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