TY - JOUR
T1 - IMEX Evolution of Scalar Fields on Curved Backgrounds
JO - Communications in Computational Physics
VL - 5
SP - 1063
EP - 1094
PY - 2009
DA - 2009/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cicp/7717.html
KW - 
AB - <p style="text-align: justify;">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.</p>