Adaptive Finite Elements and Colliding Black Holes

Details Adaptive Finite Elements and Colliding Black Holes Adaptive Finite Elements and Colliding Black Holes

1997-09-15

arxiv.org/abs/gr-qc/9709038v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 6 figures, to be published in "Numerical Analysis 1997: Proceedings of the 17th Biennial Conference on Numerical Ana

Scientific paper

According to the theory of general relativity, the relative acceleration of masses generates gravitational radiation. Although gravitational radiation has not yet been detected, it is believed that extremely violent cosmic events, such as the collision of black holes, should generate gravity waves of sufficient amplitude to detect on earth. The massive Laser Interferometer Gravitational-wave Observatory, or LIGO, is now being constructed to detect gravity waves. Consequently there is great interest in the computer simulation of black hole collisions and similar events, based on the numerical solution of the Einstein field equations. In this note we introduce the scientific, mathematical, and computational problems and discuss the development of a computer code to solve the initial data problem for colliding black holes, a nonlinear elliptic boundary value problem posed in an unbounded three dimensional domain which is a key step in solving the full field equations. The code is based on finite elements, adaptive meshes, and a multigrid solution process. Here we will particularly emphasize the mathematical and algorithmic issues arising in the generation of adaptive tetrahedral meshes.

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