IMEX Evolution of Scalar Fields on Curved Backgrounds

S. R. Lau, H. P. Pfeiffer, J. S. Hesthaven
2009 Communications in Computational Physics  
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
more » ... iders 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.
doi:10.4208/cicp.2009.v6.p1063 fatcat:rvsrbuwjz5exxpc44nvgxvfuiq