The Plane Waves Method for Numerical Boundary Identification

The Plane Waves Method for Numerical Boundary Identification

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

A. Karageorghis

D. Lesnic

L. Marin

  1. The method of fundamental solutions for the Oseen steady‐state viscous flow past obstacles of known or unknown shapes

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    Lesnic, Daniel

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    https://doi.org/10.1002/num.22404 [Citations: 11]