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

[41] A note on the relation between the boundary- and finite-element method with application to Laplace's equation in two dimensions
Pozrikidis, C
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2006, 30 (02) : 143 - 147
[42] Asymptotic analysis of solving an inverse boundary value problem for a nonlinear singularly perturbed time-periodic reaction-diffusion-advection equation
Lukyanenko, Dmitry, V
Shishlenin, Maxim A.
Volkov, Vladimir T.
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS, 2019, 27 (05): : 745 - 758
[43] A transform method for Laplace's equation in multiply connected circular domains
Crowdy, Darren
IMA JOURNAL OF APPLIED MATHEMATICS, 2015, 80 (06) : 1902 - 1931
[44] Solutions of Laplace's equation with simple boundary conditions, and their applications for capacitors with multiple symmetries
Morales, Mayckol
Diaz, Rodolfo A.
Herrera, William J.
JOURNAL OF ELECTROSTATICS, 2015, 78 : 31 - 45
[45] A kind regularization method for solving Cauchy problem of the Schrödinger equation
Lv, Xianli
Feng, Xiufang
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2025, 457
[46] Numerical method for solving a kind of Volterra integral equation using differential transform method
Seihe, Hadis
Alavi, Majid
Ghadami, Fatemeh
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2013, 6 (03): : 220 - 229
[47] Modeling the shape of boundary using NURBS curves directly in modified boundary integral equations for Laplace’s equation
Eugeniusz Zieniuk
Marta Kapturczak
Computational and Applied Mathematics, 2018, 37 : 4835 - 4855
[48] Modeling the shape of boundary using NURBS curves directly in modified boundary integral equations for Laplace's equation
Zieniuk, Eugeniusz
Kapturczak, Marta
COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04) : 4835 - 4855
[49] A FOURIER BOUNDARY INTEGRAL METHOD FOR SOLVING LAPLACES-EQUATION IN 2 DIMENSIONS
HUESTIS, SP
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING, 1995, 11 (07): : 575 - 584
[50] Mathematical and numerical analysis of initial boundary value problem for a linear nonlocal equation
Wrobel, Mateusz
MATHEMATICS AND COMPUTERS IN SIMULATION, 2019, 166 : 113 - 125

← 1 2 3 4 5 →