On inverse problems for characteristic sources in Helmholtz equations
type: Item
instance of: scholarly article
title: On inverse problems for characteristic sources in Helmholtz equations
zbMATH Open document ID: 1426.65166
DOI: 10.1155/2017/2472060
author: Carlos J. S. Alves
author: Roberto Mamud
author: Nuno F. M. Martins
author: Nilson C. Roberty
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: We consider the inverse problem that consists in the determination of characteristic sources, in the modified and classical Helmholtz equations, based on external boundary measurements. We identify the location of the barycenter establishing a simple formula for symmetric shapes, which also holds for the determination of a single source point. We use this for the reconstruction of the characteristic source, based on the Method of Fundamental Solutions (MFS). The MFS is also applied as a solver for the direct problem, using an equivalent formulation as a jump or transmission problem. As a solver for the inverse problem, we may apply minimization using an equivalent reciprocity functional formulation. Numerical experiments with the barycenter and the boundary reconstructions are presented.
Mathematics Subject Classification ID: 65N21
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 6971868
Wikidata QID: Q59147404
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/2472060
OpenAlex ID: W2591650455
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description: scientific article; zbMATH DE number 6971868