IMEX Evolution of Scalar Fields on Curved Backgrounds (Communications in Computational Physics, 2020)
Inspiral of binary black holes occurs over a time-scale of many orbits, farlonger than the dynamical time-scale of the individual black holes. Explicit evolutionsof a binary system therefore require excessively many time-steps to capture interestingdynamics. We present a strategy to overcome the Courant-Friedrichs-Lewy conditionin such evolutions, one relying on modern implicit-explicit ODE solvers and multidomainspectral methods for elliptic equations. Our analysis considers the model problemof a forced scalar field propagating on a generic curved background. Nevertheless,we encounter and address a number of issues pertinent to the binary black holeproblem in full general relativity. Specializing to the Schwarzschild geometry in Kerr-Schildcoordinates, we document the results of several numerical experiments testingour strategy.