Volume 9, Issue 6
The Plane Waves Method for Numerical Boundary Identification

A. Karageorghis, D. Lesnic & L. Marin

Adv. Appl. Math. Mech., 9 (2017), pp. 1312-1329.

Published online: 2017-09

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  • 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.

  • Keywords

Plane waves method, collocation, inverse problem, regularization.

  • AMS Subject Headings

65N35, 65N21, 65N38

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1312, author = {}, title = {The Plane Waves Method for Numerical Boundary Identification}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2017}, volume = {9}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0185}, url = {http://global-sci.org/intro/article_detail/aamm/10180.html} }
TY - JOUR T1 - The Plane Waves Method for Numerical Boundary Identification JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1312 EP - 1329 PY - 2017 DA - 2017/09 SN - 9 DO - http://doi.org/10.4208/aamm.OA-2016-0185 UR - https://global-sci.org/intro/article_detail/aamm/10180.html KW - Plane waves method, collocation, inverse problem, regularization. AB -

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.

A. Karageorghis, D. Lesnic & L. Marin. (2020). The Plane Waves Method for Numerical Boundary Identification. Advances in Applied Mathematics and Mechanics. 9 (6). 1312-1329. doi:10.4208/aamm.OA-2016-0185
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