Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2003-06-12
Class.Quant.Grav.21:743-766,2004
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
26 pages + 3 page supplement, LaTeX2e, RevTeX4, includes color postscript figures; changes from v2: revised based on referee c
Scientific paper
10.1088/0264-9381/21/2/026
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.
No associations
LandOfFree
A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Fast Apparent-Horizon Finder for 3-Dimensional Cartesian Grids in Numerical Relativity will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-26533