Absorbing boundaries for wave propagation problems
Journal of Computational Physics
Coulomb and Bessel functions of complex arguments and order
Journal of Computational Physics
Non-reflecting boundary conditions
Journal of Computational Physics
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Exact nonreflecting boundary conditions for the time dependent wave equation
SIAM Journal on Applied Mathematics
On nonreflecting boundary conditions
Journal of Computational Physics
Nonreflecting boundary conditions for time-dependent scattering
Journal of Computational Physics
Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation
SIAM Journal on Numerical Analysis
Nonreflecting boundary conditions for the time-dependent wave equation
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Multidomain spectral method for the helically reduced wave equation
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
For scalar, electromagnetic, or gravitational wave propagation on a fixed Schwarzschild blackhole background, we describe the exact nonlocal radiation outer boundary conditions (ROBC) appropriate for a spherical outer boundary of finite radius enclosing the blackhole. Derivation of the ROBC is based on Laplace and spherical-harmonic transformation of the Regge-Wheeler equation, the PDE governing the wave propagation, with the resulting radial ODE an incarnation of the confluent Heun equation. For a given angular index I the ROBC feature integral convolution between a time-domain radiation boundary kernel (TDRK) and each of the corresponding 21+1 spherical-harmonic modes of the radiation field. The TDRK is the inverse Laplace transform of a frequency-domain radiation kernel (FDRK) which is essentially the logarithmic derivative of the asymptotically outgoing solution to the radial ODE. We develop several numerical methods for examining the frequency dependence of both the outgoing solution and the FDRK. Using these methods we numerically implement the ROBC in a follow-up article. Our work is a partial generalization to Schwarzschild wave propagation and Heun functions of the methods developed for flatspace wave propagation and Bessel functions by Alpert, Greengard, and Hagstrom (AGH), save for one key difference. Whereas AGH had the usual armamentarium of analytical results (asymptotics, order recursion relations, bispectrality) for Bessel functions at their disposal, what we need to know about Heun functions must be gathered numerically as relatively less is known about them.