CONFORMAL MAPPING VIA A DENSITY CORRESPONDENCE FOR THE DOUBLE-LAYER POTENTIAL

被引：5
|
作者：
Wala, Matt [1 ]
Klockner, Andreas [1 ]
机构：
[1] Univ Illinois, Dept Comp Sci, Urbana, IL 61801 USA
来源：
SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2018年 / 40卷 / 06期
基金：
美国国家科学基金会;
关键词：
conformal map; integral equations; Faber polynomial; high-order methods; FAST DIRECT SOLVER; INTEGRAL-EQUATION; FAST ALGORITHM; QUADRATURE; BOUNDARY; APPROXIMATION; EXPANSION; SYSTEMS; LAPLACE;
D O I：
10.1137/18M1174982
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：A3715 / A3732
页数：18
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