User: diener Date: 2012/04/04 09:19 AM

Modified: /numerical_relativity/ numerical_relativity.tex

Log: A few more slides.

File Changes:

Directory: /numerical_relativity/ =================================

File [modified]: numerical_relativity.tex Delta lines: +43 -2 =================================================================== --- numerical_relativity/numerical_relativity.tex 2012-04-04 14:08:10 UTC (rev 38) +++ numerical_relativity/numerical_relativity.tex 2012-04-04 14:19:38 UTC (rev 39) @@ -8,6 +8,8 @@

\begin{document}

+\newcommand{\code}[1]{\texttt{#1}} + \frame{\titlepage}

\frame{\frametitle{Outline} @@ -17,6 +19,7 @@ \item Puncture data. \item Finite differencing. \item The method of lines. + \item McLachlan. \end{itemize} }

@@ -96,7 +99,7 @@ }

\frame{\frametitle{The BSSN formulation (continued)} -The evolution equation for all the BSSN variables are +The evolution equation for all the BSSN variables are\footnote{Note: the matter terms are left out.} \begin{align} \partial_t \tg_{ij} = {} & -2 \alpha \tA_{ij} + \lbt{\tg}{i}{j}{k}, \ \partial_t \phi = {} & - \frac{1}{6} \alpha K + \beta^{k}\partial_{k}\phi @@ -298,8 +301,46 @@ integrator.\pause

Often Runge-Kutta integration schemes are the scheme of choice. +}

+\frame{\frametitle{The method of lines (continued)} +Advantages of using the method of lines: +\begin{itemize} + \item It is easy to change the time integration scheme (e.g.\ going to higher + order).\pause + \item It is easy to couple different evolution equations maintaining + high order coupling.\pause +\end{itemize} +The method of lines is implemented in Cactus in the thorn +\code{CactusNumerical/MoL}.\pause +To use: +\begin{itemize} + \item Schedule a routine to register the evolution variables and RHS + variables with \code{MoL}.\pause + \item Schedule routines to set the RHS variables.\pause + \item Set parameters when launching job to choose the time integration + scheme. +\end{itemize} +}

+\frame{\frametitle{McLachlan} +\code{McLachlan} is the Einstein Toolkit implementation of BSSN.\pause + +\code{McLachlan} is named in honor of the Canadian Singer/Song writer Sarah +McLachlan.\pause + +It is based on finite differencing and the method of lines.\pause + +It supports high order finite differencing (8th order).\pause + +Since it is generated from the tensor equations by Kranc it is easy to +maintain and modify.\pause + +It is highly optimized (supports vectorization and OpenMP) and an effort is +ongoing to make it be able to run on GPU's as well.\pause + +In the future it may be necessary to generate different versions optimized +for specific computer architectures. }

@@ -428,9 +469,9 @@ }

\frame{\frametitle{Conservation Laws} +}

- \end{document}