LinearPDE class

This is the general class to define a linear PDE in esys.escript. We list a selction of the most important methods of the class only and refer to reference guide http://www.iservo.edu.au/esys/epydoc/index.htmlfor a complete list.

$\begin{classdesc}{LinearPDE}{domain,numEquations=0,numSolutions=0} opens a linea... ...ons, respctively, stay undefined until a coefficient is defined. \end{classdesc}$

$\begin{methoddesc}[LinearPDE]{setValue}{ \optional{A}\optional{, B}, \optional{,... ...xspace object in the appropriate \class{FunctionSpace}\xspace . \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getCoefficient}{name} return the value assigned to... ...ame}. If \var{name} is not a valid name an exception is raised. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getShapeOfCoefficient}{name} returns the shape of coefficient \var{name} even if no value has been assigned to it. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getFunctionSpaceForCoefficient}{name} returns the ... ...oefficient \var{name} even if no value has been assigned to it. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setDebugOn}{} switches the debug mode to on. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setDebugOff}{} switches the debug mode to on. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{isUsingLumping}{} returns \constant{True}\xspace i... ...ienar equations. Otherwise \constant{False}\xspace is returned. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setSolverMethod}{\optional{solver=LinearPDE.DEFAUL... ...lver method but may choose a similar method and preconditioner. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getSolverMethodName}{} returns the name of the solver method and preconditioner which is currently been used. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getSolverMethod}{} returns the solver method and preconditioner which is currently been used. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setSolverPackage}{\optional{package=LinearPDE.DEFA... ...ecified, the default package of the PDE solver library is used. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getSolverPackage}{} returns the linear solver package currently by the PDE solver library \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setTolerance}{\optional{tol=1.e-8}}: resets the to... ...scerete problem but will not consider any discretization error. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getTolerance}{} returns the current tolerance of the solution \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getDomain}{} returns the \class{Domain}\xspace of the PDE. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getDim}{} returns the spatial dimension of the PDE. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getNumEquations}{} returns the number of equations. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getNumSolutions}{} returns the number of components of the solution. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{checkSymmetry}{verbose=\constant{False}\xspace } r... ...space information about where symmetry is violated are printed. \end{methoddesc}$

$\begin{methoddesc} % latex2html id marker 4666 [LinearPDE]{getFlux}{u} returns t... ...STEM.5}) and Equation (\ref{LINEARPDE.SINGLE.5}), respectively. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{isSymmetric}{} returns \constant{True}\xspace if t... ...to be symmetric. Otherwise \constant{False}\xspace is returned. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setSymmetryOn}{} indicates that the PDE is symmetric. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setSymmetryOff}{} indicates that the PDE is not symmetric. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setReducedOrderOn}{} switches on the reduction of ... ...space . This feature may not be supported by all PDE libraries. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{setReducedOrderOff}{} switches off the reduction of polynomial order for the solution and equation evaluation. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getOperator}{} returns the \class{Operator}\xspace of the PDE. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getRightHandSide}{} returns the right hand side of... ...raints are not considered when building up the right hand side. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getSystem}{} returns the \class{Operator}\xspace and right hand side of the PDE. \end{methoddesc}$

$\begin{methoddesc}[LinearPDE]{getSolution}{ \optional{verbose=False} \optional{,... ... the stiffness matrix. \var{truncation} defines the truncation. \end{methoddesc}$

$\begin{memberdesc}[LinearPDE]{DEFAULT} default method, preconditioner or package... ...opriate method should be chosen by the used PDE solver library. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{SCSL} the SCSL library by SGI, Reference \cite{SCSL}\footnotemark \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{MKL} the MKL library by Intel, Reference \cite{MKL}\footnotemark . \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{UMFPACK} the UMFPACK, Reference \cite{UMFPACK}. Remark: UMFPACK is not parallelized. \end{memberdesc}$

$\begin{memberdesc} % latex2html id marker 4742 [LinearPDE]{PASO} the solver libr... ...dule{esys.finley}\xspace , see Section \ref{CHAPTER ON FINLEY}. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{ITERATIVE} the default iterative method and precon... ...space\index{preconditioner!Jacobi}\index{Jacobi}preconditioner. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{DIRECT} the default direct linear solver. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{CHOLEVSKY} direct solver based on Cholevsky factor... ...Reference \cite{Saad}. The solver will require a symmetric PDE. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{PCG} preconditioned conjugate gradient method, see... ...olver!PCG}\index{PCG}. The solver will require a symmetric PDE. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{GMRES} the GMRES method, see Reference \cite{WEIS... ...ers \var{truncation} and \var{restart} of \method{getSolution}. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{LUMPING} uses lumping to solve the system of linea... ...s finer. Lumping does not use the linear system solver library. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{PRES20} the GMRES method with truncation after fiv... ...iduals and restart after 20 steps, see Reference \cite{WEISS}. \end{memberdesc}$
[LinearPDE]CR

$\begin{memberdesc}[LinearPDE]{CGS} conjugate gradient squared method, see Reference \cite{WEISS}. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{BICGSTAB} stabilized bi-conjugate gradients methods, see Reference \cite{WEISS}. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{SSOR} symmetric successive over-relaxation method,... ...oner but some linear solver libraries support this as a solver. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{ILU0} the incomplete LU factorization preconditioner with no fill-in, see Reference \cite{Saad}. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{ILUT} the incomplete LU factorization precondition... ...ar{drop_storage} are both set in the \method{getSolution} call. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{JACOBI} the Jacobi preconditioner, see Reference \cite{Saad}. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{AMG} the algebraic-multi grid method, see Refere... ...solver method but is more robust when used in a preconditioner. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{RILU} recursive incomplete LU factorization precon... ...ar{drop_storage} are both set in the \method{getSolution} call. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{NO_REORDERING} no ordering is used during factorization. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{MINIMUM_FILL_IN} applies reordering before factori... ... advisable to apply reordering on the mesh to minimize fill-in. \end{memberdesc}$

$\begin{memberdesc}[LinearPDE]{NESTED_DISSECTION} applies reordering before facto... ... advisable to apply reordering on the mesh to minimize fill-in. \end{memberdesc}$

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