The Plane Waves Method for Numerical Boundary Identification (Advances in Applied Mathematics and Mechanics, 2021)
We study the numerical identification of an unknown portion of the boundaryon which either the Dirichlet or the Neumann condition is provided from theknowledge of Cauchy data on the remaining, accessible and known part of the boundaryof 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 regularizationparameter is chosen according to Hansen's L-curve criterion. The stability, convergence,accuracy and efficiency of the proposed method are investigated by consideringseveral examples.