Stability and convergence of collocation schemes for retarded potential integral equations

P.J. Davies, D.B. Duncan

Research output: Contribution to journalArticle

54 Citations (Scopus)

Abstract

Time domain boundary integral formulations of transient scattering problems involve retarded potential integral equations. 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. Here we derive and analyze some new stable collocation schemes for the single layer equation for transient acoustic scattering, and use (spatial) Fourier and (temporal) Laplace transform techniques to demonstrate that such stable schemes are second order convergent.
LanguageEnglish
Pages1167-1188
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume42
Issue number3
DOIs
Publication statusPublished - 2004

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Stability and Convergence
Collocation
Integral equations
Integral Equations
Scattering
Laplace transforms
Numerical methods
Acoustic Scattering
Formulation
Acoustics
Boundary Integral
Scattering Problems
Laplace transform
Time Domain
Unstable
Numerical Methods
Finite Element
Demonstrate

Keywords

  • convergence
  • stability
  • retarded potential
  • boundary integral

Cite this

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Stability and convergence of collocation schemes for retarded potential integral equations. / Davies, P.J.; Duncan, D.B.

In: SIAM Journal on Numerical Analysis, Vol. 42, No. 3, 2004, p. 1167-1188.

Research output: Contribution to journalArticle

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AU - Duncan, D.B.

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KW - stability

KW - retarded potential

KW - boundary integral

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