20110720-ICIAMIce.tex

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\title{Scalable Implicit Methods for Free Surface Flows in Glaciology}
\subtitle{Scalable Ice-sheet Solvers and Infrastructure for Petascale, High-resolution, Unstructured Simulations (SISIPHUS) \\
DOE ASCR ISICLES}

\author{Jed Brown\inst{1,2}, Iulian Grindeanu\inst{1}, Dmitry Karpeev\inst{1}, Barry F. Smith\inst{1}, and Timothy J. Tautges\inst{1}}


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

\date{2011-07-20}

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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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\section{Objectives}
\input{slides/GroundingLine/BindschadlerNaturalHistory.tex}
\begin{frame}
  \begin{block}{Glaciology and society}
    \begin{itemize}
    \item Quantitative analysis of ice dynamics in changing climate
    \item Inversion to determine current state
    \item Stability and sensitivity, mostly at grounding line
    \item Prediect sea level rise as a function of sea surface temperature [energy policy]
    \end{itemize}
  \end{block}
  \begin{block}{Our efforts}
    \begin{itemize}
    \item Unstructured meshing, geometric models of boundaries
    \item Fully implicit formulations to enable analysis
    \item Implicit solver components
      \begin{itemize}
      \item saddle points, anisotropy, heterogeneity, transport
      \item composability and multi-physics coupling
      \end{itemize}
    \item High order accuracy and high throughput
    \item Adjoints using restricted AD
    \end{itemize}
  \end{block}
\end{frame}

\section{Some opinionated commentary}
\input{slides/GroundingLine/Steepness.tex}
\input{slides/THI/ItWorks.tex}

\section{Conservative steady-state energy transport}
\input{slides/VHTEquations.tex}
\input{slides/VHTNondimensional.tex}
\input{slides/VHTSolvers.tex}
\input{slides/VHTSmoother.tex}
\input{slides/VHTJako.tex}

\section{Code verification}
\input{slides/Dohp/ElasticityCodeVerification.tex}

\section{Coupling software}
\input{slides/GroundingLine/ALEBlockForm.tex}
\input{slides/PETSc/Coupling.tex}

\section{High order with unassembled representations}
\begin{frame}{Performance of assembled versus unassembled}
  \includegraphics[width=\textwidth]{figures/TensorVsAssembly} \\
  \begin{itemize}
  \item Same linear operator, smaller to not store unassembled
  \item Use local symbolic math or AD, runtime choice of order, precondition with low-order method
  \item Dual order $h$ and $p$ FEM: \url{github.com/jedbrown/dohp}
  \item PETSc: \url{mcs.anl.gov/petsc}
  \end{itemize}
\end{frame}

\begin{frame}[shrink=5]{Automation}
  \begin{itemize}
  \item For unassembled representations, decomposition, and assembly
  \item Continuous weak form: find $u$
    \[ v^T F(u) \sim \int_\Omega v \cdot {\color{green!70!black} f_0(u,\nabla u)}
    + \nabla v \tcolon {\color{green!70!black} f_1(u,\nabla u)} = 0, \qquad \forall v \in \VV_0 \]
  \item Weak form of the Jacobian $J(w)$: find $u$
    \begin{gather*}
      v^T J(w) u \sim \int_\Omega \begin{bmatrix} v^T & \nabla v^T \end{bmatrix}
      {\color{blue} \begin{bmatrix} f_{0,0} & f_{0,1} \\ f_{1,0} & f_{1,1} \end{bmatrix}}
      \begin{bmatrix} u \\ \nabla u \end{bmatrix} \\
      {\color{blue} [f_{i,j}] = \begin{bmatrix} \dfrac{\partial f_0}{\partial u} & \dfrac{\partial f_0}{\partial \nabla u} \\[1em]
          \dfrac{\partial f_1}{\partial u} & \dfrac{\partial f_1}{\partial \nabla u} \end{bmatrix} (w,\nabla w) }
    \end{gather*}
  \item Terms in ${\color{blue} [f_{i,j}]}$ easy to compute symbolically, AD more scalable.
  \item Nonlinear terms ${\color{green!70!black}f_0,f_1}$ usually have the most expensive nonlinearities in the computation of scalars
    \begin{itemize}
    \item Equations of state, effective viscosity
    \item Compute gradient with reverse-mode, store at quadrature points.
    \item Perturb scalars, then use forward-mode to complete the Jacobian.
    \item Flip forward/reverse for action of the adjoint.
    \end{itemize}
  \end{itemize}
\end{frame}

\begin{frame}{Outlook}
  \begin{itemize}
  \item Stabilized continuous FEM is terrible, need to implement DG for transport.
  \item Issues defining conservative normals for slip: all-positive (\eg spline) basis?
  \item Geometric coupling to surface causes delicate stiffness at large time steps.
  \item Visualization should have hooks for solving equations of state.
  \item Need good hierarchical solver diagnostic tools.
  \item Solution transfer after remeshing.
  \item Have active set and semi-smooth Newton for contact, but there are many types of contact and much work to be done.
  \item \emph{Strongly Coupled Solvers with Loosely Coupled Software} \\
    CP76 11:00 tomorrow, Room 304.
  \end{itemize}
\end{frame}

\end{document}