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)

Research output: Chapter in Book/Report/Conference proceedingChapter

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.
LanguageEnglish
Title of host publicationMathematical and numerical aspects of wave propagation phenomena
Place of PublicationLondon, UK
PublisherSpringer
Pages770-775
Number of pages5
ISBN (Print)354040127X
Publication statusPublished - 2003

Fingerprint

Collocation
Integral Equations
Fourier Method
Formulation
Boundary Integral
Volterra Integral Equations
Stability and Convergence
Scattering Problems
Time Domain
Unstable
Numerical Methods
Finite Element
Demonstrate

Keywords

  • wave propagation
  • mathematics
  • integral equations

Cite this

Duncan, D. B., Cohen, G. (Ed.), Heikkola, E. (Ed.), Joly, P. (Ed.), & Neittaanmäki, P. (Ed.) (2003). Convergence of a collocation scheme for a retarded potential integral equation. In Mathematical and numerical aspects of wave propagation phenomena (pp. 770-775). London, UK: Springer.
Duncan, D.B. ; Cohen, Gary (Editor) ; Heikkola, E. (Editor) ; Joly, Patrick (Editor) ; Neittaanmäki, P. (Editor). / Convergence of a collocation scheme for a retarded potential integral equation. Mathematical and numerical aspects of wave propagation phenomena. London, UK : Springer, 2003. pp. 770-775
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Duncan, DB, Cohen, G (ed.), Heikkola, E (ed.), Joly, P (ed.) & Neittaanmäki, P (ed.) 2003, Convergence of a collocation scheme for a retarded potential integral equation. in Mathematical and numerical aspects of wave propagation phenomena. Springer, London, UK, pp. 770-775.

Convergence of a collocation scheme for a retarded potential integral equation. / Duncan, D.B.; Cohen, Gary (Editor); Heikkola, E. (Editor); Joly, Patrick (Editor); Neittaanmäki, P. (Editor).

Mathematical and numerical aspects of wave propagation phenomena. London, UK : Springer, 2003. p. 770-775.

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

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

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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 -

Duncan DB, Cohen G, (ed.), Heikkola E, (ed.), Joly P, (ed.), Neittaanmäki P, (ed.). Convergence of a collocation scheme for a retarded potential integral equation. In Mathematical and numerical aspects of wave propagation phenomena. London, UK: Springer. 2003. p. 770-775