Nonreflecting boundary conditions for time-dependent scattering
type: Item
instance of: scholarly article
title: Nonreflecting boundary conditions for time-dependent scattering
zbMATH Open document ID: 0860.65080
author: Marcus J. Grote
author: Joseph B. Keller
published in: Journal of Computational Physics
publication date: 1997-04-24T00:00:00Z
review text: The paper presents a computational method for the calculation of a time dependent field scattered from a bounded scattering region in \(\mathbb{R}^3\). The model problem is described by the wave equation with a nonlinear source term and the exact nonreflecting boundary condition derived by the authors [SIAM J. Appl. Math. 55, No. 2, 280-297 (1995; Zbl 0817.35049)]. For this model the uniqueness of the solution is proved and both the finite element and the finite difference methods are applied. In the considered computational method, due to the truncation of an infinite sum to a finite value, the boundary condition becomes inexact. It is shown how to modify this boundary condition to improve its accuracy. Moreover, it is proved that despite the incorrect boundary condition, the energy of the solution remains bounded. The stability of the ordinary differential equation occurring in the boundary condition is also examined. Numerical examples demonstrate the long time stability of the proposed method and the improvement in accuracy over standard ones.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35L05
zbMATH DE Number: 938007
zbMATH Keywords: nonreflecting boundary conditions
zbMATH Keywords: artificial boundary
zbMATH Keywords: numerical examples
zbMATH Keywords: scattering
zbMATH Keywords: wave equation
zbMATH Keywords: nonlinear
zbMATH Keywords: finite element
zbMATH Keywords: finite difference
zbMATH Keywords: stability
reviewed by: Stanisław Migórski
MaRDI profile type: Publication
OpenAlex ID: W2062890439
DOI: 10.1006/JCPH.1996.0157
description: scientific article; zbMATH DE number 938007