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

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