A Boundary Integral Equation Method for Computing Numerical Conformal Mappings onto the Disk with Rectilinear Slit and Spiral Slits Regions

Abstract

This article proposes a boundary integral equation method for computing numerical conformal mappings of bounded multiply connected region Ω onto the disk with rectilinear slit and spiral slits regions, Ω1 and Ω2 Initially, the process involves calculating the boundary value of the canonical region. Cauchy’s integral formula can then be used to compute the mapping of the interior values. The effectiveness of the proposed method is demonstrated using several numerical examples.

Keywords

• numerical conformal mapping
• boundary integral equations
• multiply connected regions
• generalized neumann kernel