20121002-MathGeo.tex

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\usepackage{JedMacros}

\title{Pervasive Multiscale Modeling, Analysis, and Solvers}
\author{{\bf Jed Brown}}

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{
  {Mathematics and Computer Science Division, Argonne National Laboratory} \\
}

\date{MathGeo, Princeton, 2012-10-02}

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\subject{Talks}


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\begin{document}
\lstset{language=C}
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\begin{frame}
  \titlepage
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\begin{frame}{Motivation}
  \begin{itemize}
  \item Nature has many spatial and temporal scales
    \begin{itemize}
    \item Porous media, turbulence, kinetics, fracture
    \end{itemize}
  \item Robust discretizations and implicit solvers are needed to cope
  \item Computer architecture is increasingly hierarchical
    \begin{itemize}
    \item algorithms should conform to this structure
    \end{itemize}
  \item Solver scalability is a crucial bottleneck at scale
  \item ``black box'' solvers are not sustainable
    \begin{itemize}
    \item optimal solvers must accurately handle all scales
    \item optimality is crucial for large-scale problems
    \item hardware puts up a spirited fight to abstraction
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}
  \includegraphics[width=1.05\textwidth]{figures/KeyesAllAboutAlgorithms}
\end{frame}

\input{slides/MG/PhenomenologicalModels.tex}
\input{slides/MG/NumericalHomogenization.tex}
\input{slides/MG/CoarseGridWhyILikeSubdomainProblems.tex}
\input{slides/MG/TauFAS.tex}
\input{slides/MG/CoolThings.tex}
\input{slides/MG/MonteCarlo.tex}

\begin{frame}{Outlook}
  \begin{itemize}
  \item Multiscale processes are ubiquitous and important
  \item Multiscale computation necessary for modern simulation and analysis
  \item Embrace multiscale structure, make it work for you
  \item Raise level of abstraction at which we formulate problems
  \item Think in terms of robust functionals and statistics \\ rather than pointwise solutions
  \item Multiscale computation often reveals modeling flaws, \\
    guides their rectification
  \item Good microscale models are important for deriving and correcting coarse models
  \end{itemize}
\end{frame}

\end{document}