A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions
type: Item
instance of: scholarly article
title: A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions
zbMATH Open document ID: 0849.65079
author: R. A. Renaut
author: J. Fröhlich
published in: Journal of Computational Physics
publication date: 1996-07-02T00:00:00Z
review text: A new numerical method for simulation of wave propagation in artificially bounded domains is presented. The approach consists in solving the 2D acoustic wave equation \(u_{tt}= c^2(u_{xx}+ u_{yy})\) by the pseudospectral Chebychev method at all points away from the boundary of \(D= \{(x, y): 0< x< 1, 0< y< 1\}\) in conjunction with the first-order one-way wave equation \(u_t= cu_x\) at the \(x= 0\) boundary. The spatial derivatives in both above equations are approximated using the same Chebychev expansions. Integration in time is performed by a Crank-Nicolson method at the boundary and a standard discretization in time at the interior points. The numerical results presented show the superior performance of the introduced method and its efficiency comparable to that of the Fourier method.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 881890
zbMATH Keywords: absorbing boundary conditions
zbMATH Keywords: numerical examples
zbMATH Keywords: comparison of methods
zbMATH Keywords: wave propagation
zbMATH Keywords: acoustic wave equation
zbMATH Keywords: pseudospectral Chebychev method
zbMATH Keywords: first-order one-way wave equation
zbMATH Keywords: Crank-Nicolson method
zbMATH Keywords: performance
zbMATH Keywords: Fourier method
reviewed by: Stanisław Migórski
MaRDI profile type: Publication
OpenAlex ID: W2012631405
DOI: 10.1006/JCPH.1996.0063
description: scientific article; zbMATH DE number 881890