[Commits] [svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 287)

[schnetter at cct.lsu.edu]

User: eschnett
Date: 2012/03/12 11:09 AM

Modified:
 /
  ET.tex

Log:
 Describe ghost zones

File Changes:

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

File [modified]: ET.tex
Delta lines: +28 -10
===================================================================
--- ET.tex	2012-03-12 15:57:39 UTC (rev 286)
+++ ET.tex	2012-03-12 16:09:44 UTC (rev 287)
@@ -447,7 +447,23 @@
 with parallelization, time evolution, or mesh refinement. The
 information provided in the interface declarations of the individual
 components allows a highly efficient execution of the combined
-program.
+program. Cactus's parallelization paradigm is based on a spatial
+domain decomposition, and is briefly explained in figure
+\ref{fig:ghosts}.
+\begin{figure}
+  % Figure taken from Cactus users' guide
+  \centering
+  \includegraphics[width=0.7\textwidth]{withghost}
+  \caption{Cactus employs spatial domain decomposition to distribute
+    workload and storage across processors. It stores \emph{ghost
+      zones} (additional, ``dummy'' grid points, here shown as bold
+    and blue crosses) at inter-process boundaries to allow evaluating
+    computational stencils near these boundaries. After modifying
+    data, these ghost zones need to be \emph{synchronized}, which
+    requires inter-processor communication. This is handled by a
+    special \emph{driver} component (see main text).}
+  \label{fig:ghosts}
+\end{figure}
 
 The Einstein Toolkit offers two drivers, \codename{PUGH} and
 {\tt Carpet}. \codename{PUGH} provides domains consisting of a uniform 
@@ -537,8 +553,8 @@
     \small
     \centering
     \begin{tabular}{lll|rrr}
-      Name & Architecture (CPU) & Interconnect & nodes & cores/node & CPU
-      freq. \\\hline
+      Name & Architecture (CPU) & Interconnect & nodes & cores/node &
+      CPU freq. \\\hline
       Franklin (NERSC) & Cray XT4 (AMD) & SeaStar2 & 8502 & 4 & 2.3
       GHz \\
       HLRB II (LRZ Munich) & SGI Altix (Itanium) & NUMAlink & 1 & 9728
@@ -2265,8 +2281,7 @@
 \codename{Cartoon2D} allows fully
 three dimensional codes to be used in axisymmetric problems by evolving
 a slice in the $y=0$ plane and using the rotational symmetry to populate
-ghost points
-\todo{ES: this is the first mention of ``ghost''}
+boundary points
 off the plane (see Figure~\ref{fig:cartoon-plane}). 
 \begin{figure}[htbp]
     \begin{center}
@@ -2285,7 +2300,7 @@
     \label{fig:cartoon-plane}
 \end{figure}
 
-In applying symmetries to populate ghost zones, the
+In applying symmetries to populate boundary zones, the
 transformation properties of tensorial quantities (including tensor
 densities and non-tensors such as Christoffel symbols) are correctly
 taken into account, just as they are in the interpolation routines present in {\tt Cactus}.
@@ -2384,11 +2399,14 @@
     % algorithm described below doesn't know about buffer points --
     % these are handled before and afterwards.)
     \caption{Example of a grid layout created by
-      \codename{CarpetRegrid2}. In this example we use one boundary
-      point and one ghost point, as well as
-      \codename{RotatingSymmetry180}. This figure shows two refinement
+      \codename{CarpetRegrid2}. This figure shows two refinement
       levels, a coarse (big red circles) and a fine one (small black
-      circles). Starting from a user-specified refined region
+      circles). In this example we use one boundary point and one
+      ghost point, as well as \codename{RotatingSymmetry180}. The
+      boundary points are filled by the symmetry condition, the ghost
+      points are filled via interpolation from the coarse
+      grid.\newline
+      Starting from a user-specified refined region
       consisting of $5\times3$ points (small, dark, filled circles in
       the upper half), \codename{CarpetRegrid2} enforced the the
       $\pi$-symmetry by adding the $2\times3$ block of refined points