TY - JOUR
T1 - The Plane Waves Method for Numerical Boundary Identification
AU - Karageorghis , A.
AU - Lesnic , D.
AU - Marin , L.
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 - <p style="text-align: justify;">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&#39;s L-curve criterion. The stability, convergence,
accuracy and efficiency of the proposed method are investigated by considering
several examples.</p>