Numerical Method for Solving an Inverse Problem for Laplace's Equation in a Domain with an Unknown Inner Boundary

被引：1

作者：

Gavrilov, S. V. ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Computat Math & Cybernet, Moscow 119991, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2019年 / 59卷 / 01期

关键词：

Laplace's equation; unknown boundary; numerical method;

D O I：

10.1134/S0965542519010093

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An inverse problem for Laplace's equation in a doubly connected two-dimensional domain is considered. Given Dirichlet and Neumann data specified on the known outer boundary of the domain, the task is to determine an unknown inner boundary on which the function takes a constant value. The uniqueness of the solution to this inverse problem is proved. An iterative numerical method for determining the unknown boundary is proposed. Numerical results are presented.

引用

页码：59 / 65

页数：7

共 50 条

[31] An Efficient Direct Method for Numerically Solving the Cauchy Problem for Laplace’s Equation
S. B. Sorokin
Numerical Analysis and Applications, 2019, 12 : 87 - 103
[32] An Efficient Direct Method for Numerically Solving the Cauchy Problem for Laplace's Equation
Sorokin, S. B.
NUMERICAL ANALYSIS AND APPLICATIONS, 2019, 12 (01) : 87 - 103
[33] A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain
Fornberg, Bengt
Flyer, Natasha
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2011, 467 (2134): : 2983 - 3003
[34] A numerical method for solving an inverse thermoacoustic problem
Kabanikhin S.I.
Krivorot'ko O.I.
Shishlenin M.A.
Kabanikhin, S. I. (kabanikhin@sscc.nsc.ru), 1600, Maik Nauka Publishing / Springer SBM (06): : 34 - 39
[35] On the Effect of Irregularity of the Domain Boundary on the Solution of a Boundary Value Problem for the Laplace Equation
L. E. Rossovskii
R. V. Shamin
Differential Equations, 2023, 59 : 664 - 669
[36] On the Effect of Irregularity of the Domain Boundary on the Solution of a Boundary Value Problem for the Laplace Equation
Rossovskii, L. E.
Shamin, R. V.
DIFFERENTIAL EQUATIONS, 2023, 59 (05) : 664 - 669
[37] A DIFFERENCE METHOD FOR SOLVING THE INVERSE BOUNDARY-VALUE PROBLEM FOR THE HEAT-EQUATION
GROMYKO, GF
DIFFERENTIAL EQUATIONS, 1994, 30 (07) : 1107 - 1113
[38] Recovering nonlinear terms in an inverse boundary value problem for Laplace's equation: A stability estimate
Fasino, Dario
Inglese, Gabriele
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 198 (02) : 460 - 470
[39] Numerical Method for Solving a Strongly Mixed Boundary Value Problem in an Unbounded Domain
Dang Quang, A.
Dinh Hung Tran
ADVANCES IN INFORMATION AND COMMUNICATION TECHNOLOGY, 2017, 538 : 403 - 412
[40] Estimating the Accuracy of a Method of Auxiliary Boundary Conditions in Solving an Inverse Boundary Value Problem for a Nonlinear Equation
Tabarintseva, E., V
NUMERICAL ANALYSIS AND APPLICATIONS, 2018, 11 (03) : 236 - 255

← 1 2 3 4 5 →