A Fast Apparent‐Horizon Finder for 3‐Dimensional Cartesian Grids in Numerical Relativity

By J. Thornburg. 2003

256 citations recorded by the source corpus.

In 3 + 1 numerical simulations of dynamic black-hole spacetimes, it is 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 are 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 ~10−5m accuracy on a GHz-class processor. I assume that an AH to be searched for is a Strahlkorper ('star-shaped region') with respect to some local origin, and so parametrize the AH shape by r = h(angle) for some single-valued function h:S2 → +. The AH equation then becomes a nonlinear elliptic PDE in h on S2, whose coefficients are algebraic functions of gij, Kij, and the Cartesian-coordinate spatial derivatives of gij. I discretize S2 using six angular patches (one each in the neighbourhood of the ±x, ± y, and ±z axes) to avoid coordinate singularities, and finite difference the AH equation in the angular coordinates using fourth-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.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/0109c7ff1c1210bb5d4a80e3b5a553dbfc954a54

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Citations in the corpus

THE MISSING LINK: MERGING NEUTRON STARS NATURALLY PRODUCE JET-LIKE STRUCTURES AND CAN POWER SHORT GAMMA-RAY BURSTS (2011, methodology): “For the simulations we use the Cactus/Carpet/Whisky codes (Schnetter et al. 2002; Thornburg 2004; Giacomazzo et al. 2007; Pollney et al. 2007) and we consider a configuration that could represent the properties of a NS-binary a few orbits before its coalescence, within a fully general-relativistic…”
Numerical relativity using a generalized harmonic decomposition (2004, methodology): “We use the following flow method to search for single, simply-connected apparent horizons in the spacetime (this is the same algorithm used in [38]; see [39] for a review of most current methods, and [40, 41] for some recent work on fast, elliptic-solver-based apparent horizon finders).”
Unequal mass binary black hole plunges and gravitational recoil (2006, methodology): “Mesh refinement in the code is provided by Carpet [28], and tracking of AHs is handled by AHFinderDirect [29].”
Turduckening black holes: An Analytical and computational study (2008, background): “Thornburg’s apparent horizon finder [48, 49], the GNU Scientific Library [50], and the LAPACK [51] and BLAS [52] libraries from the Netlib Repository [53].”
Black-hole binaries, gravitational waves, and numerical relativity (2010, methodology): “It is useful to compute this during a simulation, for example by finding surfaces on which the expansion of light rays are minimized (Thornburg, 2004).”