Accurate finite difference methods for time-harmonic wave propagation
type: Item
instance of: scholarly article
title: Accurate finite difference methods for time-harmonic wave propagation
zbMATH Open document ID: 0848.65072
author: Isaac Harari
author: Eli Turkel
published in: Journal of Computational Physics
publication date: 1996-10-27T00:00:00Z
full work available at URL: http://hdl.handle.net/2060/19940025704
review text: In this very interesting study the authors examine a number of finite difference stencils for the Helmholtz or reduced wave equation on non-uniform as well as uniform grids in one, two or three dimensions. These schemes are divided into: pointwise, which are the standard finite difference approximations; weighted-average, where the undifferentiated terms are averaged over adjacent grid points; exact-phase representations, where the second difference term is scaled by a parameter designed to eliminate numerical dispersion; and higher-order, based on Padé approximations of the second derivative. These schemes are analyzed by substituting in plane waves. The authors examine and catalogue dispersion relations, anisotropy (directionally varying dispersion), and spurious reflections caused by grid-size transitions or changes in physical properties. They conclude with general suggestions for enhancing performance of difference schemes.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 819441
zbMATH Keywords: finite difference methods
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: reduced wave equation
zbMATH Keywords: dispersion
zbMATH Keywords: spurious reflections
reviewed by: James R. Kuttler
MaRDI profile type: Publication
OpenAlex ID: W2070875961
DOI: 10.1006/JCPH.1995.1134
description: scientific article; zbMATH DE number 819441