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

Matt Wala; Andreas Klockner

doi:10.1137/18M1174982

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

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	A3715-A3732
Journal	SIAM Journal on Scientific Computing
Volume	40
Issue number	6
DOIs	https://doi.org/10.1137/18M1174982
State	Published - Jan 2018

Keywords

Conformal map
Faber polynomial
High-order methods
Integral equations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Online availability

10.1137/18M1174982

Library availability

Discover UIUC Full Text

Cite this

@article{b1305d5dd99b49b3a438d64b32108a44,

title = "Conformal mapping via a density correspondence for the double-layer potential",

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.",

keywords = "Conformal map, Faber polynomial, High-order methods, Integral equations",

author = "Matt Wala and Andreas Klockner",

note = "Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",

year = "2018",

month = jan,

doi = "10.1137/18M1174982",

language = "English (US)",

volume = "40",

pages = "A3715--A3732",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "6",

}

TY - JOUR

T1 - Conformal mapping via a density correspondence for the double-layer potential

AU - Wala, Matt

AU - Klockner, Andreas

PY - 2018/1

Y1 - 2018/1

N2 - 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.

AB - 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.

KW - Conformal map

KW - Faber polynomial

KW - High-order methods

KW - Integral equations

UR - http://www.scopus.com/inward/record.url?scp=85060053935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85060053935&partnerID=8YFLogxK

U2 - 10.1137/18M1174982

DO - 10.1137/18M1174982

M3 - Article

AN - SCOPUS:85060053935

SN - 1064-8275

VL - 40

SP - A3715-A3732

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 6

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this