Work

Conformal Mapping via a Density Correspondence for the Double-Layer Potential

Year: 2018

Type: article

Abstract: We derive a representation formula for harmonic polynomials and Laurent polynomials in terms of densities of the double-layer potential on bounded piecewise smooth and simply connected domains. From this result, we obtain a method for the numerical computation of conformal maps that applies to both exterior and interior regions. We present analysis and numerical experiments supporting the accuracy and broad applicability of the method.

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/18m1174982

Authors: Matt Wala, Andreas Klöckner

Institution: University of Illinois Urbana-Champaign

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Hong Kong University of Science and Technology

Awards: Collaborative Research: Efficient High-Order Parallel Algorithms for Large-Scale Photonics Simulation, CAREER: Towards General-Purpose, High-Order Integral Equation Methods for Computer Simulation in Engineering: Analysis, Algorithm Design, and Applications