/[escript]/trunk/doc/user/linearPDE.tex
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revision 2975 by jfenwick, Thu Jan 28 02:03:15 2010 UTC revision 2976 by artak, Mon Mar 8 01:18:33 2010 UTC
# Line 364  assigns new values to \var{omega}, \var{ Line 364  assigns new values to \var{omega}, \var{
364  \subsection{The \Lame Class}  \subsection{The \Lame Class}
365  The \Lame class defines a Lame equation problem:  The \Lame class defines a Lame equation problem:
366  \begin{equation}\label{LE.1}  \begin{equation}\label{LE.1}
367  -\mu (u\hackscore{i,j}+u\hackscore{j,i})+\lambda u\hackscore{k,k})\hackscore{j} = F\hackscore{i}-\sigma\hackscore{ij,j}  -(\mu (u\hackscore{i,j}+u\hackscore{j,i})+\lambda u\hackscore{k,k}\delta\hackscore{ij})\hackscore{j} = F\hackscore{i}-\sigma\hackscore{ij,j}
368  \end{equation}  \end{equation}
369  with natural boundary conditions:  with natural boundary conditions:
370  \begin{equation}\label{LE.2}  \begin{equation}\label{LE.2}
371  n\hackscore{j}(\mu \; (u\hackscore{i,j}+u\hackscore{j,i})+\lambda*u\hackscore{k,k}) = f\hackscore{i}+n\hackscore{j}\sigma\hackscore{ij}  n\hackscore{j}(\mu \; (u\hackscore{i,j}+u\hackscore{j,i})+\lambda u\hackscore{k,k}\delta\hackscore{ij}) = f\hackscore{i}+n\hackscore{j}\sigma\hackscore{ij}
372  \end{equation}  \end{equation}
373  and constraint  and constraint
374  \begin{equation}\label{LE.3}  \begin{equation}\label{LE.3}
# Line 498  Returns the name as a string of a given Line 498  Returns the name as a string of a given
498  Sets the solver method to be used. Use \var{method}=\member{SolverOptions.DIRECT} to indicate that a direct rather than an iterative solver should be used and use \var{method}=\member{SolverOptions.ITERATIVE} to indicate that an iterative rather than a direct solver should be used.  Sets the solver method to be used. Use \var{method}=\member{SolverOptions.DIRECT} to indicate that a direct rather than an iterative solver should be used and use \var{method}=\member{SolverOptions.ITERATIVE} to indicate that an iterative rather than a direct solver should be used.
499  The value of \var{method} must be one of the constants  The value of \var{method} must be one of the constants
500   \member{SolverOptions.DEFAULT}, \member{SolverOptions.DIRECT}, \member{SolverOptions.CHOLEVSKY}, \member{SolverOptions.PCG},\member{SolverOptions.CR}, \member{SolverOptions.CGS}, \member{SolverOptions.BICGSTAB}, \member{SolverOptions.SSOR},   \member{SolverOptions.DEFAULT}, \member{SolverOptions.DIRECT}, \member{SolverOptions.CHOLEVSKY}, \member{SolverOptions.PCG},\member{SolverOptions.CR}, \member{SolverOptions.CGS}, \member{SolverOptions.BICGSTAB}, \member{SolverOptions.SSOR},
501   \member{SolverOptions.GMRES}, \member{SolverOptions.PRES20}, \member{SolverOptions.LUMPING}, \member{SolverOptions.ITERATIVE}, \member{SolverOptions.AMG}, \member{SolverOptions.NONLINEAR_GMRES}, \member{SolverOptions.TFQMR}, \member{SolverOptions.MINRES},   \member{SolverOptions.GMRES}, \member{SolverOptions.PRES20}, \member{SolverOptions.LUMPING}, \member{SolverOptions.ITERATIVE},  \member{SolverOptions.NONLINEAR_GMRES}, \member{SolverOptions.TFQMR}, \member{SolverOptions.MINRES},
502   or \member{SolverOptions.GAUSS_SEIDEL}.   or \member{SolverOptions.GAUSS_SEIDEL}.
503  Not all packages support all solvers. It can be assumed that a package makes a reasonable choice if it encounters. See Table~\ref{TAB FINLEY SOLVER OPTIONS 1} for the solvers supported by \finley.  Not all packages support all solvers. It can be assumed that a package makes a reasonable choice if it encounters. See Table~\ref{TAB FINLEY SOLVER OPTIONS 1} for the solvers supported by \finley.
504  \end{methoddesc}  \end{methoddesc}
# Line 571  If an exception has been thrown by the s Line 571  If an exception has been thrown by the s
571  Sets the key of the coarsening method to be applied in \AMG.  Sets the key of the coarsening method to be applied in \AMG.
572  The value of \var{method} must be one of the constants  The value of \var{method} must be one of the constants
573  \member{SolverOptions.DEFAULT}  \member{SolverOptions.DEFAULT}
574    \member{SolverOptions.STANDARD_COARSENING}
575  \member{SolverOptions.YAIR_SHAPIRA_COARSENING}, \\  \member{SolverOptions.YAIR_SHAPIRA_COARSENING}, \\
576  \member{SolverOptions.RUGE_STUEBEN_COARSENING}, \\or \member{SolverOptions.AGGREGATION_COARSENING}.  \member{SolverOptions.RUGE_STUEBEN_COARSENING}~\footnote{The Ruge-Stueben and aggregation coarsening algorithms used for measuring the strength of connection only, but splitting is done with greedy algorithm.}, \\or \member{SolverOptions.AGGREGATION_COARSENING}.
577  \end{methoddesc}  \end{methoddesc}
578    
579  \begin{methoddesc}[SolverOptions]{getCoarsening}{}  \begin{methoddesc}[SolverOptions]{getCoarsening}{}
# Line 624  Sets the maximum number of coarsening le Line 625  Sets the maximum number of coarsening le
625  Returns the maximum number of coarsening levels to be used in an algebraic multi level solver or preconditioner  Returns the maximum number of coarsening levels to be used in an algebraic multi level solver or preconditioner
626  \end{methoddesc}  \end{methoddesc}
627    
628  \begin{methoddesc}[SolverOptions]{setCoarseningThreshold}{\optional{theta=0.05}}  \begin{methoddesc}[SolverOptions]{setCoarseningThreshold}{\optional{theta=0.25}}
629  Sets the threshold for coarsening in the \AMG solver or preconditioner  Sets the threshold for coarsening in the \AMG solver or preconditioner
630  \end{methoddesc}  \end{methoddesc}
631    
# Line 633  Returns the threshold for coarsening in Line 634  Returns the threshold for coarsening in
634  \end{methoddesc}  \end{methoddesc}
635    
636  \begin{methoddesc}[SolverOptions]{setMinCoarseMatrixSize}{\optional{size=500}}  \begin{methoddesc}[SolverOptions]{setMinCoarseMatrixSize}{\optional{size=500}}
637  Sets the minumum size of the coarsest level matrix in AMG.  Sets the minumum size of the coarsest level matrix in \AMG.
638  \end{methoddesc}  \end{methoddesc}
639    
640  \begin{methoddesc}[SolverOptions]{getMinCoarseMatrixSize}{}  \begin{methoddesc}[SolverOptions]{getMinCoarseMatrixSize}{}
641  Returns the minumum size of the coarsest level matrix in AMG.  Returns the minumum size of the coarsest level matrix in \AMG.
642    \end{methoddesc}
643    
644    \begin{methoddesc}[SolverOptions]{setSmoother}{\optional{smoother=\GAUSSSEIDEL}}
645    Sets the \JACOBI or \GAUSSSEIDEL smoother to be used in \AMG.
646    \end{methoddesc}
647    
648    \begin{methoddesc}[SolverOptions]{getSmoother}{}
649    Returns the key for \JACOBI or \GAUSSSEIDEL smoother used in \AMG.
650  \end{methoddesc}  \end{methoddesc}
651    
652  \begin{methoddesc}[SolverOptions]{setNumSweeps}{\optional{sweeps=2}}  \begin{methoddesc}[SolverOptions]{setNumSweeps}{\optional{sweeps=2}}
# Line 922  the Pastix library is used as a solver~\ Line 931  the Pastix library is used as a solver~\
931  \end{memberdesc}  \end{memberdesc}
932    
933    
934    \begin{memberdesc}[SolverOptions]{STANDARD_COARSENING}
935    \AMG coarsening method by  Ruge and Stueben using measure of importance principle~\cite{Multigrid}.
936    \end{memberdesc}
937    
938  \begin{memberdesc}[SolverOptions]{YAIR_SHAPIRA_COARSENING}  \begin{memberdesc}[SolverOptions]{YAIR_SHAPIRA_COARSENING}
939  \AMG coarsening method by Yair-Shapira  \AMG coarsening method by Yair-Shapira
940  \end{memberdesc}  \end{memberdesc}
941    
942  \begin{memberdesc}[SolverOptions]{RUGE_STUEBEN_COARSENING} \AMG coarsening method by Ruge and Stueben  \begin{memberdesc}[SolverOptions]{RUGE_STUEBEN_COARSENING} \AMG coarsening method by Ruge and Stueben using greedy algorithm for splitting.
943  \end{memberdesc}  \end{memberdesc}
944    
945  \begin{memberdesc}[SolverOptions]{AGGREGATION_COARSENING} \AMG coarsening using (symmetric) aggregation  \begin{memberdesc}[SolverOptions]{AGGREGATION_COARSENING} \AMG coarsening using (symmetric) aggregation using greedy algorithm for splitting.
946  \end{memberdesc}  \end{memberdesc}
947    
948  \begin{memberdesc}[SolverOptions]{NO_PRECONDITIONER}  \begin{memberdesc}[SolverOptions]{NO_PRECONDITIONER}

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