Convergence of a collocation scheme for a retarded potential integral equation

D.B. Duncan; Gary Cohen; E. Heikkola; Patrick Joly; P. Neittaanmäki

Convergence of a collocation scheme for a retarded potential integral equation

D.B. Duncan, Gary Cohen (Editor), E. Heikkola (Editor), Patrick Joly (Editor), P. Neittaanmäki (Editor)

Mathematics And Statistics

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Abstract

Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability and convergence. We shall describe some new stable collocation schemes and use Fourier methods and techniques from the analysis of one dimensional Volterra integral equations of the first kind to demonstrate that such stable schemes are convergent.

Original language	English
Title of host publication	Mathematical and numerical aspects of wave propagation phenomena
Place of Publication	London, UK
Publisher	Springer
Pages	770-775
Number of pages	5
ISBN (Print)	354040127X
Publication status	Published - 2003

Keywords

wave propagation
mathematics
integral equations

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title = "Convergence of a collocation scheme for a retarded potential integral equation",

abstract = "Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability and convergence. We shall describe some new stable collocation schemes and use Fourier methods and techniques from the analysis of one dimensional Volterra integral equations of the first kind to demonstrate that such stable schemes are convergent.",

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T1 - Convergence of a collocation scheme for a retarded potential integral equation

AU - Duncan, D.B.

A2 - Cohen, Gary

A2 - Heikkola, E.

A2 - Joly, Patrick

A2 - Neittaanmäki, P.

PY - 2003

Y1 - 2003

N2 - Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability and convergence. We shall describe some new stable collocation schemes and use Fourier methods and techniques from the analysis of one dimensional Volterra integral equations of the first kind to demonstrate that such stable schemes are convergent.

AB - Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations (RPIEs). Solving such equations numerically is both complicated and computationally intensive, and numerical methods often prove to be unstable. Collocation schemes are easier to implement than full finite element formulations, but little appears to be known about their stability and convergence. We shall describe some new stable collocation schemes and use Fourier methods and techniques from the analysis of one dimensional Volterra integral equations of the first kind to demonstrate that such stable schemes are convergent.

KW - wave propagation

KW - mathematics

KW - integral equations

M3 - Chapter

SN - 354040127X

SP - 770

EP - 775

BT - Mathematical and numerical aspects of wave propagation phenomena

PB - Springer

CY - London, UK

ER -

Convergence of a collocation scheme for a retarded potential integral equation

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