Determination of locations of point-like masses in an inverse source problem of the Poisson equation
type: Item
instance of: scholarly article
title: Determination of locations of point-like masses in an inverse source problem of the Poisson equation
zbMATH Open document ID: 0821.65080
DOI: 10.1016/0377-0427(94)90180-5
author: Takashi Ohe
author: Kohzaburo Ohnaka
published in: Journal of Computational and Applied Mathematics
publication date: 1995-04-02T00:00:00Z
review text: Many inverse problems are formulated by inverse problems of partial differential equations. In this article, an inverse source problem of the Poisson equation is discussed with a boundary element approach and discrete Fourier transform. The case that several point-like masses are placed in a disk domain is studied. The author considers the problem to determine the mass positions from the potential and flux on the boundary. In Section 2 an expression of the logarithmic potential using boundary integrals is derived. A Fourier expansion of the logarithmic potentials of point-like masses is discussed in Section 3, and an algebraic relation between Fourier coefficients and mass positions is also given. Section 4 shows error estimations for the discrete Fourier transform of the logarithmic potential. In Section 5 several procedures to solve the problem are proposed, and to estimate errors of numerical solutions. Section 6 shows some numerical experiments and illustrates the effectiveness of the algorithms.
Mathematics Subject Classification ID: 65Z05
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 739556
zbMATH Keywords: inverse source problem
zbMATH Keywords: Poisson equation
zbMATH Keywords: boundary element
zbMATH Keywords: discrete Fourier transform
zbMATH Keywords: logarithmic potential
zbMATH Keywords: Fourier expansion
zbMATH Keywords: error estimations
zbMATH Keywords: numerical experiments
reviewed by: G. Dimitriu
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90180-5
OpenAlex ID: W1970172009
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cites work: Boundary element approach for an inverse source problem of the Poisson equation with a one-point-mass-like source
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description: scientific article; zbMATH DE number 739556