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

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

Oct 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003aipc..686..247t&link_type=abstract

THE ASTROPHYSICS OF GRAVITATIONAL WAVE SOURCES. AIP Conference Proceedings, Volume 686, pp. 247-252 (2003).

Astronomy and Astrophysics

Astrophysics

10

Black Holes, Relativity And Gravitation, Mathematical Procedures And Computer Techniques, Wave Generation And Sources

Scientific paper

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, typically taking 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 Strahlkörper (``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: S2 --> R+. 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 6 angular patches (one each in the neighborhood of the +/-x, +/-y, and +/-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 will be made freely available starting in fall 2003.

Affiliated with

Also associated with

No associations

Rating

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.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-912529