20110721-ICIAMStronglyCoupledSolversLooselyCoupledSoftware.tex

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\title{Strongly Coupled Solvers with Loosely Coupled Software}

\author{Jed Brown\inst{1,2}, Dave May\inst{2}, and Barry Smith\inst{1}}


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{
  \inst{1}{Argonne National Laboratory} \\
  \inst{2}{ETH Z\"urich}
}

\date{2011-07-21}

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\subject{Talks}


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\begin{frame}
  \titlepage
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\input{slides/MonolithicOrSplit.tex}

\section{Coupling software}
\input{slides/PETSc/Coupling.tex}
\input{slides/PETSc/MatGetLocalSubMatrixUsage.tex}
\input{slides/PETSc/MatGetLocalSubMatrix.tex}

\section{Applications}
\input{slides/GroundingLine/ALEBlockForm.tex}
\subsection{Ice Flow}
\input{slides/VHTSolvers.tex}
\subsection{Geodynamics}
\begin{frame}[shrink=5]{The Drunken Seaman instability}
  \includegraphics[width=0.9\textwidth]{figures/DrunkenSeaman} \\
  \begin{columns}
    \begin{column}{0.8\textwidth}
      \begin{itemize}
      \item Subduction and mantle convection with a free surface.
      \item Free surface critical to long-term dynamics \\
        (\eg mountain range formation)
      \item Advective 0.01 CFL for stability.
      \item Semi-implicit helps: Kaus, M\"uhlhaus, and May, 2010
      \end{itemize}
    \end{column}
    \begin{column}{0.2\textwidth}
      \includegraphics[width=0.9\textwidth]{figures/DrunkenSeamanBottle}
    \end{column}
  \end{columns}
\end{frame}
\begin{frame}[fragile]{Fully implicit free surface}
  \begin{itemize}
  \item Velocity $u$, pressure $p$, Lagrangian/ALE coordinates $x$.
    \begin{equation*}
      J =
      \begin{pmatrix}
        J_{uu} & J_{up} & J_{ux} \\
        J_{pu} & 0 & J_{ux} \\
        J_{xu} & 0 & J_{xx}
      \end{pmatrix} .
    \end{equation*}
  \item Precondition with
    \begin{align*}
      P &=
      \begin{bmatrix}
        \begin{pmatrix}
          J_{uu} & J_{up} \\
          J_{pu} & 0
        \end{pmatrix} & \\
        \begin{pmatrix}
          J_{xu} & 0
        \end{pmatrix}
        & J_{xx}
      \end{bmatrix} &
      P_{\text{Stokes}} &=
      \begin{pmatrix}
        J_{uu} & 0 \\
        J_{pu} & B_{pp}
      \end{pmatrix}
    \end{align*}
  \item {\scriptsize
\begin{verbatim}
-dm_mat_type nest -pc_type fieldsplit
-fieldsplit_stokes_pc_type fieldsplit
-fieldsplit_stokes_pc_fieldsplit_type schur
-fieldsplit_stokes_pc_fieldsplit_schur_factorization_type lower
-fieldsplit_stokes_fieldsplit_u_pc_type mg
\end{verbatim}
}
\item {\scriptsize
\begin{verbatim}
-dm_mat_type aij -pc_type lu -pc_factor_mat_solver_package mumps
\end{verbatim}
}
  \end{itemize}
\end{frame}

\begin{frame}{Outlook}
  \begin{itemize}
  \item Block and symmetric formats, monolithic or nested
  \item Multigrid inside or outside field splits
  \item Can use IMEX methods $g(t,x,\dot x) = f(t,x)$
  \item Preallocation for off-diagonal blocks
  \item Nonlinear solvers for IMEX systems with structure
  \item General/nonsymmetric pivoting.
  \end{itemize}
\end{frame}

\end{document}