20120403-SCA.tex

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\title{Scalable and Composable Implicit Solvers for Polythermal Ice Flow with Steep Topography}
\author{{\bf Jed Brown}\inst{1},\\
Matt Knepley\inst{2}, Dave May\inst{3}, Barry Smith\inst{1}}


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

\date{SCA 2012-04-03}

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\subject{Talks}


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  \titlepage
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%\input{slides/GroundingLine/ThwaitesPIG.tex}
\input{slides/GroundingLine/Steepness.tex}
\input{slides/THI/Equations.tex}
\begin{frame}
  \includegraphics[width=\textwidth]{figures/THI/x-80km-m16p2l6-ew} \\
  Grid-sequenced Newton-Krylov solution of test $X$.  The solid lines denote nonlinear iterations, and the dotted lines with $\times$ denote linear residuals.
\end{frame}
\input{slides/THI/Y5kmClip.tex}
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  \begin{figure}
    \includegraphics[width=\textwidth]{figures/THI/y-10km-m10p6l5-ew}
    \centering\caption{Grid sequenced Newton-Krylov convergence for test $Y$.
    The ``cliff'' has \SI{58}{\degree} angle in the red line ($12\times 125$ meter elements), \SI{73}{\degree} for the cyan line ($6\times 62$ meter elements).}\label{fig:testy}
  \end{figure}
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  \includegraphics[width=0.8\textwidth]{figures/VHT/VHTJakoContourStream}
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\input{slides/VHTMotivation.tex}
\input{slides/VHTEquationsSimple.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/Stokes/OptionsTour.tex}
\input{slides/Stokes/CoupledMGOptions.tex}
%\input{slides/PETSc/RediscretizedMultigrid.tex}

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

\input{slides/VHTSolvers.tex}
%\input{slides/VHTSolverOptions.tex}
\input{slides/Dohp/TensorVsAssembly.tex}
\input{slides/HardwareArithmeticIntensity.tex}
\input{slides/Dohp/PMultigrid.tex}

\input{slides/GroundingLine/Normals.tex}

\begin{frame}{Outlook}
  \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
  \item Preliminary implementations on GPU
  \end{itemize}
  \begin{block}{In development}
    \begin{itemize}
    \item Distributive relaxation and Vanka smoothers
    \item Improved operator-dependent semi-geometric multigrid
    \item Automated support for mixing analysis/UQ into levels
    \item IMEX time stepping for geometry evolution
    \item Special basis functions for corners
  \end{itemize}
\end{block}
\end{frame}
\end{document}