Year: 2017
Author: A. Karageorghis, D. Lesnic, L. Marin
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1312–1329
Abstract
We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining, accessible and known part of the boundary of a two-dimensional domain, for problems governed by Helmholtz-type equations. This inverse geometric problem is solved using the plane waves method (PWM) in conjunction with the Tikhonov regularization method. The value for the regularization parameter is chosen according to Hansen's L-curve criterion. The stability, convergence, accuracy and efficiency of the proposed method are investigated by considering several examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2016-0185
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 6 : pp. 1312–1329
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Plane waves method collocation inverse problem regularization.
Author Details
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The method of fundamental solutions for the Oseen steady‐state viscous flow past obstacles of known or unknown shapes
Karageorghis, Andreas
Lesnic, Daniel
Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 6 P.2103
https://doi.org/10.1002/num.22404 [Citations: 11]