Spectral versus pseudospectral solutions of the wave equation by waveform relaxation methods
Spectral and pseudospectral methods for the wave equation in 1D are examined. The performance of block Gauss-Jacobi waveform relaxation schemes which can be efficiently implemented in a parallel computing environment is studied. It is demonstrated that the spectral formulations lead to implicit systems of ordinary differential equations which can be efficiently solved by Runge-Kutta methods. Waveform relaxations based on splittings demonstrate that these iterations are only linearly convergent. Waveform relaxations applied to the explicit system are somewhat faster. The pseudospectral methods lead to systems with differentation matrices where the corresponding waveform relaxation converges faster than for the spectral method.
block-Gauss-Jacobi waveform relaxation schemes
scientific article; zbMATH DE number 2069184