The plane wave method for inverse problems associated with Helmholtz-type equations

In this paper, a numerical scheme based on the meshfree plane wave method applied to inverse boundary value problems associated with Helmholtz-type equations is investigated. The resulting ill-conditioned system of linear algebraic equations is solved in a stable manner by employing the truncated singular value decomposition, while the optimal truncation number, i.e. the regularization parameter, is determined using the LL-curve criterion. Numerical results are presented for two- and three-dimensional problems in smooth and piecewise smooth geometries, with both exact and noisy data. The accuracy, convergence and stability of the numerical method are analysed and, furthermore, a comparison with other meshless methods is also performed.