20120709-SIAMAnnual.tex

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\title{Composable multilevel methods for multiphysics}
\author{{\bf Jed Brown}\inst{1},\\
Mark Adams\inst{2}, Peter Brune\inst{1}, Matt Knepley\inst{3}, Dave May\inst{4}, \\ Lois Curfman McInnes\inst{1}, Barry Smith\inst{1}}


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  \inst{1}{Mathematics and Computer Science Division, Argonne National Laboratory} \\
  \inst{2}{Columbia University} \\
  \inst{3}{Computation Institute, University of Chicago} \\
  \inst{4}{ETH Z\"urich}
}

\date{SIAM Annual 2012-07-09}

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\subject{Talks}


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\input{slides/MultiphysicsExamples.tex}
\input{slides/MonolithicOrSplit.tex}
\input{slides/PETSc/Coupling.tex}
\input{slides/FieldSplit.tex}
\input{slides/PETSc/LocalSpaces.tex}
\input{slides/SNES/MultiphysicsAssemblyJacobians.tex}
\input{slides/PETSc/MatGetLocalSubMatrix.tex}
\input{slides/Stokes/OptionsTour.tex}
\input{slides/Stokes/CoupledMGOptions.tex}
\input{slides/PETSc/DistributiveSmoothing.tex}
\input{slides/PETSc/RediscretizedMultigrid.tex}

\input{slides/SNES/MonolithicFASMultistage.tex}
\input{slides/SNES/NonlinearSolversList.tex}
\input{slides/SNES/QuasiNewtonRevisited.tex}

\input{slides/DrunkenSeaman.tex}
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\begin{frame}{Outlook on Solver Composition}
  \begin{itemize}
  \item Unintrusive composition of multigrid and block preconditioning
  \item We can build many preconditioners from the literature \\
    \emph{on the command line}
  \item User code does not depend on matrix format, preconditioning method, nonlinear solution method, time integration method (implicit or IMEX), or size of coupled system (except for driver).
  \item Similar infrastructure extends to nonlinear methods
  \end{itemize}
  \begin{block}{In development}
    \begin{itemize}
    \item Distributive relaxation, Vanka smoothers, coarsening for ``dual'' variables
    \item Improving operator-dependent semi-geometric multigrid
    \item More automatic spectral analysis and smoother optimization
    \item Automated support for mixing analysis into levels
    \item Nonlinear change of basis for preconditioner
  \end{itemize}
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