publication . Article . 2019

reconstruction of a volumetric source domain

Bin-Mohsin, B; Lesnic, D;
Open Access
  • Published: 05 May 2019 Journal: Journal of Computational Methods in Sciences and Engineering, volume 19, pages 367-385 (issn: 1472-7978, eissn: 1875-8983, Copyright policy)
  • Publisher: IOS Press
  • Country: United Kingdom
Abstract
Inverse and ill-posed problems which consist of reconstructing the unknown support of a three-dimensional volumetric source from a single pair of exterior boundary Cauchy data are investigated. The underlying dependent variable may satisfy the Laplace, Poisson, Helmholtz or modified Helmholtz equations. In the case of constant physical properties, the solutions of these elliptic PDEs are sought as linear combinations of fundamental solutions, as in the method of fundamental solutions (MFS). The unknown source domain is parametrized by the radial coordinate, as a function of the spherical angles. The resulting least-squares functional estimating the gap between t...
Subjects
free text keywords: General Engineering, Computational Mathematics, Computer Science Applications, Method of fundamental solutions, Laplace transform, Helmholtz equation, Inverse, Linear combination, Cauchy distribution, Parametrization, Helmholtz free energy, symbols.namesake, symbols, Mathematical analysis, Mathematics
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