Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in
  Numerical Relativity   In 3+1 numerical simulations of dynamic black hole spacetimes, it's useful to
be able to find the apparent horizon(s) (AH) in each slice of a time evolution.
A number of AH finders are available, but they often take many minutes to run,
so they're too slow to be practically usable at each time step. Here I present
a new AH finder,_AHFinderDirect_, which is very fast and accurate: at typical
resolutions it takes only a few seconds to find an AH to $\sim 10^{-5} m$
accuracy on a GHz-class processor.
  I assume that an AH to be searched for is a Strahlk\"orper (star-shaped
region) with respect to some local origin, and so parameterize the AH shape by
$r = h(angle)$ for some single-valued function $h: S^2 \to \Re^+$. The AH
equation then becomes a nonlinear elliptic PDE in $h$ on $S^2$, whose
coefficients are algebraic functions of $g_{ij}$, $K_{ij}$, and the
Cartesian-coordinate spatial derivatives of $g_{ij}$. I discretize $S^2$ using
6 angular patches (one each in the neighborhood of the $\pm x$, $\pm y$, and
$\pm z$ axes) to avoid coordinate singularities, and finite difference the AH
equation in the angular coordinates using 4th order finite differencing. I
solve the resulting system of nonlinear algebraic equations (for $h$ at the
angular grid points) by Newton's method, using a "symbolic differentiation"
technique to compute the Jacobian matrix._AHFinderDirect_ is implemented as a
thorn in the_Cactus_ computational toolkit, and is freely available by
anonymous CVS checkout.

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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: nucl-th