20110327-HPC3.tex

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\input{JedMacros.tex}

\title{Tightly coupled solvers with loosely coupled software}
\subtitle{Modular linear algebra for multi-physics}

\author{Jed Brown}


% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.
\institute[ETH Z\"urich]
{
  Laboratory of Hydrology, Hydraulics, and Glaciology \\
  ETH Z\"urich
}

\date{KAUST 2011-03-27}

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\subject{Talks}


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\frametitle{Outline}
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\section{Throughput for matrices}
\input{slides/JFNKBottlenecks.tex}
\input{slides/HardwareCapability.tex}
\input{slides/StreamTriad-XT5-BGP.tex}
\input{slides/SpMVPerformanceModel.tex}
\input{slides/OptimizingSpMV.tex}
\input{slides/BAIJPerformance.tex}
\input{slides/OptimizingSpMVUnassembled.tex}
\input{slides/Dohp/StokesScaling.tex}
\begin{frame}{What you can do}
  \begin{itemize}
  \item Speak at the most specific language possible
    \begin{itemize}
    \item 3D structural analysis: symmetric block size 3
    \item 3D compressible flow: nonsymmetric block size 5
    \end{itemize}
  \item Order unknowns for cache reuse (low-bandwidth like RCM is good)
  \item Dual order
    \begin{itemize}
    \item Assemble a low-order discretization
    \item Provide matrix-free high-order operator \\
      (FD, ADI, caching at quadrature points)
    \item More robust with SOR and ILU due to $h$-ellipticity
    \item Sometimes Picard linearization has a more compact stencil
    \end{itemize}
  \end{itemize}
\end{frame}

\section{Stiffness}
\input{slides/WhyImplicit.tex}
\input{slides/CoupledMultiphysics.tex}
\input{slides/Anisotropy.tex}
\input{slides/FieldSplit.tex}
\input{slides/SIPreconditioning.tex}
\input{slides/Stokes/WeakFormNewtonStep.tex}
\input{slides/Stokes/PropertiesOfSchurComplement.tex}
\input{slides/Stokes/PreconditioningSchur.tex}
\input{slides/Stokes/NavierStokesSchur.tex}

\section{Coupling}
\input{slides/SNES/FlowControl.tex}
\begin{frame}{Overwhelmed with choices}
  \begin{itemize}
  \item If you have a hard problem, no black-box solver will work well
  \item Everything in PETSc has a plugin architecture
    \begin{itemize}
    \item Put in the ``special sauce'' for your problem
    \item Your implementations are first-class
    \end{itemize}
  \item PETSc exposes an algebra of composition at runtime
    \begin{itemize}
    \item Build a good solver from existing components, at runtime
    \item Multigrid, domain decomposition, factorization, relaxation, field-split
    \item Choose matrix format that works best with your preconditioner
    \item structural blocking, Neumann matrices, monolithic versus nested
    \end{itemize}
  \end{itemize}
\end{frame}
\input{slides/PETSc/Coupling.tex}
\input{slides/PETSc/MatNest.tex}
\input{slides/PETSc/MatGetLocalSubMatrix.tex}

\begin{frame}{Wrap-up}
  \begin{itemize}
  \item Software modularity while retaining access to good solvers
    \begin{itemize}
    \item Reuse single-physics modules
    \item Unintrusive ``special sauce'' (once you figure it out)
    \end{itemize}
  \item Choose the matrix format at runtime, best for your preconditioner
    \begin{itemize}
    \item monolithic, nested, Neumann
    \item scalar or block, symmetric
    \end{itemize}
  \item Break into pieces that are ``understood'', keep some block structure for high throughput
  \end{itemize}
\end{frame}

\end{document}