A stability analysis of a time marching scheme for the general surface electric field integral equation
type: Item
instance of: scholarly article
title: A stability analysis of a time marching scheme for the general surface electric field integral equation
zbMATH Open document ID: 0930.65141
DOI: 10.1016/S0168-9274(97)00107-4
author: Penny J. Davies
published in: Applied Numerical Mathematics
publication date: 1999-09-12T00:00:00Z
review text: Approximating the electric field integral equation (EFIE) is a popular way of computing the current which is induced on the surface of a perfect conductor by an incident pulsed electric field. In the present paper a rigorous Fourier stability analysis of a general surface EFIE algorithm applied to a large flat plate is carried out. The analysis shows that the scheme has two different types of fast growing high frequency instabilities. One of these can be reduced by averaging the computed current in time, but the other is due to an interaction between the finite element basis functions and the (midpoint) quadrature rule used to approximate the retarded potential integral equations. The author explains why this is the case and shows how these unstable modes can be removed when the mesh is infinite. This can be done very efficiently, and is enough to make the resulting scheme effectively stable on any flat plate of computationally feasible size. The EFIE scheme analyzed here is essentially that due to \textit{B.~P.~Rynne} [Time domain scattering from arbitrary surfaces using the electric field equation, J. Electromagn. Waves Appl. 5, 93-112 (1991)]. The author choses this one scheme as an example since it is of comparable performance to many other EFIE approximation algorithms (and is more clearly described than most), but note that the techniques used here do not depend on this particular scheme. The rest of the paper is organized as follows. The author begins by describing the equations, basis functions and Rynne's algorithm (which is unstable on a fine mesh). The equations are a coupled system of partial differential equations and retarded potential integral equations (RPIEs), and it is the unusual (and often unfamiliar) properties of numerical schemes for RPIEs that make the problem interesting and challenging. The stability analysis requires the algorithm to be written in terms of shift operators on an infinite mesh, and this is described for a uniform equilateral…
reviewed by: Nikolay Yakovlevich Tikhonenko
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45E10
Mathematics Subject Classification ID: 78A45
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 78M15
zbMATH DE Number: 1311325
zbMATH Keywords: electric field integral equation
zbMATH Keywords: Fourier stability analysis
zbMATH Keywords: time marching algorithm
zbMATH Keywords: retarded potential integral equations
zbMATH Keywords: perfect conductor
zbMATH Keywords: stability
zbMATH Keywords: triangulation
MaRDI profile type: Publication
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full work available at URL: s0168-9274(97)00107-4
OpenAlex ID: W2042550170
description: scientific article; zbMATH DE number 1311325