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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 614 by elspeth, Wed Mar 22 01:37:07 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{AdvectionDiffusion}
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 __license__: licence agreement
16  @var __url__: url entry point on documentation  @var __url__: url entry point on documentation
17  @var __version__: version  @var __version__: version
18  @var __date__: date of the version  @var __date__: date of the version
# Line 33  import util Line 23  import util
23  import numarray  import numarray
24    
25  __author__="Lutz Gross, l.gross@uq.edu.au"  __author__="Lutz Gross, l.gross@uq.edu.au"
26  __licence__="contact: esys@access.uq.edu.au"  __copyright__="""  Copyright (c) 2006 by ACcESS MNRF
27                        http://www.access.edu.au
28                    Primary Business: Queensland, Australia"""
29    __license__="""Licensed under the Open Software License version 3.0
30                 http://www.opensource.org/licenses/osl-3.0.php"""
31  __url__="http://www.iservo.edu.au/esys/escript"  __url__="http://www.iservo.edu.au/esys/escript"
32  __version__="$Revision$"  __version__="$Revision$"
33  __date__="$Date$"  __date__="$Date$"
# Line 54  class UndefinedPDEError(ValueError): Line 48  class UndefinedPDEError(ValueError):
48     raised if a PDE is not fully defined yet.     raised if a PDE is not fully defined yet.
49     """     """
50    
51  class PDECoefficient:  class PDECoefficient(object):
52      """      """
53      A class for describing a PDE coefficient      A class for describing a PDE coefficient
54    
# Line 86  class PDECoefficient: Line 80  class PDECoefficient:
80      def __init__(self,where,pattern,altering):      def __init__(self,where,pattern,altering):
81         """         """
82         Initialise a PDE Coefficient type         Initialise a PDE Coefficient type
83          
84         @param where: describes where the coefficient lives         @param where: describes where the coefficient lives
85         @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}
86         @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
87                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,
88                (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
89                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 95  class PDECoefficient:
95         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}         @type altering: one of L{OPERATOR}, L{RIGHTHANDSIDE}, L{BOTH}
96    
97         """         """
98           super(PDECoefficient, self).__init__()
99         self.what=where         self.what=where
100         self.pattern=pattern         self.pattern=pattern
101         self.altering=altering         self.altering=altering
# Line 125  class PDECoefficient: Line 120  class PDECoefficient:
120         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient         @return:  L{FunctionSpace<escript.FunctionSpace>} of the coefficient
121         @rtype:  L{FunctionSpace<escript.FunctionSpace>}         @rtype:  L{FunctionSpace<escript.FunctionSpace>}
122         """         """
123         if self.what==self.INTERIOR:         if self.what==self.INTERIOR:
124              return escript.Function(domain)              return escript.Function(domain)
125         elif self.what==self.BOUNDARY:         elif self.what==self.BOUNDARY:
126              return escript.FunctionOnBoundary(domain)              return escript.FunctionOnBoundary(domain)
127         elif self.what==self.CONTACT:         elif self.what==self.CONTACT:
128              return escript.FunctionOnContactZero(domain)              return escript.FunctionOnContactZero(domain)
129         elif self.what==self.SOLUTION:         elif self.what==self.SOLUTION:
130              if reducedEquationOrder and reducedSolutionOrder:              if reducedEquationOrder and reducedSolutionOrder:
131                  return escript.ReducedSolution(domain)                  return escript.ReducedSolution(domain)
132              else:              else:
133                  return escript.Solution(domain)                  return escript.Solution(domain)
134         elif self.what==self.REDUCED:         elif self.what==self.REDUCED:
135              if reducedEquationOrder and reducedSolutionOrder:              return escript.ReducedSolution(domain)
                 return escript.ReducedSolution(domain)  
             else:  
                 return escript.ReducedSolution(domain)  
136    
137      def getValue(self):      def getValue(self):
138         """         """
# Line 313  class PDECoefficient: Line 305  class PDECoefficient:
305                  s=s+(dim,)                  s=s+(dim,)
306         return s         return s
307    
308  class LinearPDE:  class LinearPDE(object):
309     """     """
310     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
311     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.
312    
313     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:
314      
315     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}
316    
317     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,
318     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.
319     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
320     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.
321     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.
322    
323     The following natural boundary conditions are considered:     The following natural boundary conditions are considered:
324    
325     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}
326    
327     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>}.
328     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
329     each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.       each a scalar in the L{FunctionOnBoundary<escript.FunctionOnBoundary>}.
330    
331    
332     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 335  class LinearPDE:
335    
336     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.
337     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.
338      
339     The PDE is symmetrical if     The PDE is symmetrical if
340    
341     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]}
342    
343     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
344    
345     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] }
346    
347     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.
348     The natural boundary conditions take the form:     The natural boundary conditions take the form:
349    
350     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 355  class LinearPDE:
355    
356     M{u[i]=r[i]}  where  M{q[i]>0}     M{u[i]=r[i]}  where  M{q[i]>0}
357    
358     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.
359    
360     The system of PDEs is symmetrical if     The system of PDEs is symmetrical if
361    
# Line 372  class LinearPDE: Line 364  class LinearPDE:
364          - M{D[i,k]=D[i,k]}          - M{D[i,k]=D[i,k]}
365          - M{d[i,k]=d[k,i]}          - M{d[i,k]=d[k,i]}
366    
367     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
368     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
369     defined as     defined as
370    
371     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]}
372    
# Line 387  class LinearPDE: Line 379  class LinearPDE:
379     the contact condition takes the form     the contact condition takes the form
380    
381     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]}
382      
383     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
384     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
385     L{jump<util.jump>}.     L{jump<util.jump>}.
386     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>}.
387     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 395  class LinearPDE:
395     @cvar DIRECT: The direct solver based on LDU factorization     @cvar DIRECT: The direct solver based on LDU factorization
396     @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)
397     @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)
398     @cvar CR: The conjugate residual method     @cvar CR: The conjugate residual method
399     @cvar CGS: The conjugate gardient square method     @cvar CGS: The conjugate gardient square method
400     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.     @cvar BICGSTAB: The stabilized BiConjugate Gradient method.
401     @cvar SSOR: The symmetric overrealaxtion method     @cvar SSOR: The symmetric overrealaxtion method
# Line 419  class LinearPDE: Line 411  class LinearPDE:
411     @cvar PASO: PASO solver package     @cvar PASO: PASO solver package
412     @cvar SCSL: SGI SCSL solver library     @cvar SCSL: SGI SCSL solver library
413     @cvar MKL: Intel's MKL solver library     @cvar MKL: Intel's MKL solver library
414     @cvar UMFPACK: the UMFPACK library     @cvar UMFPACK: the UMFPACK library
415     @cvar ITERATIVE: The default iterative solver     @cvar ITERATIVE: The default iterative solver
416       @cvar AMG: algebraic multi grid
417       @cvar RILU: recursive ILU
418    
419     """     """
420     DEFAULT= 0     DEFAULT= 0
# Line 445  class LinearPDE: Line 439  class LinearPDE:
439     UMFPACK= 16     UMFPACK= 16
440     ITERATIVE= 20     ITERATIVE= 20
441     PASO= 21     PASO= 21
442       AMG= 22
443       RILU = 23
444    
445     __TOL=1.e-13     SMALL_TOLERANCE=1.e-13
446     __PACKAGE_KEY="package"     __PACKAGE_KEY="package"
447     __METHOD_KEY="method"     __METHOD_KEY="method"
448     __SYMMETRY_KEY="symmetric"     __SYMMETRY_KEY="symmetric"
449     __TOLERANCE_KEY="tolerance"     __TOLERANCE_KEY="tolerance"
450       __PRECONDITIONER_KEY="preconditioner"
451    
452    
453     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 463  class LinearPDE:
463       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
464    
465       """       """
466         super(LinearPDE, self).__init__()
467       #       #
468       #   the coefficients of the general PDE:       #   the coefficients of the general PDE:
469       #       #
# Line 499  class LinearPDE: Line 497  class LinearPDE:
497       self.__tolerance=1.e-8       self.__tolerance=1.e-8
498       self.__solver_method=self.DEFAULT       self.__solver_method=self.DEFAULT
499       self.__solver_package=self.DEFAULT       self.__solver_package=self.DEFAULT
500         self.__preconditioner=self.DEFAULT
501       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)       self.__matrix_type=self.__domain.getSystemMatrixTypeId(self.DEFAULT,self.DEFAULT,False)
502       self.__sym=False       self.__sym=False
503    
# Line 602  class LinearPDE: Line 601  class LinearPDE:
601       @rtype: L{bool}       @rtype: L{bool}
602       """       """
603       return self.__reduce_solution_order       return self.__reduce_solution_order
604    
605     def getFunctionSpaceForEquation(self):     def getFunctionSpaceForEquation(self):
606       """       """
607       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 697  class LinearPDE:
697        else:        else:
698           A=self.getCoefficientOfGeneralPDE("A")           A=self.getCoefficientOfGeneralPDE("A")
699           if not A.isEmpty():           if not A.isEmpty():
700              tol=util.Lsup(A)*self.__TOL              tol=util.Lsup(A)*self.SMALL_TOLERANCE
701              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
702                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
703                    for j in range(self.getDim()):                    for j in range(self.getDim()):
# Line 722  class LinearPDE: Line 721  class LinearPDE:
721              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"
722              out=False              out=False
723           elif not B.isEmpty() and not C.isEmpty():           elif not B.isEmpty() and not C.isEmpty():
724              tol=(util.Lsup(B)+util.Lsup(C))*self.__TOL/2.              tol=(util.Lsup(B)+util.Lsup(C))*self.SMALL_TOLERANCE/2.
725              if self.getNumSolutions()>1:              if self.getNumSolutions()>1:
726                 for i in range(self.getNumEquations()):                 for i in range(self.getNumEquations()):
727                     for j in range(self.getDim()):                     for j in range(self.getDim()):
# Line 738  class LinearPDE: Line 737  class LinearPDE:
737           if self.getNumSolutions()>1:           if self.getNumSolutions()>1:
738             D=self.getCoefficientOfGeneralPDE("D")             D=self.getCoefficientOfGeneralPDE("D")
739             if not D.isEmpty():             if not D.isEmpty():
740               tol=util.Lsup(D)*self.__TOL               tol=util.Lsup(D)*self.SMALL_TOLERANCE
741               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
742                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
743                    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 745  class LinearPDE:
745                        out=False                        out=False
746             d=self.getCoefficientOfGeneralPDE("d")             d=self.getCoefficientOfGeneralPDE("d")
747             if not d.isEmpty():             if not d.isEmpty():
748               tol=util.Lsup(d)*self.__TOL               tol=util.Lsup(d)*self.SMALL_TOLERANCE
749               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
750                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
751                    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 753  class LinearPDE:
753                        out=False                        out=False
754             d_contact=self.getCoefficientOfGeneralPDE("d_contact")             d_contact=self.getCoefficientOfGeneralPDE("d_contact")
755             if not d_contact.isEmpty():             if not d_contact.isEmpty():
756               tol=util.Lsup(d_contact)*self.__TOL               tol=util.Lsup(d_contact)*self.SMALL_TOLERANCE
757               for i in range(self.getNumEquations()):               for i in range(self.getNumEquations()):
758                  for k in range(self.getNumSolutions()):                  for k in range(self.getNumSolutions()):
759                    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 772  class LinearPDE:
772         @type verbose: C{bool}         @type verbose: C{bool}
773         @keyword reordering: reordering scheme to be used during elimination. Allowed values are         @keyword reordering: reordering scheme to be used during elimination. Allowed values are
774                              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}  
775         @keyword iter_max: maximum number of iteration steps allowed.         @keyword iter_max: maximum number of iteration steps allowed.
776         @keyword drop_tolerance: threshold for drupping in L{ILUT}         @keyword drop_tolerance: threshold for drupping in L{ILUT}
777         @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 784  class LinearPDE:
784               self.__solution=self.copyConstraint(f*mat)               self.__solution=self.copyConstraint(f*mat)
785            else:            else:
786               options[self.__TOLERANCE_KEY]=self.getTolerance()               options[self.__TOLERANCE_KEY]=self.getTolerance()
787               options[self.__METHOD_KEY]=self.getSolverMethod()               options[self.__METHOD_KEY]=self.getSolverMethod()[0]
788                 options[self.__PRECONDITIONER_KEY]=self.getSolverMethod()[1]
789               options[self.__PACKAGE_KEY]=self.getSolverPackage()               options[self.__PACKAGE_KEY]=self.getSolverPackage()
790               options[self.__SYMMETRY_KEY]=self.isSymmetric()               options[self.__SYMMETRY_KEY]=self.isSymmetric()
791               self.trace("PDE is resolved.")               self.trace("PDE is resolved.")
# Line 802  class LinearPDE: Line 800  class LinearPDE:
800    
801       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]}
802    
803       or       or
804    
805       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]}
806    
# Line 816  class LinearPDE: Line 814  class LinearPDE:
814     # =============================================================================     # =============================================================================
815     #   solver settings:     #   solver settings:
816     # =============================================================================     # =============================================================================
817     def setSolverMethod(self,solver=None):     def setSolverMethod(self,solver=None,preconditioner=None):
818         """         """
819         sets a new solver         sets a new solver
820    
821         @param solver: sets a new solver method.         @param solver: sets a new solver method.
822         @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}
823           @param preconditioner: sets a new solver method.
824           @type preconditioner: one of L{DEFAULT}, L{JACOBI} L{ILU0}, L{ILUT},L{SSOR}, L{RILU}
825         """         """
826         if solver==None: solve=self.DEFAULT         if solver==None: solve=self.DEFAULT
827         if not solver==self.getSolverMethod():         if preconditioner==None: preconditioner=self.DEFAULT
828           if not (solver,preconditioner)==self.getSolverMethod():
829             self.__solver_method=solver             self.__solver_method=solver
830               self.__preconditioner=preconditioner
831             self.__checkMatrixType()             self.__checkMatrixType()
832             self.trace("New solver is %s"%self.getSolverMethodName())             self.trace("New solver is %s"%self.getSolverMethodName())
833    
# Line 839  class LinearPDE: Line 841  class LinearPDE:
841    
842         m=self.getSolverMethod()         m=self.getSolverMethod()
843         p=self.getSolverPackage()         p=self.getSolverPackage()
844         if m==self.DEFAULT: method="DEFAULT"         method=""
845         elif m==self.DIRECT: method= "DIRECT"         if m[0]==self.DEFAULT: method="DEFAULT"
846         elif m==self.ITERATIVE: method= "ITERATIVE"         elif m[0]==self.DIRECT: method= "DIRECT"
847         elif m==self.CHOLEVSKY: method= "CHOLEVSKY"         elif m[0]==self.ITERATIVE: method= "ITERATIVE"
848         elif m==self.PCG: method= "PCG"         elif m[0]==self.CHOLEVSKY: method= "CHOLEVSKY"
849         elif m==self.CR: method= "CR"         elif m[0]==self.PCG: method= "PCG"
850         elif m==self.CGS: method= "CGS"         elif m[0]==self.CR: method= "CR"
851         elif m==self.BICGSTAB: method= "BICGSTAB"         elif m[0]==self.CGS: method= "CGS"
852         elif m==self.SSOR: method= "SSOR"         elif m[0]==self.BICGSTAB: method= "BICGSTAB"
853         elif m==self.GMRES: method= "GMRES"         elif m[0]==self.SSOR: method= "SSOR"
854         elif m==self.PRES20: method= "PRES20"         elif m[0]==self.GMRES: method= "GMRES"
855         elif m==self.LUMPING: method= "LUMPING"         elif m[0]==self.PRES20: method= "PRES20"
856         else : method="unknown"         elif m[0]==self.LUMPING: method= "LUMPING"
857           elif m[0]==self.AMG: method= "AMG"
858           if m[1]==self.DEFAULT: method+="+DEFAULT"
859           elif m[1]==self.JACOBI: method+= "+JACOBI"
860           elif m[1]==self.ILU0: method+= "+ILU0"
861           elif m[1]==self.ILUT: method+= "+ILUT"
862           elif m[1]==self.SSOR: method+= "+SSOR"
863           elif m[1]==self.AMG: method+= "+AMG"
864           elif m[1]==self.RILU: method+= "+RILU"
865         if p==self.DEFAULT: package="DEFAULT"         if p==self.DEFAULT: package="DEFAULT"
866         elif p==self.PASO: package= "PASO"         elif p==self.PASO: package= "PASO"
867         elif p==self.MKL: package= "MKL"         elif p==self.MKL: package= "MKL"
# Line 865  class LinearPDE: Line 875  class LinearPDE:
875         """         """
876         returns the solver method         returns the solver method
877    
878         @return: the solver method currently be used.         @return: the solver method currently be used.
879         @rtype: C{int}         @rtype: C{int}
880         """         """
881         return self.__solver_method         return self.__solver_method,self.__preconditioner
882    
883     def setSolverPackage(self,package=None):     def setSolverPackage(self,package=None):
884         """         """
# Line 887  class LinearPDE: Line 897  class LinearPDE:
897         """         """
898         returns the package of the solver         returns the package of the solver
899    
900         @return: the solver package currently being used.         @return: the solver package currently being used.
901         @rtype: C{int}         @rtype: C{int}
902         """         """
903         return self.__solver_package         return self.__solver_package
# Line 899  class LinearPDE: Line 909  class LinearPDE:
909        @return: True is lumping is currently used a solver method.        @return: True is lumping is currently used a solver method.
910        @rtype: C{bool}        @rtype: C{bool}
911        """        """
912        return self.getSolverMethod()==self.LUMPING        return self.getSolverMethod()[0]==self.LUMPING
913    
914     def setTolerance(self,tol=1.e-8):     def setTolerance(self,tol=1.e-8):
915         """         """
# Line 1092  class LinearPDE: Line 1102  class LinearPDE:
1102       """       """
1103       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.
1104       """       """
1105       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())
1106       if not new_matrix_type==self.__matrix_type:       if not new_matrix_type==self.__matrix_type:
1107           self.trace("Matrix type is now %d."%new_matrix_type)           self.trace("Matrix type is now %d."%new_matrix_type)
1108           self.__matrix_type=new_matrix_type           self.__matrix_type=new_matrix_type
# Line 1516  class LinearPDE: Line 1526  class LinearPDE:
1526         if not self.__operator_is_Valid or not self.__righthandside_isValid:         if not self.__operator_is_Valid or not self.__righthandside_isValid:
1527            if self.isUsingLumping():            if self.isUsingLumping():
1528                if not self.__operator_is_Valid:                if not self.__operator_is_Valid:
1529                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution(): raise TypeError,"Lumped matrix requires same order for equations and unknowns"                   if not self.getFunctionSpaceForEquation()==self.getFunctionSpaceForSolution():
1530                   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"
1531                   if not self.getCoefficientOfGeneralPDE("B").isEmpty(): raise Warning,"Using coefficient B in lumped matrix can produce wrong results"                   if not self.getCoefficientOfGeneralPDE("A").isEmpty():
1532                   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."
1533                   mat=self.__getNewOperator()                   if not self.getCoefficientOfGeneralPDE("B").isEmpty():
1534                   self.getDomain().addPDEToSystem(mat,escript.Data(), \                        raise ValueError,"coefficient A in lumped matrix may not be present."
1535                             self.getCoefficientOfGeneralPDE("A"), \                   if not self.getCoefficientOfGeneralPDE("C").isEmpty():
1536                             self.getCoefficientOfGeneralPDE("B"), \                        raise ValueError,"coefficient A in lumped matrix may not be present."
1537                             self.getCoefficientOfGeneralPDE("C"), \                   D=self.getCoefficientOfGeneralPDE("D")
1538                             self.getCoefficientOfGeneralPDE("D"), \                   if not D.isEmpty():
1539                             escript.Data(), \                       if self.getNumSolutions()>1:
1540                             escript.Data(), \                          D_times_e=util.matrixmult(D,numarray.ones((self.getNumSolutions(),)))
1541                             self.getCoefficientOfGeneralPDE("d"), \                       else:
1542                             escript.Data(),\                          D_times_e=D
1543                             self.getCoefficientOfGeneralPDE("d_contact"), \                   else:
1544                             escript.Data())                      D_times_e=escript.Data()
1545                   self.__operator=1./(mat*escript.Data(1,(self.getNumSolutions(),),self.getFunctionSpaceForSolution(),True))                   d=self.getCoefficientOfGeneralPDE("d")
1546                   del mat                   if not d.isEmpty():
1547                         if self.getNumSolutions()>1:
1548                            d_times_e=util.matrixmult(d,numarray.ones((self.getNumSolutions(),)))
1549                         else:
1550                            d_times_e=d
1551                     else:
1552                        d_times_e=escript.Data()
1553                     d_contact=self.getCoefficientOfGeneralPDE("d_contact")
1554                     if not d_contact.isEmpty():
1555                         if self.getNumSolutions()>1:
1556                            d_contact_times_e=util.matrixmult(d_contact,numarray.ones((self.getNumSolutions(),)))
1557                         else:
1558                            d_contact_times_e=d_contact
1559                     else:
1560                        d_contact_times_e=escript.Data()
1561        
1562                     self.__operator=self.__getNewRightHandSide()
1563                     self.getDomain().addPDEToRHS(self.__operator, \
1564                                                  escript.Data(), \
1565                                                  D_times_e, \
1566                                                  d_times_e,\
1567                                                  d_contact_times_e)
1568                     self.__operator=1./self.__operator
1569                   self.trace("New lumped operator has been built.")                   self.trace("New lumped operator has been built.")
1570                   self.__operator_is_Valid=True                   self.__operator_is_Valid=True
1571                if not self.__righthandside_isValid:                if not self.__righthandside_isValid:
# Line 1605  class Poisson(LinearPDE): Line 1637  class Poisson(LinearPDE):
1637    
1638     """     """
1639    
1640     def __init__(self,domain,f=escript.Data(),q=escript.Data(),debug=False):     def __init__(self,domain,debug=False):
1641       """       """
1642       initializes a new Poisson equation       initializes a new Poisson equation
1643    
# Line 1614  class Poisson(LinearPDE): Line 1646  class Poisson(LinearPDE):
1646       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
1647    
1648       """       """
1649       LinearPDE.__init__(self,domain,1,1,debug)       super(Poisson, self).__init__(domain,1,1,debug)
1650       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),       self.COEFFICIENTS={"f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1651                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                            "q": PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1652       self.setSymmetryOn()       self.setSymmetryOn()
# Line 1631  class Poisson(LinearPDE): Line 1663  class Poisson(LinearPDE):
1663                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1664       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1665       """       """
1666       LinearPDE.setValue(self,**coefficients)       super(Poisson, self).setValue(**coefficients)
1667    
1668     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1669       """       """
# Line 1645  class Poisson(LinearPDE): Line 1677  class Poisson(LinearPDE):
1677       @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.
1678       """       """
1679       if name == "A" :       if name == "A" :
1680           return escript.Data(numarray.identity(self.getDim()),escript.Function(self.getDomain()))           return escript.Data(util.kronecker(self.getDim()),escript.Function(self.getDomain()))
1681       elif name == "B" :       elif name == "B" :
1682           return escript.Data()           return escript.Data()
1683       elif name == "C" :       elif name == "C" :
# Line 1696  class Helmholtz(LinearPDE): Line 1728  class Helmholtz(LinearPDE):
1728       @param debug: if True debug informations are printed.       @param debug: if True debug informations are printed.
1729    
1730       """       """
1731       LinearPDE.__init__(self,domain,1,1,debug)       super(Helmholtz, self).__init__(domain,1,1,debug)
1732       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),       self.COEFFICIENTS={"omega": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1733                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),                          "k": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.OPERATOR),
1734                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                          "f": PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
# Line 1729  class Helmholtz(LinearPDE): Line 1761  class Helmholtz(LinearPDE):
1761                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1762       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1763       """       """
1764       LinearPDE.setValue(self,**coefficients)       super(Helmholtz, self).setValue(**coefficients)
1765    
1766     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1767       """       """
# Line 1787  class LameEquation(LinearPDE): Line 1819  class LameEquation(LinearPDE):
1819     """     """
1820    
1821     def __init__(self,domain,debug=False):     def __init__(self,domain,debug=False):
1822         LinearPDE.__init__(self,domain,domain.getDim(),domain.getDim(),debug)        super(LameEquation, self).__init__(domain,\
1823         self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                                           domain.getDim(),domain.getDim(),debug)
1824          self.COEFFICIENTS={ "lame_lambda"  : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1825                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),                            "lame_mu"      : PDECoefficient(PDECoefficient.INTERIOR,(),PDECoefficient.OPERATOR),
1826                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "F"            : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1827                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),                            "sigma"        : PDECoefficient(PDECoefficient.INTERIOR,(PDECoefficient.BY_EQUATION,PDECoefficient.BY_DIM),PDECoefficient.RIGHTHANDSIDE),
1828                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),                            "f"            : PDECoefficient(PDECoefficient.BOUNDARY,(PDECoefficient.BY_EQUATION,),PDECoefficient.RIGHTHANDSIDE),
1829                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),                            "r"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH),
1830                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}                            "q"            : PDECoefficient(PDECoefficient.SOLUTION,(PDECoefficient.BY_EQUATION,),PDECoefficient.BOTH)}
1831         self.setSymmetryOn()        self.setSymmetryOn()
1832    
1833     def setValue(self,**coefficients):     def setValues(self,**coefficients):
1834       """       """
1835       sets new values to coefficients       sets new values to coefficients
1836    
# Line 1820  class LameEquation(LinearPDE): Line 1853  class LameEquation(LinearPDE):
1853                 depending of reduced order is used for the representation of the equation.                 depending of reduced order is used for the representation of the equation.
1854       @raise IllegalCoefficient: if an unknown coefficient keyword is used.       @raise IllegalCoefficient: if an unknown coefficient keyword is used.
1855       """       """
1856       LinearPDE.setValue(self,**coefficients)       super(LameEquation, self).setValues(**coefficients)
1857    
1858     def getCoefficientOfGeneralPDE(self,name):     def getCoefficientOfGeneralPDE(self,name):
1859       """       """
# Line 1876  class AdvectivePDE(LinearPDE): Line 1909  class AdvectivePDE(LinearPDE):
1909    
1910     M{Z[j]=C[j]-B[j]}     M{Z[j]=C[j]-B[j]}
1911    
1912     or     or
1913    
1914     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]}
1915    
1916     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
1917     X{Pelclet number} M{P} is used. It is defined as     X{Pelclet number} M{P} is used. It is defined as
1918    
1919     M{P=h|Z|/(2|A|)}     M{P=h|Z|/(2|A|)}
1920    
1921     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
1922     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}}.
1923    
1924     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 1946  class AdvectivePDE(LinearPDE):
1946     """     """
1947     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):     def __init__(self,domain,numEquations=None,numSolutions=None,xi=None,debug=False):
1948        """        """
1949        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>}
1950    
1951        @param domain: domain of the PDE        @param domain: domain of the PDE
1952        @type domain: L{Domain<escript.Domain>}        @type domain: L{Domain<escript.Domain>}
# Line 1921  class AdvectivePDE(LinearPDE): Line 1954  class AdvectivePDE(LinearPDE):
1954                             is exracted from the PDE coefficients.                             is exracted from the PDE coefficients.
1955        @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
1956                             is exracted from the PDE coefficients.                             is exracted from the PDE coefficients.
1957        @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
1958                   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.
1959        @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.        @type xi: callable object which returns a L{Scalar<escript.Scalar>} object.
1960        @param debug: if True debug informations are printed.        @param debug: if True debug informations are printed.
1961        """        """
1962          super(AdvectivePDE, self).__init__(domain,\
1963        LinearPDE.__init__(self,domain,numEquations,numSolutions,debug)                                           numEquations,numSolutions,debug)
1964        if xi==None:        if xi==None:
1965           self.__xi=AdvectivePDE.ELMAN_RAMAGE           self.__xi=AdvectivePDE.ELMAN_RAMAGE
1966        else:        else:
# Line 1971  class AdvectivePDE(LinearPDE): Line 2004  class AdvectivePDE(LinearPDE):
2004    
2005        """        """
2006        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()
2007        LinearPDE.setValue(self,**coefficients)        super(AdvectivePDE, self).setValue(**coefficients)
2008    
2009     def ELMAN_RAMAGE(self,P):     def ELMAN_RAMAGE(self,P):
2010       """       """
2011       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}.
2012       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)
2013            - M{S{xi}(P)=0} for M{P<1}            - M{S{xi}(P)=0} for M{P<1}
2014            - M{S{xi}(P)=(1-1/P)/2} otherwise            - M{S{xi}(P)=(1-1/P)/2} otherwise
2015    
2016       @param P: Preclet number       @param P: Preclet number
2017       @type P: L{Scalar<escript.Scalar>}       @type P: L{Scalar<escript.Scalar>}
2018       @return: up-wind weightimg factor       @return: up-wind weightimg factor
2019       @rtype: L{Scalar<escript.Scalar>}       @rtype: L{Scalar<escript.Scalar>}
2020       """       """
2021       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))
2022    
2023     def SIMPLIFIED_BROOK_HUGHES(self,P):     def SIMPLIFIED_BROOK_HUGHES(self,P):
2024       """       """
2025       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}.
2026       The original methods is       The original methods is
2027        
2028       M{S{xi}(P)=coth(P)-1/P}       M{S{xi}(P)=coth(P)-1/P}
2029    
2030       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:
2031        
2032           - M{S{xi}(P)=P/3} where M{P<3}           - M{S{xi}(P)=P/3} where M{P<3}
2033           - M{S{xi}(P)=1/2} otherwise           - M{S{xi}(P)=1/2} otherwise
2034    
2035       @param P: Preclet number       @param P: Preclet number
2036       @type P: L{Scalar<escript.Scalar>}       @type P: L{Scalar<escript.Scalar>}
2037       @return: up-wind weightimg factor       @return: up-wind weightimg factor
2038       @rtype: L{Scalar<escript.Scalar>}       @rtype: L{Scalar<escript.Scalar>}
2039       """       """
2040       c=(P-3.).whereNegative()       c=util.whereNegative(P-3.)
2041       return P/6.*c+1./2.*(1.-c)       return P/6.*c+1./2.*(1.-c)
2042    
2043     def HALF(self,P):     def HALF(self,P):
2044       """       """
2045       Predefined function to set value M{1/2} for M{S{xi}}       Predefined function to set value M{1/2} for M{S{xi}}
2046    
2047       @param P: Preclet number       @param P: Preclet number
2048       @type P: L{Scalar<escript.Scalar>}       @type P: L{Scalar<escript.Scalar>}
2049       @return: up-wind weightimg factor       @return: up-wind weightimg factor
2050       @rtype: L{Scalar<escript.Scalar>}       @rtype: L{Scalar<escript.Scalar>}
2051       """       """
2052       return escript.Scalar(0.5,P.getFunctionSpace())       return escript.Scalar(0.5,P.getFunctionSpace())
2053    
    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.  
   
2054     def __getXi(self):     def __getXi(self):
2055        if self.__Xi.isEmpty():        if self.__Xi.isEmpty():
2056           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 2034  class AdvectivePDE(LinearPDE): Line 2060  class AdvectivePDE(LinearPDE):
2060           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))           self.__Xi=escript.Scalar(0.,self.getFunctionSpaceForCoefficient("A"))
2061           if not C.isEmpty() or not B.isEmpty():           if not C.isEmpty() or not B.isEmpty():
2062              if not C.isEmpty() and not B.isEmpty():              if not C.isEmpty() and not B.isEmpty():
                 Z2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))  
2063                  if self.getNumEquations()>1:                  if self.getNumEquations()>1:
2064                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2065                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2066                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2067                           for k in range(self.getNumSolutions()):                           for k in range(self.getNumSolutions()):
2068                              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
2069                          length_of_flux=util.sqrt(flux2)
2070                          # flux=C-util.reorderComponents(B,[0,2,1])
2071                     else:                     else:
2072                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2073                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2074                           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
2075                          length_of_flux=util.sqrt(flux2)
2076                          # flux=C-B
2077                  else:                  else:
2078                     if self.getNumSolutions()>1:                     if self.getNumSolutions()>1:
2079                          flux2=escript.Scalar(0,self.getFunctionSpaceForCoefficient("A"))
2080                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2081                           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
2082                          # flux=C-util.reorderComponents(B,[1,0])
2083                          length_of_flux=util.sqrt(flux2)
2084                     else:                     else:
2085                        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)  
2086              elif C.isEmpty():              elif C.isEmpty():
2087                length_of_Z=util.length(B)                length_of_flux=util.length(B)
2088              else:              else:
2089                length_of_Z=util.length(C)                length_of_flux=util.length(C)
2090                flux_max=util.Lsup(length_of_flux)
2091              Z_max=util.Lsup(length_of_Z)              if flux_max>0.:
2092              if Z_max>0.:                if A.isEmpty():
2093                 length_of_A=util.length(A)                    inv_A=1./self.SMALL_TOLERANCE
2094                 A_max=util.Lsup(length_of_A)                    peclet_number=escript.Scalar(inv_A,length_of_flux.getFunctionSpace())
2095                 if A_max>0:                    xi=self.__xi(self,peclet_number)
2096                      inv_A=1./(length_of_A+A_max*self.__TOL)                else:
2097                 else:                    # length_of_A=util.inner(flux,util.tensormutiply(A,flux))
2098                      inv_A=1./self.__TOL                    length_of_A=util.length(A)
2099                 peclet_number=length_of_Z*h/2*inv_A                    A_max=util.Lsup(length_of_A)
2100                 xi=self.__xi(peclet_number)                    if A_max>0:
2101                 self.__Xi=h*xi/(length_of_Z+Z_max*self.__TOL)                         inv_A=1./(length_of_A+A_max*self.SMALL_TOLERANCE)
2102                 self.trace("preclet number = %e"%util.Lsup(peclet_number))                    else:
2103                           inv_A=1./self.SMALL_TOLERANCE
2104                      peclet_number=length_of_flux*h/2*inv_A
2105                      xi=self.__xi(self,peclet_number)
2106                  self.__Xi=h*xi/(length_of_flux+flux_max*self.SMALL_TOLERANCE)
2107                  self.trace("preclet number = %e"%util.Lsup(peclet_number))
2108                else:
2109                  self.__Xi=escript.Scalar(0.,length_of_flux.getFunctionSpace())
2110        return self.__Xi        return self.__Xi
2111    
2112    
# Line 2093  class AdvectivePDE(LinearPDE): Line 2133  class AdvectivePDE(LinearPDE):
2133              Aout=A              Aout=A
2134           else:           else:
2135              if A.isEmpty():              if A.isEmpty():
2136                 Aout=self.createNewCoefficient("A")                 Aout=self.createCoefficientOfGeneralPDE("A")
2137              else:              else:
2138                 Aout=A[:]                 Aout=A[:]
2139              Xi=self.__getXi()              Xi=self.__getXi()
# Line 2103  class AdvectivePDE(LinearPDE): Line 2143  class AdvectivePDE(LinearPDE):
2143                        for k in range(self.getNumSolutions()):                        for k in range(self.getNumSolutions()):
2144                           for l in range(self.getDim()):                           for l in range(self.getDim()):
2145                              if not C.isEmpty() and not B.isEmpty():                              if not C.isEmpty() and not B.isEmpty():
2146                                   # tmp=C-util.reorderComponents(B,[0,2,1])
2147                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(tmp,[1,2,0]),tmp,offset=1)
2148                                 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])
2149                              elif C.isEmpty():                              elif C.isEmpty():
2150                                 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]
2151                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(B,[2,1,0]),util.reorder(B,[0,2,1]),offset=1)
2152                              else:                              else:
2153                                 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]
2154                                   # Aout=Aout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),C,offset=1)
2155              else:              else:
2156                  for j in range(self.getDim()):                 if not C.isEmpty() and not B.isEmpty():
2157                     for l in range(self.getDim()):                     delta=(C-B)
2158                        if not C.isEmpty() and not B.isEmpty():                     Aout+=util.outer(Xi*delta,delta)
2159                            Aout[j,l]+=Xi*(C[j]-B[j])*(C[l]-B[l])                 elif not B.isEmpty():
2160                        elif C.isEmpty():                     Aout+=util.outer(Xi*B,B)
2161                            Aout[j,l]+=Xi*B[j]*B[l]                 elif not C.isEmpty():
2162                        else:                     Aout+=util.outer(Xi*C,C)
                           Aout[j,l]+=Xi*C[j]*C[l]  
2163           return Aout           return Aout
2164       elif name == "B" :       elif name == "B" :
2165             # return self.getCoefficient("B")
2166           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2167           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2168           D=self.getCoefficient("D")           D=self.getCoefficient("D")
# Line 2127  class AdvectivePDE(LinearPDE): Line 2171  class AdvectivePDE(LinearPDE):
2171           else:           else:
2172              Xi=self.__getXi()              Xi=self.__getXi()
2173              if B.isEmpty():              if B.isEmpty():
2174                  Bout=self.createNewCoefficient("B")                  Bout=self.createCoefficientOfGeneralPDE("B")
2175              else:              else:
2176                  Bout=B[:]                  Bout=B[:]
2177              if self.getNumEquations()>1:              if self.getNumEquations()>1:
# Line 2137  class AdvectivePDE(LinearPDE): Line 2181  class AdvectivePDE(LinearPDE):
2181                       for i in range(self.getNumEquations()):                       for i in range(self.getNumEquations()):
2182                          for j in range(self.getDim()):                          for j in range(self.getDim()):
2183                             Bout[i,j,k]+=tmp*C[p,i,j]                             Bout[i,j,k]+=tmp*C[p,i,j]
2184                               # Bout=Bout+Xi*util.generalTensorProduct(util.reorder(C,[1,2,0]),D,offset=1)
2185              else:              else:
2186                 tmp=Xi*D                 Bout+=(Xi*D)*C
                for j in range(self.getDim()): Bout[j]+=tmp*C[j]  
2187           return Bout           return Bout
2188       elif name == "C" :       elif name == "C" :
2189             # return self.getCoefficient("C")
2190           B=self.getCoefficient("B")           B=self.getCoefficient("B")
2191           C=self.getCoefficient("C")           C=self.getCoefficient("C")
2192           D=self.getCoefficient("D")           D=self.getCoefficient("D")
# Line 2150  class AdvectivePDE(LinearPDE): Line 2195  class AdvectivePDE(LinearPDE):
2195           else:           else:
2196              Xi=self.__getXi()              Xi=self.__getXi()
2197              if C.isEmpty():              if C.isEmpty():
2198                  Cout=self.createNewCoefficient("C")                  Cout=self.createCoefficientOfGeneralPDE("C")
2199              else:              else:
2200                  Cout=C[:]                  Cout=C[:]
2201              if self.getNumEquations()>1:              if self.getNumEquations()>1:
# Line 2160  class AdvectivePDE(LinearPDE): Line 2205  class AdvectivePDE(LinearPDE):
2205                        for i in range(self.getNumEquations()):                        for i in range(self.getNumEquations()):
2206                          for l in range(self.getDim()):                          for l in range(self.getDim()):
2207                                   Cout[i,k,l]+=tmp*B[p,l,i]                                   Cout[i,k,l]+=tmp*B[p,l,i]
2208                                     # Cout=Cout+Xi*B[p,l,i]*D[p,k]
2209              else:              else:
2210                 tmp=Xi*D                 Cout+=(Xi*D)*B
                for j in range(self.getDim()): Cout[j]+=tmp*B[j]  
2211           return Cout           return Cout
2212       elif name == "D" :       elif name == "D" :
2213           return self.getCoefficient("D")           return self.getCoefficient("D")
2214       elif name == "X" :       elif name == "X" :
2215             # return self.getCoefficient("X")
2216           X=self.getCoefficient("X")           X=self.getCoefficient("X")
2217           Y=self.getCoefficient("Y")           Y=self.getCoefficient("Y")
2218           B=self.getCoefficient("B")           B=self.getCoefficient("B")
# Line 2175  class AdvectivePDE(LinearPDE): Line 2221  class AdvectivePDE(LinearPDE):
2221              Xout=X              Xout=X
2222           else:           else:
2223              if X.isEmpty():              if X.isEmpty():
2224                  Xout=self.createNewCoefficient("X")                  Xout=self.createCoefficientOfGeneralPDE("X")
2225              else:              else:
2226                  Xout=X[:]                  Xout=X[:]
2227              Xi=self.__getXi()              Xi=self.__getXi()
# Line 2186  class AdvectivePDE(LinearPDE): Line 2232  class AdvectivePDE(LinearPDE):
2232                         for j in range(self.getDim()):                         for j in range(self.getDim()):
2233                            if not C.isEmpty() and not B.isEmpty():                            if not C.isEmpty() and not B.isEmpty():
2234                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])                               Xout[i,j]+=tmp*(C[p,i,j]-B[p,j,i])
2235                                 # Xout=X_out+Xi*util.inner(Y,C-util.reorderComponents(B,[0,2,1]),offset=1)
2236                            elif C.isEmpty():                            elif C.isEmpty():
2237                               Xout[i,j]-=tmp*B[p,j,i]                               Xout[i,j]-=tmp*B[p,j,i]
2238                                 # Xout=X_out-Xi*util.inner(Y,util.reorderComponents(B,[0,2,1]),offset=1)
2239                            else:                            else:
2240                               Xout[i,j]+=tmp*C[p,i,j]                               Xout[i,j]+=tmp*C[p,i,j]
2241                                 # Xout=X_out+Xi*util.inner(Y,C,offset=1)
2242              else:              else:
2243                   tmp=Xi*Y                if not C.isEmpty() and not B.isEmpty():
2244                   for j in range(self.getDim()):                  Xout+=(Xi*Y)*(C-B)
2245                      if not C.isEmpty() and not B.isEmpty():                elif C.isEmpty():
2246                         Xout[j]+=tmp*(C[j]-B[j])                  Xout-=(Xi*Y)*B
2247                      elif C.isEmpty():                else:
2248                         Xout[j]-=tmp*B[j]                  Xout+=(Xi*Y)*C
                     else:  
                        Xout[j]+=tmp*C[j]  
2249           return Xout           return Xout
2250       elif name == "Y" :       elif name == "Y" :
2251           return self.getCoefficient("Y")           return self.getCoefficient("Y")
# Line 2217  class AdvectivePDE(LinearPDE): Line 2264  class AdvectivePDE(LinearPDE):
2264       else:       else:
2265          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name          raise IllegalCoefficient,"illegal coefficient %s requested for general PDE."%name
2266    
   
2267  # $Log$  # $Log$
2268    # Revision 1.14  2005/09/22 01:54:57  jgs
2269    # Merge of development branch dev-02 back to main trunk on 2005-09-22
2270    #
2271  # Revision 1.13  2005/09/15 03:44:19  jgs  # Revision 1.13  2005/09/15 03:44:19  jgs
2272  # 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
2273  #  #
# Line 2231  class AdvectivePDE(LinearPDE): Line 2280  class AdvectivePDE(LinearPDE):
2280  # Revision 1.10  2005/08/12 01:45:36  jgs  # Revision 1.10  2005/08/12 01:45:36  jgs
2281  # 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
2282  #  #
2283    # Revision 1.9.2.17  2005/09/21 07:03:33  matt
2284    # PDECoefficient and LinearPDE are now new style classes (introduced in Python
2285    # 2.2). Classes Poisson, Helmholtz, LameEquation and AdvectivePDE have been
2286    # modified to instead use portable/cooperative "super" calls to extend base
2287    # class methods.
2288    #
2289    # Revision 1.9.2.16  2005/09/16 01:54:37  matt
2290    # Removed redundant if-loop.
2291    #
2292  # Revision 1.9.2.15  2005/09/14 08:09:18  matt  # Revision 1.9.2.15  2005/09/14 08:09:18  matt
2293  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.  # Added "REDUCED" solution PDECoefficient descriptors for LinearPDEs.
2294  #  #

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