Abstract and Applied Analysis

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

Johan Helsing

Full-text: Open access

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 938167, 20 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393443489

Digital Object Identifier
doi:10.1155/2013/938167

Mathematical Reviews number (MathSciNet)
MR3045054

Zentralblatt MATH identifier
1328.65271

Citation

Helsing, Johan. Solving Integral Equations on Piecewise Smooth Boundaries Using the RCIP Method: A Tutorial. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 938167, 20 pages. doi:10.1155/2013/938167. https://projecteuclid.org/euclid.aaa/1393443489


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