Numerical boundary identification for Helmholtz-type equations

摘要

We study the identification of an unknown portion of the boundary of a two-dimensional domain occupied by a material satisfying Helmholtz-type equations from additional Cauchy data on the remaining known portion of the boundary. This inverse geometric problem is approached using the boundary element method (BEM) in conjunction with the Tikhonov first-order regularization procedure, whilst the choice of the regularization parameter is based on the L-curve criterion. The numerical results obtained show that the proposed method produces a convergent and stable solution