneous:        # check if the systrem is inhomogeneous:
1662        if len(coefficients)>0 and not self.isUsingLumping():        if len(coefficients)>0 and not self.isUsingLumping():
# Line 1513  class LinearPDE(object): Line 1664  class LinearPDE(object):
1664           r=self.getCoefficientOfGeneralPDE("r")           r=self.getCoefficientOfGeneralPDE("r")
1665           homogeneous_constraint=True           homogeneous_constraint=True
1666           if not q.isEmpty() and not r.isEmpty():           if not q.isEmpty() and not r.isEmpty():
1667               if util.Lsup(q*r)>=1.e-13*util.Lsup(r):               if util.Lsup(q*r)>0.:
1668                 self.trace("Inhomogeneous constraint detected.")                 self.trace("Inhomogeneous constraint detected.")
1669                 self.__invalidateSystem()                 self.__invalidateSystem()
1670    
# Line 1532  class LinearPDE(object): Line 1683  class LinearPDE(object):
1683                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1684                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient A in lumped matrix may not be present."
1685                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1686                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient B in lumped matrix may not be present."
1687                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1688                        raise ValueError,"coefficient A in lumped matrix may not be present."                        raise ValueError,"coefficient C in lumped matrix may not be present."
1689                     if not self.getCoefficientOfGeneralPDE("d_contact").isEmpty():
1690                          raise ValueError,"coefficient d_contact in lumped matrix may not be present."
1691                     if not self.getCoefficientOfGeneralPDE("A_reduced").isEmpty():
1692                          raise ValueError,"coefficient A_reduced in lumped matrix may not be present."
1693                     if not self.getCoefficientOfGeneralPDE("B_reduced").isEmpty():
1694                          raise ValueError,"coefficient B_reduced in lumped matrix may not be present."
1695                     if not self.getCoefficientOfGeneralPDE("C_reduced").isEmpty():
1696                          raise ValueError,"coefficient C_reduced in lumped matrix may not be present."
1697                     if not self.getCoefficientOfGeneralPDE("d_contact_reduced").isEmpty():
1698                          raise ValueError,"coefficient d_contact_reduced in lumped matrix may not be present."
1699                   D=self.getCoefficientOfGeneralPDE("D")                   D=self.getCoefficientOfGeneralPDE("D")
1700                     d=self.getCoefficientOfGeneralPDE("d")
1701                     D_reduced=self.getCoefficientOfGeneralPDE("D_reduced")
1702                     d_reduced=self.getCoefficientOfGeneralPDE("d_reduced")
1703                   if not D.isEmpty():                   if not D.isEmpty():
1704                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1705                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))                          D_times_e=util.matrix_mult(D,numarray.ones((self.getNumSolutions(),)))
1706                       else:                       else:
1707                          D_times_e=D                          D_times_e=D
1708                   else:                   else:
1709                      D_times_e=escript.Data()                      D_times_e=escript.Data()
                  d=self.getCoefficientOfGeneralPDE("d")  
1710                   if not d.isEmpty():                   if not d.isEmpty():
1711                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1712                          d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))                          d_times_e=util.matrix_mult(d,numarray.ones((self.getNumSolutions(),)))
1713                       else:                       else:
1714                          d_times_e=d                          d_times_e=d
1715                   else:                   else:
1716                      d_times_e=escript.Data()                      d_times_e=escript.Data()
1717                   d_contact=self.getCoefficientOfGeneralPDE("d_contact")        
1718                   if not d_contact.isEmpty():                   if not D_reduced.isEmpty():
1719                         if self.getNumSolutions()>1:
1720                            D_reduced_times_e=util.matrix_mult(D_reduced,numarray.ones((self.getNumSolutions(),)))
1721                         else:
1722                            D_reduced_times_e=D_reduced
1723                     else:
1724                        D_reduced_times_e=escript.Data()
1725                     if not d_reduced.isEmpty():
1726                       if self.getNumSolutions()>1:                       if self.getNumSolutions()>1:
1727                          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(),)))
1728                       else:                       else:
1729                          d_contact_times_e=d_contact                          d_reduced_times_e=d_reduced
1730                   else:                   else:
1731                      d_contact_times_e=escript.Data()                      d_reduced_times_e=escript.Data()
1732        
1733                   self.__operator=self.__getNewRightHandSide()                   self.__operator=self.__getNewRightHandSide()
1734                   self.getDomain().addPDEToRHS(self.__operator, \                   if hasattr(self.getDomain(), "addPDEToLumpedSystem") :
1735                                                escript.Data(), \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_times_e, d_times_e)
1736                                                D_times_e, \                      self.getDomain().addPDEToLumpedSystem(self.__operator, D_reduced_times_e, d_reduced_times_e)
1737                                                d_times_e,\                   else:
1738                                                d_contact_times_e)                      self.getDomain().addPDEToRHS(self.__operator, \
1739                                                     escript.Data(), \
1740                                                     D_times_e, \
1741                                                     d_times_e,\
1742                                                     escript.Data())
1743                        self.getDomain().addPDEToRHS(self.__operator, \
1744                                                     escript.Data(), \
1745                                                     D_reduced_times_e, \
1746                                                     d_reduced_times_e,\
1747                                                     escript.Data())
1748                   self.__operator=1./self.__operator                   self.__operator=1./self.__operator
1749                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1750                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1575  class LinearPDE(object): Line 1754  class LinearPDE(object):
1754                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1755                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1756                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1757                     self.getDomain().addPDEToRHS(self.__righthandside, \
1758                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1759                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1760                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1761                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1762                   self.trace("New right hand side as been built.")                   self.trace("New right hand side as been built.")
1763                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
1764            else:            else:
# Line 1590  class LinearPDE(object): Line 1774  class LinearPDE(object):
1774                                 self.getCoefficientOfGeneralPDE("y"), \                                 self.getCoefficientOfGeneralPDE("y"), \
1775                                 self.getCoefficientOfGeneralPDE("d_contact"), \                                 self.getCoefficientOfGeneralPDE("d_contact"), \
1776                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1777                     self.getDomain().addPDEToSystem(self.__operator,self.__righthandside, \
1778                                   self.getCoefficientOfGeneralPDE("A_reduced"), \
1779                                   self.getCoefficientOfGeneralPDE("B_reduced"), \
1780                                   self.getCoefficientOfGeneralPDE("C_reduced"), \
1781                                   self.getCoefficientOfGeneralPDE("D_reduced"), \
1782                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1783                                   self.getCoefficientOfGeneralPDE("Y_reduced"), \
1784                                   self.getCoefficientOfGeneralPDE("d_reduced"), \
1785                                   self.getCoefficientOfGeneralPDE("y_reduced"), \
1786                                   self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1787                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1788                   self.__applyConstraint()                   self.__applyConstraint()
1789                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1790                   self.trace("New system has been built.")                   self.trace("New system has been built.")
# Line 1601  class LinearPDE(object): Line 1796  class LinearPDE(object):
1796                                 self.getCoefficientOfGeneralPDE("Y"),\                                 self.getCoefficientOfGeneralPDE("Y"),\
1797                                 self.getCoefficientOfGeneralPDE("y"),\                                 self.getCoefficientOfGeneralPDE("y"),\
1798                                 self.getCoefficientOfGeneralPDE("y_contact"))                                 self.getCoefficientOfGeneralPDE("y_contact"))
1799                     self.getDomain().addPDEToRHS(self.__righthandside, \
1800                                   self.getCoefficientOfGeneralPDE("X_reduced"), \
1801                                   self.getCoefficientOfGeneralPDE("Y_reduced"),\
1802                                   self.getCoefficientOfGeneralPDE("y_reduced"),\
1803                                   self.getCoefficientOfGeneralPDE("y_contact_reduced"))
1804                   self.__righthandside=self.copyConstraint(self.__righthandside)                   self.__righthandside=self.copyConstraint(self.__righthandside)
1805                   self.trace("New right hand side has been built.")                   self.trace("New right hand side has been built.")
1806                   self.__righthandside_isValid=True                   self.__righthandside_isValid=True
# Line 1616  class LinearPDE(object): Line 1816  class LinearPDE(object):
1816                              escript.Data(),\                              escript.Data(),\
1817                              self.getCoefficientOfGeneralPDE("d_contact"), \                              self.getCoefficientOfGeneralPDE("d_contact"), \
1818                              escript.Data())                              escript.Data())
1819                     self.getDomain().addPDEToSystem(self.__operator,escript.Data(), \
1820                                self.getCoefficientOfGeneralPDE("A_reduced"), \
1821                                self.getCoefficientOfGeneralPDE("B_reduced"), \
1822                                self.getCoefficientOfGeneralPDE("C_reduced"), \
1823                                self.getCoefficientOfGeneralPDE("D_reduced"), \
1824                                escript.Data(), \
1825                                escript.Data(), \
1826                                self.getCoefficientOfGeneralPDE("d_reduced"), \
1827                                escript.Data(),\
1828                                self.getCoefficientOfGeneralPDE("d_contact_reduced"), \
1829                                escript.Data())
1830                   self.__applyConstraint()                   self.__applyConstraint()
1831                   self.trace("New operator has been built.")                   self.trace("New operator has been built.")
1832                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
# Line 1649  class Poisson(LinearPDE): Line 1860  class Poisson(LinearPDE):
1860       """       """
1861       super(Poisson, self).__init__(domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1862       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1863                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1864                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1865       self.setSymmetryOn()       self.setSymmetryOn()
1866    
1867     def setValue(self,**coefficients):     def setValue(self,**coefficients):
# Line 1697  class Poisson(LinearPDE): Line 1909  class Poisson(LinearPDE):
1909           return escript.Data()           return escript.Data()
1910       elif name == "y_contact" :       elif name == "y_contact" :
1911           return escript.Data()           return escript.Data()
1912         elif name == "A_reduced" :
1913             return escript.Data()
1914         elif name == "B_reduced" :
1915             return escript.Data()
1916         elif name == "C_reduced" :
1917             return escript.Data()
1918         elif name == "D_reduced" :
1919             return escript.Data()
1920         elif name == "X_reduced" :
1921             return escript.Data()
1922         elif name == "Y_reduced" :
1923             return self.getCoefficient("f_reduced")
1924         elif name == "d_reduced" :
1925             return escript.Data()
1926         elif name == "y_reduced" :
1927             return escript.Data()
1928         elif name == "d_contact_reduced" :
1929             return escript.Data()
1930         elif name == "y_contact_reduced" :
1931             return escript.Data()
1932       elif name == "r" :       elif name == "r" :
1933           return escript.Data()           return escript.Data()
1934       elif name == "q" :       elif name == "q" :
# Line 1733  class Helmholtz(LinearPDE): Line 1965  class Helmholtz(LinearPDE):
1965       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1966                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1967                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1968                            "f_reduced": PDECoefficient(PDECoefficient.INTERIOR_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1969                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "alpha": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1970                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "g": PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1971                            "g_reduced": PDECoefficient(PDECoefficient.BOUNDARY_REDUCED,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1972                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                          "r": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1973                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                          "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1974       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1796  class Helmholtz(LinearPDE): Line 2030  class Helmholtz(LinearPDE):
2030           return escript.Data()           return escript.Data()
2031       elif name == "y_contact" :       elif name == "y_contact" :
2032           return escript.Data()           return escript.Data()
2033         elif name == "A_reduced" :
2034             return escript.Data()
2035         elif name == "B_reduced" :
2036             return escript.Data()
2037         elif name == "C_reduced" :
2038             return escript.Data()
2039         elif name == "D_reduced" :
2040             return escript.Data()
2041         elif name == "X_reduced" :
2042             return escript.Data()
2043         elif name == "Y_reduced" :
2044             return self.getCoefficient("f_reduced")
2045         elif name == "d_reduced" :
2046             return escript.Data()
2047         elif name == "y_reduced" :
2048            return self.getCoefficient("g_reduced")
2049         elif name == "d_contact_reduced" :
2050             return escript.Data()
2051         elif name == "y_contact_reduced" :
2052             return escript.Data()
2053       elif name == "r" :       elif name == "r" :
2054           return self.getCoefficient("r")           return self.getCoefficient("r")
2055       elif name == "q" :       elif name == "q" :
# Line 1894  class LameEquation(LinearPDE): Line 2148  class LameEquation(LinearPDE):
2148           return escript.Data()           return escript.Data()
2149       elif name == "y_contact" :       elif name == "y_contact" :
2150           return escript.Data()           return escript.Data()
2151         elif name == "A_reduced" :
2152             return escript.Data()
2153         elif name == "B_reduced" :
2154             return escript.Data()
2155         elif name == "C_reduced" :
2156             return escript.Data()
2157         elif name == "D_reduced" :
2158             return escript.Data()
2159         elif name == "X_reduced" :
2160             return escript.Data()
2161         elif name == "Y_reduced" :
2162             return escript.Data()
2163         elif name == "d_reduced" :
2164             return escript.Data()
2165         elif name == "y_reduced" :
2166             return escript.Data()
2167         elif name == "d_contact_reduced" :
2168             return escript.Data()
2169         elif name == "y_contact_reduced" :
2170             return escript.Data()
2171       elif name == "r" :       elif name == "r" :
2172           return self.getCoefficient("r")           return self.getCoefficient("r")
2173       elif name == "q" :       elif name == "q" :
# Line 1901  class LameEquation(LinearPDE): Line 2175  class LameEquation(LinearPDE):
2175       else:       else:
2176          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2177    
 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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