Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation
Mathematics of Computation
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
Journal of Computational Physics
A Stable Penalty Method for the Compressible Navier--Stokes Equations: I. Open Boundary Conditions
SIAM Journal on Scientific Computing
Pseudospectra for the wave equation with an absorbing boundary
Journal of Computational and Applied Mathematics
Stability of a Chebychev pseudospectral solution of the wave equation with absorbing boundaries
Journal of Computational and Applied Mathematics
Spectral methods in MatLab
Journal of Scientific Computing
Stability of Gauss–Radau Pseudospectral Approximations of the One-Dimensional Wave Equation
Journal of Scientific Computing
Mathematics and Computers in Simulation
Hi-index | 7.30 |
In this paper we deal with the effects on stability of subtle differences in formulations of pseudospectral methods for solution of the acoustic wave equation. We suppose that spatial derivatives are approximated by Chebyshev pseudospectral discretizations. Through reformulation of the equations as first order hyperbolic systems any appropriate ordinary differential equation solver can be used to integrate in time. However, the resulting stability, and hence efficiency, properties of the numerical algorithms are drastically impacted by the manner in which the absorbing boundary conditions are incorporated. Specifically, mathematically equivalent well-posed approaches are not equivalent numerically. An analysis of the spectrum of the resultant system operator predicts these properties.