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

[21] Numerical method for the inverse boundary-value problem of the heat equation
Dmitriev V.I.
Stolyarov L.V.
Computational Mathematics and Modeling, 2017, 28 (2) : 141 - 147
[22] Numerical method for determining the inhomogeneity boundary in the Dirichlet problem for Laplace's equation in a piecewise homogeneous medium
Gavrilov, S. V.
Denisov, A. M.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2010, 50 (08) : 1391 - 1398
[23] Numerical method for determining the inhomogeneity boundary in the Dirichlet problem for Laplace’s equation in a piecewise homogeneous medium
S. V. Gavrilov
A. M. Denisov
Computational Mathematics and Mathematical Physics, 2010, 50 : 1391 - 1398
[24] Fourier boundary integral method for solving Laplace's equation in two dimensions
Huestis, S.P.
Communications in Numerical Methods in Engineering, 1995, 11 (07):
[25] A method of solving the inverse solving the inverse problem for a nonlinear differential equation problem for a nonlinear differential equation
Solov'Eva S.I.
Computational Mathematics and Modeling, 1999, 10 (3) : 215 - 219
[26] Solving an inverse obstacle problem for the wave equation by using the boundary control method
Oksanen, Lauri
INVERSE PROBLEMS, 2013, 29 (03)
[27] A regularization method for a Cauchy problem of Laplace's equation in an annular domain
Wei, T.
Chen, Y. G.
MATHEMATICS AND COMPUTERS IN SIMULATION, 2012, 82 (11) : 2129 - 2144
[28] AN EFFECTIVE METHOD OF SOLVING A DIRICHLET PROBLEM FOR LAPLACE EQUATION
VOLKOV, AP
DIFFERENTIAL EQUATIONS, 1983, 19 (06) : 736 - 742
[29] LAPLACE TRANSFORM METHOD OF SOLVING A MOVING BOUNDARY PROBLEM
WRIGHT, TP
BULLETIN OF THE AMERICAN PHYSICAL SOCIETY, 1970, 15 (11): : 1484 - &
[30] The regularization B-spline wavelet method for the inverse boundary problem of the Laplace equation from noisy data in an irregular domain
Zhang, Xinming
Zeng, Wenxuan
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2021, 125 : 1 - 11

← 1 2 3 4 5 →