Conformal mapping via a density correspondence for the double-layer potential

Matt Wala, Andreas Klockner

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)A3715-A3732
JournalSIAM Journal on Scientific Computing
Volume40
Issue number6
DOIs
StatePublished - Jan 2018
Externally publishedYes

Keywords

  • Conformal map
  • Faber polynomial
  • High-order methods
  • Integral equations

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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