Spectral versus pseudospectral solutions of the wave equation by waveform relaxation methods
type: Item
instance of: scholarly article
title: Spectral versus pseudospectral solutions of the wave equation by waveform relaxation methods
zbMATH Open document ID: 1047.65092
DOI: 10.1023/A:1025900611963
published in: Journal of Scientific Computing
publication date: 2004-05-27T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 2069184
zbMATH Keywords: wave equation
zbMATH Keywords: spectral and pseudospectral methods
zbMATH Keywords: waveform relaxation
zbMATH Keywords: spectra and pseudospectra
zbMATH Keywords: convergence
zbMATH Keywords: comparisonof methods
zbMATH Keywords: block-Gauss-Jacobi waveform relaxation schemes
zbMATH Keywords: parallel computing
zbMATH Keywords: Runge-Kutta methods
author: Zdzislaw Jackiewicz
author: Bruno D. Welfert
author: B. Zubik-Kowal
reviewed by: Wilhelm Heinrichs
MaRDI profile type: Publication
full work available at URL: a:1025900611963
OpenAlex ID: W1623316936
description: scientific article; zbMATH DE number 2069184