[Commits] [svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 39)

[diener at cct.lsu.edu]

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}