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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 938167, 20 pages
http://dx.doi.org/10.1155/2013/938167
Research Article

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

Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden

Received 31 October 2012; Accepted 21 December 2012

Academic Editor: Juan J. Nieto

Copyright © 2013 Johan Helsing. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.