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trunk/esys2/escript/py_src/linearPDEs.py revision 150 by jgs, Thu Sep 15 03:44:45 2005 UTC trunk/escript/py_src/linearPDEs.py revision 720 by gross, Thu Apr 27 10:16:05 2006 UTC
# Line 1  Line 1 
1  # $Id$  # $Id$
   
 #  
 #      COPYRIGHT ACcESS 2004 -  All Rights Reserved  
 #  
 #   This software is the property of ACcESS.  No part of this code  
 #   may be copied in any form or by any means without the expressed written  
 #   consent of ACcESS.  Copying, use or modification of this software  
 #   by any unauthorised person is illegal unless that  
 #   person has a software license agreement with ACcESS.  
 #  
2  """  """
3  The module provides an interface to define and solve linear partial  The module provides an interface to define and solve linear partial
4  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any  differential equations (PDEs) within L{escript}. L{linearPDEs} does not provide any
5  solver capabilities in itself but hands the PDE over to  solver capabilities in itself but hands the PDE over to
6  the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.  the PDE solver library defined through the L{Domain<escript.Domain>} of the PDE.
7  The general interface is provided through the L{LinearPDE} class. The  The general interface is provided through the L{LinearPDE} class. The
8  L{AdvectivePDE} which is derived from the L{LinearPDE} class  L{AdvectivePDE} which is derived from the L{LinearPDE} class
9  provides an interface to PDE dominated by its advective terms. The L{Poisson},  provides an interface to PDE dominated by its advective terms. The L{Poisson},
10  L{Helmholtz}, L{LameEquation}  L{Helmholtz}, L{LameEquation}, L{AdvectivePDE}
11  classs which are also derived form the L{LinearPDE} class should be used  classs which are also derived form the L{LinearPDE} class should be used
12  to define of solve these sepecial PDEs.  to define of solve these sepecial PDEs.
13    
14  @var __author__: name of author  @var __author__: name of author
15  @var __licence__: licence agreement  @var __copyright__: copyrights
16    @var __license__: licence agreement
17  @var __url__: url entry point on documentation  @var __url__: url entry point on documentation
18  @var __version__: version  @var __version__: version
19  @var __date__: date of the version  @var __date__: date of the version
# Line 33  import util Line 24  import util
24  import numarray  import numarray
25    
26  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
27  __licence__="contact: esys@access.uq.edu.au"  __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
28  __url__="http://www.iservo.edu.au/esys/escript"                      http://www.access.edu.au
29                    Primary Business: Queensland, Australia"""
30    __license__="""Licensed under the Open Software License version 3.0
31                 http://www.opensource.org/licenses/osl-3.0.php"""
32    __url__="http://www.iservo.edu.au/esys"
33  __version__="$Revision$"  __version__="$Revision$"
34  __date__="$Date$"  __date__="$Date$"
35    
# Line 54  class UndefinedPDEError(ValueError): Line 49  class UndefinedPDEError(ValueError):
49     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
50     """     """
51    
52  class PDECoefficient:  class PDECoefficient(object):
53      """      """
54      A class for describing a PDE coefficient      A class for describing a PDE coefficient
55    
# Line 86  class PDECoefficient: Line 81  class PDECoefficient:
81      def __init__(self,where,pattern,altering):      def __init__(self,where,pattern,altering):
82         """         """
83         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
84          
85         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
86         @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}
87         @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
88                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,
89                (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
90                is instanciated as shape (3,2,2) in case of a three equations and two solution components                is instanciated as shape (3,2,2) in case of a three equations and two solution components
# Line 101  class PDECoefficient: Line 96  class PDECoefficient:
96         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
97    
98         """         """
99           super(PDECoefficient, self).__init__()
100         self.what=where         self.what=where
101         self.pattern=pattern         self.pattern=pattern
102         self.altering=altering         self.altering=altering
# Line 119  class PDECoefficient: Line 115  class PDECoefficient:
115         @param domain: domain on which the PDE uses the coefficient         @param domain: domain on which the PDE uses the coefficient
116         @type domain: L{Domain<escript.Domain>}         @type domain: L{Domain<escript.Domain>}
117         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
118         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
119         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
120         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
121         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
122         @rtype:  L{FunctionSpace<escript.FunctionSpace>}         @rtype:  L{FunctionSpace<escript.FunctionSpace>}
123         """         """
124         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
125              return escript.Function(domain)              return escript.Function(domain)
126         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
127              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
128         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
129              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
130         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
131              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
132                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
133              else:              else:
134                  return escript.Solution(domain)                  return escript.Solution(domain)
135         elif self.what==self.REDUCED:         elif self.what==self.REDUCED:
136              if reducedEquationOrder and reducedSolutionOrder:              return escript.ReducedSolution(domain)
                 return escript.ReducedSolution(domain)  
             else:  
                 return escript.ReducedSolution(domain)  
137    
138      def getValue(self):      def getValue(self):
139         """         """
# Line 162  class PDECoefficient: Line 155  class PDECoefficient:
155         @param numSolutions: number of components of the PDE solution         @param numSolutions: number of components of the PDE solution
156         @type numSolutions: C{int}         @type numSolutions: C{int}
157         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation         @param reducedEquationOrder: True to indicate that reduced order is used to represent the equation
158         @type domain: C{bool}         @type reducedEquationOrder: C{bool}
159         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution         @param reducedSolutionOrder: True to indicate that reduced order is used to represent the solution
160         @type domain: C{bool}         @type reducedSolutionOrder: C{bool}
161         @param newValue: number of components of the PDE solution         @param newValue: number of components of the PDE solution
162         @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>}
163         @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
# Line 313  class PDECoefficient: Line 306  class PDECoefficient:
306                  s=s+(dim,)                  s=s+(dim,)
307         return s         return s
308    
309  class LinearPDE:  class LinearPDE(object):
310     """     """
311     This class is used to define a general linear, steady, second order PDE     This class is used to define a general linear, steady, second order PDE
312     for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.     for an unknown function M{u} on a given domain defined through a L{Domain<escript.Domain>} object.
313    
314     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:
315      
316     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]*grad(u)[l]+B[j]u)[j]+C[l]*grad(u)[l]+D*u =-grad(X)[j,j]+Y}
317    
318     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,
319     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.
320     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
321     L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.     L{Function<escript.Function>} on the PDE or objects that can be converted into such L{Data<escript.Data>} objects.
322     M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.     M{A} is a rank two, M{B}, M{C} and M{X} are rank one and M{D} and M{Y} are scalar.
323    
324     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
325    
326     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]*grad(u)[l]+B[j]*u)+d*u=n[j]*X[j]+y}
327    
328     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 calculated by L{getNormal<escript.FunctionSpace.getNormal>} of L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
329     Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are       Notice that the coefficients M{A}, M{B} and M{X} are defined in the PDE. The coefficients M{d} and M{y} are
330     each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.       each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
331    
332    
333     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 343  class LinearPDE: Line 336  class LinearPDE:
336    
337     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.     M{r} and M{q} are each scalar where M{q} is the characteristic function defining where the constraint is applied.
338     The constraints override any other condition set by the PDE or the boundary condition.     The constraints override any other condition set by the PDE or the boundary condition.
339      
340     The PDE is symmetrical if     The PDE is symmetrical if
341    
342     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]}
343    
344     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
345    
346     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]*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] }
347    
348     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} 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.
349     The natural boundary conditions take the form:     The natural boundary conditions take the form:
350    
351     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]*grad(u[k])[l]+B[i,j,k]*u[k])+d[i,k]*u[k]=n[j]*X[i,j]+y[i]}
# Line 363  class LinearPDE: Line 356  class LinearPDE:
356    
357     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
358    
359     M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.     M{r} and M{q} are each rank one. Notice that at some locations not necessarily all components must have a constraint.
360    
361     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
362    
# Line 372  class LinearPDE: Line 365  class LinearPDE:
365          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
366          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
367    
368     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
369     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
370     defined as     defined as
371    
372     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]*grad(u[k])[l]+B[i,j,k]*u[k]-X[i,j]}
373    
# Line 387  class LinearPDE: Line 380  class LinearPDE:
380     the contact condition takes the form     the contact condition takes the form
381    
382     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]- d_contact[i,k]*jump(u)[k]}
383      
384     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
385     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
386     L{jump<util.jump>}.     L{jump<util.jump>}.
387     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>}.
388     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
# Line 403  class LinearPDE: Line 396  class LinearPDE:
396     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
397     @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)     @cvar CHOLEVSKY: The direct solver based on LDLt factorization (can only be applied for symmetric PDEs)
398     @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)     @cvar PCG: The preconditioned conjugate gradient method (can only be applied for symmetric PDEs)
399     @cvar CR: The conjugate residual method     @cvar CR: The conjugate residual method
400     @cvar CGS: The conjugate gardient square method     @cvar CGS: The conjugate gardient square method
401     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
402     @cvar SSOR: The symmetric overrealaxtion method     @cvar SSOR: The symmetric overrealaxtion method
# Line 419  class LinearPDE: Line 412  class LinearPDE:
412     @cvar PASO: PASO solver package     @cvar PASO: PASO solver package
413     @cvar SCSL: SGI SCSL solver library     @cvar SCSL: SGI SCSL solver library
414     @cvar MKL: Intel's MKL solver library     @cvar MKL: Intel's MKL solver library
415     @cvar UMFPACK: the UMFPACK library     @cvar UMFPACK: the UMFPACK library
416     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
417       @cvar AMG: algebraic multi grid
418       @cvar RILU: recursive ILU
419    
420     """     """
421     DEFAULT= 0     DEFAULT= 0
# Line 445  class LinearPDE: Line 440  class LinearPDE:
440     UMFPACK= 16     UMFPACK= 16
441     ITERATIVE= 20     ITERATIVE= 20
442     PASO= 21     PASO= 21
443       AMG= 22
444       RILU = 23
445    
446     __TOL=1.e-13     SMALL_TOLERANCE=1.e-13
447     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
448     __METHOD_KEY="method"     __METHOD_KEY="method"
449     __SYMMETRY_KEY="symmetric"     __SYMMETRY_KEY="symmetric"
450     __TOLERANCE_KEY="tolerance"     __TOLERANCE_KEY="tolerance"
451       __PRECONDITIONER_KEY="preconditioner"
452    
453    
454     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):     def __init__(self,domain,numEquations=None,numSolutions=None,debug=False):
# Line 466  class LinearPDE: Line 464  class LinearPDE:
464       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
465    
466       """       """
467         super(LinearPDE, self).__init__()
468       #       #
469       #   the coefficients of the general PDE:       #   the coefficients of the general PDE:
470       #       #
# Line 499  class LinearPDE: Line 498  class LinearPDE:
498       self.__tolerance=1.e-8       self.__tolerance=1.e-8
499       self.__solver_method=self.DEFAULT       self.__solver_method=self.DEFAULT
500       self.__solver_package=self.DEFAULT       self.__solver_package=self.DEFAULT
501         self.__preconditioner=self.DEFAULT
502       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
503       self.__sym=False       self.__sym=False
504    
# Line 602  class LinearPDE: Line 602  class LinearPDE:
602       @rtype: L{bool}       @rtype: L{bool}
603       """       """
604       return self.__reduce_solution_order       return self.__reduce_solution_order
605    
606     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
607       """       """
608       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation       returns the L{FunctionSpace<escript.FunctionSpace>} used to discretize the equation
# Line 698  class LinearPDE: Line 698  class LinearPDE:
698        else:        else:
699           A=self.getCoefficientOfGeneralPDE("A")           A=self.getCoefficientOfGeneralPDE("A")
700           if not A.isEmpty():           if not A.isEmpty():
701              tol=util.Lsup(A)*self.__TOL              tol=util.Lsup(A)*self.SMALL_TOLERANCE
702              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
703                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
704                    for j in range(self.getDim()):                    for j in range(self.getDim()):
# Line 722  class LinearPDE: Line 722  class LinearPDE:
722              if verbose: print "non-symmetric PDE because C is not present but B is"              if verbose: print "non-symmetric PDE because C is not present but B is"
723              out=False              out=False
724           elif not B.isEmpty() and not C.isEmpty():           elif not B.isEmpty() and not C.isEmpty():
725              tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.              tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
726              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
727                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
728                     for j in range(self.getDim()):                     for j in range(self.getDim()):
# Line 738  class LinearPDE: Line 738  class LinearPDE:
738           if self.getNumSolutions()>1:           if self.getNumSolutions()>1:
739             D=self.getCoefficientOfGeneralPDE("D")             D=self.getCoefficientOfGeneralPDE("D")
740             if not D.isEmpty():             if not D.isEmpty():
741               tol=util.Lsup(D)*self.__TOL               tol=util.Lsup(D)*self.SMALL_TOLERANCE
742               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
743                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
744                    if util.Lsup(D[i,k]-D[k,i])>tol:                    if util.Lsup(D[i,k]-D[k,i])>tol:
# Line 746  class LinearPDE: Line 746  class LinearPDE:
746                        out=False                        out=False
747             d=self.getCoefficientOfGeneralPDE("d")             d=self.getCoefficientOfGeneralPDE("d")
748             if not d.isEmpty():             if not d.isEmpty():
749               tol=util.Lsup(d)*self.__TOL               tol=util.Lsup(d)*self.SMALL_TOLERANCE
750               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
751                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
752                    if util.Lsup(d[i,k]-d[k,i])>tol:                    if util.Lsup(d[i,k]-d[k,i])>tol:
# Line 754  class LinearPDE: Line 754  class LinearPDE:
754                        out=False                        out=False
755             d_contact=self.getCoefficientOfGeneralPDE("d_contact")             d_contact=self.getCoefficientOfGeneralPDE("d_contact")
756             if not d_contact.isEmpty():             if not d_contact.isEmpty():
757               tol=util.Lsup(d_contact)*self.__TOL               tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
758               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
759                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
760                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:                    if util.Lsup(d_contact[i,k]-d_contact[k,i])>tol:
# Line 773  class LinearPDE: Line 773  class LinearPDE:
773         @type verbose: C{bool}         @type verbose: C{bool}
774         @keyword reordering: reordering scheme to be used during elimination. Allowed values are         @keyword reordering: reordering scheme to be used during elimination. Allowed values are
775                              L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}                              L{NO_REORDERING}, L{MINIMUM_FILL_IN}, L{NESTED_DISSECTION}
        @keyword preconditioner: preconditioner method to be used. Allowed values are  
                                 L{SSOR}, L{ILU0}, L{ILUT}, L{JACOBI}  
776         @keyword iter_max: maximum number of iteration steps allowed.         @keyword iter_max: maximum number of iteration steps allowed.
777         @keyword drop_tolerance: threshold for drupping in L{ILUT}         @keyword drop_tolerance: threshold for drupping in L{ILUT}
778         @keyword drop_storage: maximum of allowed memory in L{ILUT}         @keyword drop_storage: maximum of allowed memory in L{ILUT}
# Line 787  class LinearPDE: Line 785  class LinearPDE:
785               self.__solution=self.copyConstraint(f*mat)               self.__solution=self.copyConstraint(f*mat)
786            else:            else:
787               options[self.__TOLERANCE_KEY]=self.getTolerance()               options[self.__TOLERANCE_KEY]=self.getTolerance()
788               options[self.__METHOD_KEY]=self.getSolverMethod()               options[self.__METHOD_KEY]=self.getSolverMethod()[0]
789                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
790               options[self.__PACKAGE_KEY]=self.getSolverPackage()               options[self.__PACKAGE_KEY]=self.getSolverPackage()
791               options[self.__SYMMETRY_KEY]=self.isSymmetric()               options[self.__SYMMETRY_KEY]=self.isSymmetric()
792               self.trace("PDE is resolved.")               self.trace("PDE is resolved.")
# Line 802  class LinearPDE: Line 801  class LinearPDE:
801    
802       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]*grad(u[k])[l]+B[i,j,k]u[k]-X[i,j]}
803    
804       or       or
805    
806       M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}       M{J[j]=A[i,j]*grad(u)[l]+B[j]u-X[j]}
807    
# Line 816  class LinearPDE: Line 815  class LinearPDE:
815     # =============================================================================     # =============================================================================
816     #   solver settings:     #   solver settings:
817     # =============================================================================     # =============================================================================
818     def setSolverMethod(self,solver=None):     def setSolverMethod(self,solver=None,preconditioner=None):
819         """         """
820         sets a new solver         sets a new solver
821    
822         @param solver: sets a new solver method.         @param solver: sets a new solver method.
823         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}.         @type solver: one of L{DEFAULT}, L{ITERATIVE} L{DIRECT}, L{CHOLEVSKY}, L{PCG}, L{CR}, L{CGS}, L{BICGSTAB}, L{SSOR}, L{GMRES}, L{PRES20}, L{LUMPING}, L{AMG}
824           @param preconditioner: sets a new solver method.
825           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
826         """         """
827         if solver==None: solve=self.DEFAULT         if solver==None: solve=self.DEFAULT
828         if not solver==self.getSolverMethod():         if preconditioner==None: preconditioner=self.DEFAULT
829           if not (solver,preconditioner)==self.getSolverMethod():
830             self.__solver_method=solver             self.__solver_method=solver
831               self.__preconditioner=preconditioner
832             self.__checkMatrixType()             self.__checkMatrixType()
833             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
834    
# Line 839  class LinearPDE: Line 842  class LinearPDE:
842    
843         m=self.getSolverMethod()         m=self.getSolverMethod()
844         p=self.getSolverPackage()         p=self.getSolverPackage()
845         if m==self.DEFAULT: method="DEFAULT"         method=""
846         elif m==self.DIRECT: method= "DIRECT"         if m[0]==self.DEFAULT: method="DEFAULT"
847         elif m==self.ITERATIVE: method= "ITERATIVE"         elif m[0]==self.DIRECT: method= "DIRECT"
848         elif m==self.CHOLEVSKY: method= "CHOLEVSKY"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
849         elif m==self.PCG: method= "PCG"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
850         elif m==self.CR: method= "CR"         elif m[0]==self.PCG: method= "PCG"
851         elif m==self.CGS: method= "CGS"         elif m[0]==self.CR: method= "CR"
852         elif m==self.BICGSTAB: method= "BICGSTAB"         elif m[0]==self.CGS: method= "CGS"
853         elif m==self.SSOR: method= "SSOR"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
854         elif m==self.GMRES: method= "GMRES"         elif m[0]==self.SSOR: method= "SSOR"
855         elif m==self.PRES20: method= "PRES20"         elif m[0]==self.GMRES: method= "GMRES"
856         elif m==self.LUMPING: method= "LUMPING"         elif m[0]==self.PRES20: method= "PRES20"
857         else : method="unknown"         elif m[0]==self.LUMPING: method= "LUMPING"
858           elif m[0]==self.AMG: method= "AMG"
859           if m[1]==self.DEFAULT: method+="+DEFAULT"
860           elif m[1]==self.JACOBI: method+= "+JACOBI"
861           elif m[1]==self.ILU0: method+= "+ILU0"
862           elif m[1]==self.ILUT: method+= "+ILUT"
863           elif m[1]==self.SSOR: method+= "+SSOR"
864           elif m[1]==self.AMG: method+= "+AMG"
865           elif m[1]==self.RILU: method+= "+RILU"
866         if p==self.DEFAULT: package="DEFAULT"         if p==self.DEFAULT: package="DEFAULT"
867         elif p==self.PASO: package= "PASO"         elif p==self.PASO: package= "PASO"
868         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
# Line 865  class LinearPDE: Line 876  class LinearPDE:
876         """         """
877         returns the solver method         returns the solver method
878    
879         @return: the solver method currently be used.         @return: the solver method currently be used.
880         @rtype: C{int}         @rtype: C{int}
881         """         """
882         return self.__solver_method         return self.__solver_method,self.__preconditioner
883    
884     def setSolverPackage(self,package=None):     def setSolverPackage(self,package=None):
885         """         """
886         sets a new solver package         sets a new solver package
887    
888         @param solver: sets a new solver method.         @param package: sets a new solver method.
889         @type solver: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMLPACK}         @type package: one of L{DEFAULT}, L{PASO} L{SCSL}, L{MKL}, L{UMFPACK}
890         """         """
891         if package==None: package=self.DEFAULT         if package==None: package=self.DEFAULT
892         if not package==self.getSolverPackage():         if not package==self.getSolverPackage():
# Line 887  class LinearPDE: Line 898  class LinearPDE:
898         """         """
899         returns the package of the solver         returns the package of the solver
900    
901         @return: the solver package currently being used.         @return: the solver package currently being used.
902         @rtype: C{int}         @rtype: C{int}
903         """         """
904         return self.__solver_package         return self.__solver_package
# Line 899  class LinearPDE: Line 910  class LinearPDE:
910        @return: True is lumping is currently used a solver method.        @return: True is lumping is currently used a solver method.
911        @rtype: C{bool}        @rtype: C{bool}
912        """        """
913        return self.getSolverMethod()==self.LUMPING        return self.getSolverMethod()[0]==self.LUMPING
914    
915     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
916         """         """
# Line 1092  class LinearPDE: Line 1103  class LinearPDE:
1103       """       """
1104       reassess the matrix type and, if a new matrix is needed, resets the system.       reassess the matrix type and, if a new matrix is needed, resets the system.
1105       """       """
1106       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod(),self.getSolverPackage(),self.isSymmetric())       new_matrix_type=self.getDomain().getSystemMatrixTypeId(self.getSolverMethod()[0],self.getSolverPackage(),self.isSymmetric())
1107       if not new_matrix_type==self.__matrix_type:       if not new_matrix_type==self.__matrix_type:
1108           self.trace("Matrix type is now %d."%new_matrix_type)           self.trace("Matrix type is now %d."%new_matrix_type)
1109           self.__matrix_type=new_matrix_type           self.__matrix_type=new_matrix_type
# Line 1516  class LinearPDE: Line 1527  class LinearPDE:
1527         if not self.__operator_is_Valid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1528            if self.isUsingLumping():            if self.isUsingLumping():
1529                if not self.__operator_is_Valid:                if not self.__operator_is_Valid:
1530                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1531                   if not self.getCoefficientOfGeneralPDE("A").isEmpty(): raise Warning,"Using coefficient A in lumped matrix can produce wrong results"                        raise TypeError,"Lumped matrix requires same order for equations and unknowns"
1532                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1533                   if not self.getCoefficientOfGeneralPDE("C").isEmpty(): raise Warning,"Using coefficient C in lumped matrix can produce wrong results"                        raise ValueError,"coefficient A in lumped matrix may not be present."
1534                   mat=self.__getNewOperator()                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1535                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient A in lumped matrix may not be present."
1536                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1537                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient A in lumped matrix may not be present."
1538                             self.getCoefficientOfGeneralPDE("C"), \                   D=self.getCoefficientOfGeneralPDE("D")
1539                             self.getCoefficientOfGeneralPDE("D"), \                   if not D.isEmpty():
1540                             escript.Data(), \                       if self.getNumSolutions()>1:
1541                             escript.Data(), \                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))
1542                             self.getCoefficientOfGeneralPDE("d"), \                       else:
1543                             escript.Data(),\                          D_times_e=D
1544                             self.getCoefficientOfGeneralPDE("d_contact"), \                   else:
1545                             escript.Data())                      D_times_e=escript.Data()
1546                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                   d=self.getCoefficientOfGeneralPDE("d")
1547                   del mat                   if not d.isEmpty():
1548                         if self.getNumSolutions()>1:
1549                            d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))
1550                         else:
1551                            d_times_e=d
1552                     else:
1553                        d_times_e=escript.Data()
1554                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1555                     if not d_contact.isEmpty():
1556                         if self.getNumSolutions()>1:
1557                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1558                         else:
1559                            d_contact_times_e=d_contact
1560                     else:
1561                        d_contact_times_e=escript.Data()
1562        
1563                     self.__operator=self.__getNewRightHandSide()
1564                     self.getDomain().addPDEToRHS(self.__operator, \
1565                                                  escript.Data(), \
1566                                                  D_times_e, \
1567                                                  d_times_e,\
1568                                                  d_contact_times_e)
1569                     self.__operator=1./self.__operator
1570                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1571                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
1572                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
# Line 1605  class Poisson(LinearPDE): Line 1638  class Poisson(LinearPDE):
1638    
1639     """     """
1640    
1641     def __init__(self,domain,f=escript.Data(),q=escript.Data(),debug=False):     def __init__(self,domain,debug=False):
1642       """       """
1643       initializes a new Poisson equation       initializes a new Poisson equation
1644    
# Line 1614  class Poisson(LinearPDE): Line 1647  class Poisson(LinearPDE):
1647       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
1648    
1649       """       """
1650       LinearPDE.__init__(self,domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1651       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1652                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1653       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1631  class Poisson(LinearPDE): Line 1664  class Poisson(LinearPDE):
1664                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1665       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1666       """       """
1667       LinearPDE.setValue(self,**coefficients)       super(Poisson, self).setValue(**coefficients)
1668    
1669     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1670       """       """
# Line 1645  class Poisson(LinearPDE): Line 1678  class Poisson(LinearPDE):
1678       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.       @note: This method is called by the assembling routine to map the Possion equation onto the general PDE.
1679       """       """
1680       if name == "A" :       if name == "A" :
1681           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))           return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1682       elif name == "B" :       elif name == "B" :
1683           return escript.Data()           return escript.Data()
1684       elif name == "C" :       elif name == "C" :
# Line 1696  class Helmholtz(LinearPDE): Line 1729  class Helmholtz(LinearPDE):
1729       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
1730    
1731       """       """
1732       LinearPDE.__init__(self,domain,1,1,debug)       super(Helmholtz, self).__init__(domain,1,1,debug)
1733       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1734                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1735                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
# Line 1729  class Helmholtz(LinearPDE): Line 1762  class Helmholtz(LinearPDE):
1762                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1763       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1764       """       """
1765       LinearPDE.setValue(self,**coefficients)       super(Helmholtz, self).setValue(**coefficients)
1766    
1767     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1768       """       """
# Line 1774  class LameEquation(LinearPDE): Line 1807  class LameEquation(LinearPDE):
1807     """     """
1808     Class to define a Lame equation problem:     Class to define a Lame equation problem:
1809    
1810     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[j])[i])[j] = F_i -grad(S{sigma}[i,j])[j] }     M{-grad(S{mu}*(grad(u[i])[j]+grad(u[j])[i]))[j] - grad(S{lambda}*grad(u[k])[k])[j] = F_i -grad(S{sigma}[ij])[j] }
1811    
1812     with natural boundary conditons:     with natural boundary conditons:
1813    
1814     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) - S{lambda}*grad(u[j])[i]) = f_i -n[j]*S{sigma}[i,j] }     M{n[j]*(S{mu}*(grad(u[i])[j]+grad(u[j])[i]) + S{lambda}*grad(u[k])[k]) = f_i +n[j]*S{sigma}[ij] }
1815    
1816     and constraints:     and constraints:
1817    
# Line 1787  class LameEquation(LinearPDE): Line 1820  class LameEquation(LinearPDE):
1820     """     """
1821    
1822     def __init__(self,domain,debug=False):     def __init__(self,domain,debug=False):
1823         LinearPDE.__init__(self,domain,domain.getDim(),domain.getDim(),debug)        super(LameEquation, self).__init__(domain,\
1824         self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                                           domain.getDim(),domain.getDim(),debug)
1825          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1826                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1827                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1828                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1829                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1830                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1831                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1832         self.setSymmetryOn()        self.setSymmetryOn()
1833    
1834     def setValue(self,**coefficients):     def setValues(self,**coefficients):
1835       """       """
1836       sets new values to coefficients       sets new values to coefficients
1837    
# Line 1820  class LameEquation(LinearPDE): Line 1854  class LameEquation(LinearPDE):
1854                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1855       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1856       """       """
1857       LinearPDE.setValue(self,**coefficients)       super(LameEquation, self).setValues(**coefficients)
1858    
1859     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1860       """       """
# Line 1876  class AdvectivePDE(LinearPDE): Line 1910  class AdvectivePDE(LinearPDE):
1910    
1911     M{Z[j]=C[j]-B[j]}     M{Z[j]=C[j]-B[j]}
1912    
1913     or     or
1914    
1915     M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}     M{Z[i,k,l]=C[i,k,l]-B[i,l,k]}
1916    
1917     To measure the dominance of the advective terms over the diffusive term M{A} the     To measure the dominance of the advective terms over the diffusive term M{A} the
1918     X{Pelclet number} M{P} is used. It is defined as     X{Pelclet number} M{P} is used. It is defined as
1919    
1920     M{P=h|Z|/(2|A|)}     M{P=h|Z|/(2|A|)}
1921    
1922     where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size     where M{|.|} denotes the L{length<util.length>} of the arument and M{h} is the local cell size
1923     from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.     from L{getSize<escript.Domain.getSize>}. Where M{|A|==0} M{P} is M{S{infinity}}.
1924    
1925     From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:     From the X{Pelclet number} the stabilization parameters M{S{Xi}} and M{S{Xi}} are calculated:
# Line 1913  class AdvectivePDE(LinearPDE): Line 1947  class AdvectivePDE(LinearPDE):
1947     """     """
1948     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1949        """        """
1950        creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}        creates a linear, steady, second order PDE on a L{Domain<escript.Domain>}
1951    
1952        @param domain: domain of the PDE        @param domain: domain of the PDE
1953        @type domain: L{Domain<escript.Domain>}        @type domain: L{Domain<escript.Domain>}
# Line 1921  class AdvectivePDE(LinearPDE): Line 1955  class AdvectivePDE(LinearPDE):
1955                             is exracted from the PDE coefficients.                             is exracted from the PDE coefficients.
1956        @param numSolutions: number of solution components. If  numSolutions==None the number of solution components        @param numSolutions: number of solution components. If  numSolutions==None the number of solution components
1957                             is exracted from the PDE coefficients.                             is exracted from the PDE coefficients.
1958        @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the        @param xi: defines a function which returns for any given Preclet number as L{Scalar<escript.Scalar>} object the
1959                   M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.                   M{S{xi}}-value used to define the stabilization parameters. If equal to None, L{ELMAN_RAMAGE} is used.
1960        @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.        @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1961        @param debug: if True debug informations are printed.        @param debug: if True debug informations are printed.
1962        """        """
1963          super(AdvectivePDE, self).__init__(domain,\
1964        LinearPDE.__init__(self,domain,numEquations,numSolutions,debug)                                           numEquations,numSolutions,debug)
1965        if xi==None:        if xi==None:
1966           self.__xi=AdvectivePDE.ELMAN_RAMAGE           self.__xi=AdvectivePDE.ELMAN_RAMAGE
1967        else:        else:
# Line 1971  class AdvectivePDE(LinearPDE): Line 2005  class AdvectivePDE(LinearPDE):
2005    
2006        """        """
2007        if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()        if "A" in coefficients.keys()   or "B" in coefficients.keys() or "C" in coefficients.keys(): self.__Xi=escript.Data()
2008        LinearPDE.setValue(self,**coefficients)        super(AdvectivePDE, self).setValue(**coefficients)
2009    
2010     def ELMAN_RAMAGE(self,P):     def ELMAN_RAMAGE(self,P):
2011       """       """
2012       Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.       Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2013       This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)       This function uses the method suggested by H.C. Elman and A. Ramage, I{SIAM J. Numer. Anal.}, B{40} (2002)
2014            - M{S{xi}(P)=0} for M{P<1}            - M{S{xi}(P)=0} for M{P<1}
2015            - M{S{xi}(P)=(1-1/P)/2} otherwise            - M{S{xi}(P)=(1-1/P)/2} otherwise
2016    
2017       @param P: Preclet number       @param P: Preclet number
2018       @type P: L{Scalar<escript.Scalar>}       @type P: L{Scalar<escript.Scalar>}
2019       @return: up-wind weightimg factor       @return: up-wind weightimg factor
2020       @rtype: L{Scalar<escript.Scalar>}       @rtype: L{Scalar<escript.Scalar>}
2021       """       """
2022       return (P-1.).wherePositive()*0.5*(1.-1./(P+1.e-15))       return util.wherePositive(P-1.)*0.5*(1.-1./(P+1.e-15))
2023    
2024     def SIMPLIFIED_BROOK_HUGHES(self,P):     def SIMPLIFIED_BROOK_HUGHES(self,P):
2025       """       """
2026       Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.       Predefined function to set a values for M{S{xi}} from a Preclet number M{P}.
2027       The original methods is       The original methods is
2028        
2029       M{S{xi}(P)=coth(P)-1/P}       M{S{xi}(P)=coth(P)-1/P}
2030    
2031       As the evaluation of M{coth} is expensive we are using the approximation:       As the evaluation of M{coth} is expensive we are using the approximation:
2032        
2033           - M{S{xi}(P)=P/3} where M{P<3}           - M{S{xi}(P)=P/3} where M{P<3}
2034           - M{S{xi}(P)=1/2} otherwise           - M{S{xi}(P)=1/2} otherwise
2035    
2036       @param P: Preclet number       @param P: Preclet number
2037       @type P: L{Scalar<escript.Scalar>}       @type P: L{Scalar<escript.Scalar>}
2038       @return: up-wind weightimg factor       @return: up-wind weightimg factor
2039       @rtype: L{Scalar<escript.Scalar>}       @rtype: L{Scalar<escript.Scalar>}
2040       """       """
2041       c=(P-3.).whereNegative()       c=util.whereNegative(P-3.)
2042       return P/6.*c+1./2.*(1.-c)       return P/6.*c+1./2.*(1.-c)
2043    
2044     def HALF(self,P):     def HALF(self,P):
2045       """       """
2046       Predefined function to set value M{1/2} for M{S{xi}}       Predefined function to set value M{1/2} for M{S{xi}}
2047    
2048       @param P: Preclet number       @param P: Preclet number
2049       @type P: L{Scalar<escript.Scalar>}       @type P: L{Scalar<escript.Scalar>}
2050       @return: up-wind weightimg factor       @return: up-wind weightimg factor
2051       @rtype: L{Scalar<escript.Scalar>}       @rtype: L{Scalar<escript.Scalar>}
2052       """       """
2053       return escript.Scalar(0.5,P.getFunctionSpace())       return escript.Scalar(0.5,P.getFunctionSpace())
2054    
    def __calculateXi(self,peclet_factor,Z,h):  
        Z_max=util.Lsup(Z)  
        if Z_max>0.:  
           return h*self.__xi(Z*peclet_factor)/(Z+Z_max*self.__TOL)  
        else:  
           return 0.  
   
2055     def __getXi(self):     def __getXi(self):
2056        if self.__Xi.isEmpty():        if self.__Xi.isEmpty():
2057           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 2034  class AdvectivePDE(LinearPDE): Line 2061  class AdvectivePDE(LinearPDE):
2061           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2062           if not C.isEmpty() or not B.isEmpty():           if not C.isEmpty() or not B.isEmpty():
2063              if not C.isEmpty() and not B.isEmpty():              if not C.isEmpty() and not B.isEmpty():
                 Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
2064                  if self.getNumEquations()>1:                  if self.getNumEquations()>1:
2065                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2066                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2067                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2068                           for k in range(self.getNumSolutions()):                           for k in range(self.getNumSolutions()):
2069                              for l in range(self.getDim()): Z2+=(C[i,k,l]-B[i,l,k])**2                              for l in range(self.getDim()): flux2+=(C[i,k,l]-B[i,l,k])**2
2070                          length_of_flux=util.sqrt(flux2)
2071                          # flux=C-util.reorderComponents(B,[0,2,1])
2072                     else:                     else:
2073                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2074                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2075                           for l in range(self.getDim()): Z2+=(C[i,l]-B[i,l])**2                           for l in range(self.getDim()): flux2+=(C[i,l]-B[i,l])**2
2076                          length_of_flux=util.sqrt(flux2)
2077                          # flux=C-B
2078                  else:                  else:
2079                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2080                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2081                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2082                           for l in range(self.getDim()): Z2+=(C[k,l]-B[l,k])**2                           for l in range(self.getDim()): flux2+=(C[k,l]-B[l,k])**2
2083                          # flux=C-util.reorderComponents(B,[1,0])
2084                          length_of_flux=util.sqrt(flux2)
2085                     else:                     else:
2086                        for l in range(self.getDim()): Z2+=(C[l]-B[l])**2                        length_of_flux=util.length(C-B)
                 length_of_Z=util.sqrt(Z2)  
2087              elif C.isEmpty():              elif C.isEmpty():
2088                length_of_Z=util.length(B)                length_of_flux=util.length(B)
2089              else:              else:
2090                length_of_Z=util.length(C)                length_of_flux=util.length(C)
2091                flux_max=util.Lsup(length_of_flux)
2092              Z_max=util.Lsup(length_of_Z)              if flux_max>0.:
2093              if Z_max>0.:                if A.isEmpty():
2094                 length_of_A=util.length(A)                    inv_A=1./self.SMALL_TOLERANCE
2095                 A_max=util.Lsup(length_of_A)                    peclet_number=escript.Scalar(inv_A,length_of_flux.getFunctionSpace())
2096                 if A_max>0:                    xi=self.__xi(self,peclet_number)
2097                      inv_A=1./(length_of_A+A_max*self.__TOL)                else:
2098                 else:                    # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2099                      inv_A=1./self.__TOL                    length_of_A=util.length(A)
2100                 peclet_number=length_of_Z*h/2*inv_A                    A_max=util.Lsup(length_of_A)
2101                 xi=self.__xi(peclet_number)                    if A_max>0:
2102                 self.__Xi=h*xi/(length_of_Z+Z_max*self.__TOL)                         inv_A=1./(length_of_A+A_max*self.SMALL_TOLERANCE)
2103                 self.trace("preclet number = %e"%util.Lsup(peclet_number))                    else:
2104                           inv_A=1./self.SMALL_TOLERANCE
2105                      peclet_number=length_of_flux*h/2*inv_A
2106                      xi=self.__xi(self,peclet_number)
2107                  self.__Xi=h*xi/(length_of_flux+flux_max*self.SMALL_TOLERANCE)
2108                  self.trace("preclet number = %e"%util.Lsup(peclet_number))
2109                else:
2110                  self.__Xi=escript.Scalar(0.,length_of_flux.getFunctionSpace())
2111        return self.__Xi        return self.__Xi
2112    
2113    
# Line 2093  class AdvectivePDE(LinearPDE): Line 2134  class AdvectivePDE(LinearPDE):
2134              Aout=A              Aout=A
2135           else:           else:
2136              if A.isEmpty():              if A.isEmpty():
2137                 Aout=self.createNewCoefficient("A")                 Aout=self.createCoefficientOfGeneralPDE("A")
2138              else:              else:
2139                 Aout=A[:]                 Aout=A[:]
2140              Xi=self.__getXi()              Xi=self.__getXi()
# Line 2103  class AdvectivePDE(LinearPDE): Line 2144  class AdvectivePDE(LinearPDE):
2144                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2145                           for l in range(self.getDim()):                           for l in range(self.getDim()):
2146                              if not C.isEmpty() and not B.isEmpty():                              if not C.isEmpty() and not B.isEmpty():
2147                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2148                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2149                                 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])                                 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])
2150                              elif C.isEmpty():                              elif C.isEmpty():
2151                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*B[p,j,i]*B[p,l,k]
2152                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2153                              else:                              else:
2154                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]                                 for p in range(self.getNumEquations()): Aout[i,j,k,l]+=Xi*C[p,i,j]*C[p,k,l]
2155                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2156              else:              else:
2157                  for j in range(self.getDim()):                 if not C.isEmpty() and not B.isEmpty():
2158                     for l in range(self.getDim()):                     delta=(C-B)
2159                        if not C.isEmpty() and not B.isEmpty():                     Aout+=util.outer(Xi*delta,delta)
2160                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])                 elif not B.isEmpty():
2161                        elif C.isEmpty():                     Aout+=util.outer(Xi*B,B)
2162                            Aout[j,l]+=Xi*B[j]*B[l]                 elif not C.isEmpty():
2163                        else:                     Aout+=util.outer(Xi*C,C)
                           Aout[j,l]+=Xi*C[j]*C[l]  
2164           return Aout           return Aout
2165       elif name == "B" :       elif name == "B" :
2166             # return self.getCoefficient("B")
2167           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2168           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2169           D=self.getCoefficient("D")           D=self.getCoefficient("D")
# Line 2127  class AdvectivePDE(LinearPDE): Line 2172  class AdvectivePDE(LinearPDE):
2172           else:           else:
2173              Xi=self.__getXi()              Xi=self.__getXi()
2174              if B.isEmpty():              if B.isEmpty():
2175                  Bout=self.createNewCoefficient("B")                  Bout=self.createCoefficientOfGeneralPDE("B")
2176              else:              else:
2177                  Bout=B[:]                  Bout=B[:]
2178              if self.getNumEquations()>1:              if self.getNumEquations()>1:
# Line 2137  class AdvectivePDE(LinearPDE): Line 2182  class AdvectivePDE(LinearPDE):
2182                       for i in range(self.getNumEquations()):                       for i in range(self.getNumEquations()):
2183                          for j in range(self.getDim()):                          for j in range(self.getDim()):
2184                             Bout[i,j,k]+=tmp*C[p,i,j]                             Bout[i,j,k]+=tmp*C[p,i,j]
2185                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2186              else:              else:
2187                 tmp=Xi*D                 Bout+=(Xi*D)*C
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
2188           return Bout           return Bout
2189       elif name == "C" :       elif name == "C" :
2190             # return self.getCoefficient("C")
2191           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2192           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2193           D=self.getCoefficient("D")           D=self.getCoefficient("D")
# Line 2150  class AdvectivePDE(LinearPDE): Line 2196  class AdvectivePDE(LinearPDE):
2196           else:           else:
2197              Xi=self.__getXi()              Xi=self.__getXi()
2198              if C.isEmpty():              if C.isEmpty():
2199                  Cout=self.createNewCoefficient("C")                  Cout=self.createCoefficientOfGeneralPDE("C")
2200              else:              else:
2201                  Cout=C[:]                  Cout=C[:]
2202              if self.getNumEquations()>1:              if self.getNumEquations()>1:
# Line 2160  class AdvectivePDE(LinearPDE): Line 2206  class AdvectivePDE(LinearPDE):
2206                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2207                          for l in range(self.getDim()):                          for l in range(self.getDim()):
2208                                   Cout[i,k,l]+=tmp*B[p,l,i]                                   Cout[i,k,l]+=tmp*B[p,l,i]
2209                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2210              else:              else:
2211                 tmp=Xi*D                 Cout+=(Xi*D)*B
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
2212           return Cout           return Cout
2213       elif name == "D" :       elif name == "D" :
2214           return self.getCoefficient("D")           return self.getCoefficient("D")
2215       elif name == "X" :       elif name == "X" :
2216             # return self.getCoefficient("X")
2217           X=self.getCoefficient("X")           X=self.getCoefficient("X")
2218           Y=self.getCoefficient("Y")           Y=self.getCoefficient("Y")
2219           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 2175  class AdvectivePDE(LinearPDE): Line 2222  class AdvectivePDE(LinearPDE):
2222              Xout=X              Xout=X
2223           else:           else:
2224              if X.isEmpty():              if X.isEmpty():
2225                  Xout=self.createNewCoefficient("X")                  Xout=self.createCoefficientOfGeneralPDE("X")
2226              else:              else:
2227                  Xout=X[:]                  Xout=X[:]
2228              Xi=self.__getXi()              Xi=self.__getXi()
# Line 2186  class AdvectivePDE(LinearPDE): Line 2233  class AdvectivePDE(LinearPDE):
2233                         for j in range(self.getDim()):                         for j in range(self.getDim()):
2234                            if not C.isEmpty() and not B.isEmpty():                            if not C.isEmpty() and not B.isEmpty():
2235                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2236                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2237                            elif C.isEmpty():                            elif C.isEmpty():
2238                               Xout[i,j]-=tmp*B[p,j,i]                               Xout[i,j]-=tmp*B[p,j,i]
2239                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2240                            else:                            else:
2241                               Xout[i,j]+=tmp*C[p,i,j]                               Xout[i,j]+=tmp*C[p,i,j]
2242                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2243              else:              else:
2244                   tmp=Xi*Y                if not C.isEmpty() and not B.isEmpty():
2245                   for j in range(self.getDim()):                  Xout+=(Xi*Y)*(C-B)
2246                      if not C.isEmpty() and not B.isEmpty():                elif C.isEmpty():
2247                         Xout[j]+=tmp*(C[j]-B[j])                  Xout-=(Xi*Y)*B
2248                      elif C.isEmpty():                else:
2249                         Xout[j]-=tmp*B[j]                  Xout+=(Xi*Y)*C
                     else:  
                        Xout[j]+=tmp*C[j]  
2250           return Xout           return Xout
2251       elif name == "Y" :       elif name == "Y" :
2252           return self.getCoefficient("Y")           return self.getCoefficient("Y")
# Line 2217  class AdvectivePDE(LinearPDE): Line 2265  class AdvectivePDE(LinearPDE):
2265       else:       else:
2266          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2267    
   
2268  # $Log$  # $Log$
2269    # Revision 1.14  2005/09/22 01:54:57  jgs
2270    # Merge of development branch dev-02 back to main trunk on 2005-09-22
2271    #
2272  # Revision 1.13  2005/09/15 03:44:19  jgs  # Revision 1.13  2005/09/15 03:44:19  jgs
2273  # Merge of development branch dev-02 back to main trunk on 2005-09-15  # Merge of development branch dev-02 back to main trunk on 2005-09-15
2274  #  #
# Line 2231  class AdvectivePDE(LinearPDE): Line 2281  class AdvectivePDE(LinearPDE):
2281  # Revision 1.10  2005/08/12 01:45:36  jgs  # Revision 1.10  2005/08/12 01:45:36  jgs
2282  # erge of development branch dev-02 back to main trunk on 2005-08-12  # erge of development branch dev-02 back to main trunk on 2005-08-12
2283  #  #
2284    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2285    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2286    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2287    # modified to instead use portable/cooperative "super" calls to extend base
2288    # class methods.
2289    #
2290    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2291    # Removed redundant if-loop.
2292    #
2293  # Revision 1.9.2.15  2005/09/14 08:09:18  matt  # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2294  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2295  #  #

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