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Solving Integral Equations on Piecewise Smooth Boundaries Using the RCIP Method: A Tutorial

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  • Johan Helsing

Abstract

Recursively compressed inverse preconditioning (RCIP) is a numerical method for obtaining highly accurate solutions to integral equations on piecewise smooth surfaces. The method originated in 2008 as a technique within a scheme for solving Laplace’s equation in two-dimensional domains with corners. In a series of subsequent papers, the technique was then refined and extended as to apply to integral equation formulations of a broad range of boundary value problems in physics and engineering. The purpose of the present paper is threefold: first, to review the RCIP method in a simple setting; second, to show how easily the method can be implemented in MATLAB; third, to present new applications of RCIP to integral equations of scattering theory on planar curves with corners.

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  • Johan Helsing, 2013. "Solving Integral Equations on Piecewise Smooth Boundaries Using the RCIP Method: A Tutorial," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-20, April.
    • Handle: RePEc:hin:jnlaaa:938167
    DOI: 10.1155/2013/938167
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