IMEX evolution of scalar fields on curved backgrounds

Details IMEX evolution of scalar fields on curved backgrounds IMEX evolution of scalar fields on curved backgrounds

2008-08-19

arxiv.org/abs/0808.2597v2

Commun. Comput. Phys., 6 (2009), pp. 1063-1094

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

28 pages, uses revtex4. Revised in response to referee's report. One numerical experiment added which incorporates perturbed i

Scientific paper

Inspiral of binary black holes occurs over a time-scale of many orbits, far longer than the dynamical time-scale of the individual black holes. Explicit evolutions of a binary system therefore require excessively many time steps to capture interesting dynamics. We present a strategy to overcome the Courant-Friedrichs-Lewy condition in such evolutions, one relying on modern implicit-explicit ODE solvers and multidomain spectral methods for elliptic equations. Our analysis considers the model problem of a forced scalar field propagating on a generic curved background. Nevertheless, we encounter and address a number of issues pertinent to the binary black hole problem in full general relativity. Specializing to the Schwarzschild geometry in Kerr-Schild coordinates, we document the results of several numerical experiments testing our strategy.

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