FEI reference documentation (misc).
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docs/ref_fei.tex
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%=============================================================================
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%=============================================================================
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\chapter{Finite Element Interface (FEI)}
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\label{ch-FEI}
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The finite element interface (FEI) defines a linear solver interface
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for finite element applications. For information on how to use this
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interface, see \cite{FEI-ref}.
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This chapter describes the iterative methods and
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preconditioners in the \hypre{} implementation
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of this interface.
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Solving a linear system from a finite element problem consists of
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four steps in the FEI:
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\begin{enumerate}
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\item Initialize the structure of the finite-element data,
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including loading the element connectivity data
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\item Load the element or super-element stiffness matrices and forcing terms
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\item Set solver parameters and solve the linear system
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\item Retrieve the solution to the linear system
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\end{enumerate}
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Parameters to the \hypre{} solvers are specified by calling
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\begin{display}
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\begin{verbatim}
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void FEI_parameters(int sysHandle, int numParams, char **paramStrings);
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\end{verbatim}
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\end{display}
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where \code{sysHandle} is an identifier for the linear system being solved,
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\code{numParams} is the number of parameter strings, and \code{paramStrings} is
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an array of null-terminated strings with the format:
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``{\em parameter\_name value}''.
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For example, setting the preconditioner can be accomplished by:
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\begin{display}
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\begin{verbatim}
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char **paramStrings[1];
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paramStrings[0] = (char *) malloc(64*sizeof(char));
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strcpy(paramStrings[0], "preconditioner parasails");
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FEI_parameters(sysHandle, 1, paramStrings);
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\end{verbatim}
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\end{display}
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All possible parameters are listed in Table \ref{table-fei-param}.
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A linear system is then solved by calling
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\begin{display}
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\begin{verbatim}
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void FEI_iterateToSolve(int sysHandle);
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\end{verbatim}
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\end{display}
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%-----------------------------------------------------------------------------
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\section{Iterative methods and preconditioners available}
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%-----------------------------
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\subsection{Iterative methods}
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\begin{enumerate}
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\item Krylov solvers (conjugate gradient, GMRES, TFQMR, BiCGSTAB)
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\item BoomerAMG (a parallel algebraic multigrid solver)
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\item SuperLU direct solver (sequential)
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\item SuperLU direct solver with iterative refinement (sequential)
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%\item Y12M direct solver
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\end{enumerate}
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%-----------------------------
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\subsection{Preconditioners}
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\begin{enumerate}
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\item diagonal
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\item parallel incomplete LU with threshold (PILUT)
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\item another parallel incomplete LU (Euclid)
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\item parallel algebraic multigrid (BoomerAMG)
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\item parallel sparse approximate inverse (ParaSails)
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\end{enumerate}
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%Capabilities under development are :
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%\begin{enumerate}
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%\item to form and solve a reduced linear system (in view of constraints), and
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%\item a link to the ML's parallel smoothed aggregation method.
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%\end{enumerate}
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\begin{table}[h]
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\center
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\begin{tabular}{|l|p{4.5in}|}
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\hline
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Parameter Name & Parameter Values \\
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\hline\hline
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solver &
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\code{cg}, \code{gmres} (default), \code{bicgstab}, \code{tfqmr}, \code{boomeramg}, \code{superlu}, \code{superlux}
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\\
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preconditioner &
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\code{diagonal} (default), \code{pilut}, \code{parasails}, \code{boomeramg}, \code{euclid}
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\\
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gmresDim &
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an integer specifying the value of \code{m} in restarted GMRES(m).
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The default value is 50.
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\\
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maxIterations &
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an integer specifying the maximum number of iterations permitted for
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CG or GMRES. The default value is 1000.
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\\
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tolerance &
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a floating point number specifying the termination criterion for CG or
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GMRES. The default value is 1.0E-10.
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\\
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pilutFillin &
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an integer specifying the maximum number of nonzeros kept in the
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formation of incomplete L and U. If this is not called, a value will
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be selected based on the sparsity of the matrix.
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\\
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pilutDropTol &
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a floating point number specifying the threshold to drop small entries
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in L and U. The default value is 0.0.
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\\
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euclidNlevels &
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a non-negative integer specifying the desired sparsity of the incomplete
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factors. The default value is 0.
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\\
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euclidThreshold &
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a floating point number specifying the threshold used to sparsify the
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incomplete factors. The default value is 0.0.
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\\
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superluOrdering &
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\code{natural} (default) or \code{mmd} (minimum degree ordering). This
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ordering is used to minimize the number of nonzeros generated in the
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LU decomposition. The default is natural ordering.
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\\
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superluScale &
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\code{y} (yes; perform row and column scalings before decomposition) or
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\code{n} (no; default).
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\\
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amgCoarsenType &
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\code{falgout}, \code{ruge}, or \code{default} (CLJP) coarsening for BoomerAMG.
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\\
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amgNumSweeps &
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an integer specifying the number of pre- and post-smoothing at each
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level of BoomerAMG. The default is one pre- and one post-smoothings.
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\\
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amgRelaxType &
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\code{jacobi} (Damped Jacobi), \code{gs-slow} (sequential Gauss-Seidel),
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\code{gs-fast} (Gauss-Seidel on interior nodes), \code{hybrid}, or
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\code{direct}. The default is \code{hybrid}.
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\\
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amgRelaxWeight &
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a floating point number between 0 and 1 specifying the damping factor
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for BoomerAMG's damped Jacobi smoother. The default value is 0.5.
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\\
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amgStrongThreshold &
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a floating point number between 0 and 1 specifying the threshold used
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to determine strong coupling in BoomerAMG's coasening. The default
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value is 0.25.
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\\
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parasailsThreshold &
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a floating point number between 0 and 1 specifying the threshold used
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to prune small entries in setting up the sparse approximate inverse.
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The default value is 0.0.
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\\
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parasailsNlevels &
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an integer larger than 0 specifying the desired sparsity of the
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approximate inverse. The default value is 1.
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\\
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parasailsFilter &
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a floating point number between 0 and 1 defining the threshold used to
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prune small entries in A. The default is 0.0.
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\\
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parasailsLoadbal &
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a floating point number between 0 and 1 specifying how load balancing has
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to be done. The default is 0.0.
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\\
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parasailsSymmetric &
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set ParaSails to take A as symmetric.
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\\
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parasailsUnSymmetric &
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set ParaSails to take A as nonsymmetric (default).
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\\
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parasailsReuse &
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set ParaSails to reuse the sparsity pattern of A.
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\\
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\hline
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\end{tabular}
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\caption{%
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Parameters.
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}
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\label{table-fei-param}
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\end{table}
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