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 t...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 KerrSchild coordinates,we document the results of several numerical experiments testing our strategy.展开更多
文摘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 KerrSchild coordinates,we document the results of several numerical experiments testing our strategy.
