Solving integral equations on piecewise smooth boundaries using the RCIP method: a tutorial

Abstract: Recursively compressed inverse preconditioning (RCIP) is a kernel-independent and purely numerical method for solving Fredholm second kind boundary integral equations in situations where the boundary shape induces a non-smooth behavior in the solution. The method originated in 2008 within a scheme for Laplace's equation in two-dimensional domains with corners. In a series of subsequent papers the method 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 tutorial 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.