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Stability and convergence of collocation schemes for retarded potential integral equations

Davies, P.J. and Duncan, D.B. (2004) Stability and convergence of collocation schemes for retarded potential integral equations. SIAM Journal on Numerical Analysis, 42 (3). pp. 1167-1188. ISSN 0036-1429

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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.

Item type: Article
ID code: 2170
Keywords: convergence, stability, retarded potential, boundary integral, Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Strathprints Administrator
    Date Deposited: 04 Jan 2007
    Last modified: 12 Mar 2012 10:37
    URI: http://strathprints.strath.ac.uk/id/eprint/2170

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