On the Approximate Conformal Mapping of the Unit Disk on a Simply Connected Domain

被引：15

作者：

Shirokova, E. A. ^{[1
]}

机构：

[1] Kazan Volga Reg Fed Univ, Ul Kremlyovskaya 18, Kazan 420008, Russia

来源：

RUSSIAN MATHEMATICS | 2014年 / 58卷 / 03期

关键词：

conformal mapping; integral equation; contracting mapping;

D O I：

10.3103/S1066369X14030050

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a method of constructing the analytic function realizing an approximate conformal mapping of the unit disk on an arbitrary simply connected domain with the given smooth parametrically defined boundary. The method is based on a new boundary parameterization. Solution of the problem is reduced to the Fredholm integral equation of the second kind. We present the examples of three ways to solve the integral equation.

引用

页码：47 / 56

页数：10

共 50 条

[11] Fast Disk Conformal Parameterization of Simply-Connected Open Surfaces
Choi, Pui Tung
Lui, Lok Ming
JOURNAL OF SCIENTIFIC COMPUTING, 2015, 65 (03) : 1065 - 1090
[12] THE APPROXIMATE CONFORMAL MAPPING ONTO MULTIPLY CONNECTED DOMAINS
Abzalilov, D. F.
Shirokova, E. A.
PROBLEMY ANALIZA-ISSUES OF ANALYSIS, 2019, 8 (01): : 3 - 16
[13] CONFORMAL MAPPING OF A MULTIPLY CONNECTED PLANE DOMAIN
LEGENDRE, R
RECHERCHE AEROSPATIALE, 1971, (03): : 165 - &
[14] A linear formulation for disk conformal parameterization of simply-connected open surfaces
Choi, Gary Pui-Tung
Lui, Lok Ming
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2018, 44 (01) : 87 - 114
[15] A linear formulation for disk conformal parameterization of simply-connected open surfaces
Gary Pui-Tung Choi
Lok Ming Lui
Advances in Computational Mathematics, 2018, 44 : 87 - 114
[16] A COMPARISON OF SOME NUMERICAL CONFORMAL MAPPING METHODS FOR SIMPLY AND MULTIPLY CONNECTED DOMAINS
Badreddine, Mohamed
DeLillo, Thomas K.
Sahraei, Saman
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (01): : 55 - 82
[17] 2 NUMERICAL-METHODS FOR THE CONFORMAL MAPPING OF SIMPLY-CONNECTED DOMAINS
PAPAMICHAEL, N
KOKKINOS, CA
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1981, 28 (03) : 285 - 307
[18] BERGMAN-KERNEL METHOD FOR NUMERICAL CONFORMAL MAPPING OF SIMPLY CONNECTED DOMAINS
LEVIN, D
PAPAMICHAEL, N
SIDERIDIS, A
JOURNAL OF THE INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS, 1978, 22 (02): : 171 - 187
[19] BOUNDARY PROPERTIES OF CONFORMAL-MAPS AND COMPACTIFICATIONS OF SIMPLY CONNECTED PLANE DOMAIN
IVANOV, OV
SIBERIAN MATHEMATICAL JOURNAL, 1982, 23 (05) : 669 - 680
[20] Conformal Invariants in Simply Connected Domains
Mohamed M. S. Nasser
Matti Vuorinen
Computational Methods and Function Theory, 2020, 20 : 747 - 775

← 1 2 3 4 5 →