Dual reciprocity boundary element method solution of the Cauchy problem for Helmholtz-type equations with variable coefficients

Abstract

In this paper, the application of the dual reciprocity boundary element method (DRBEM) to the Cauchy problem for Helmholtz-type equations with variable coefficients is investigated. The resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularized by employing the zeroth-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method. Numerical results are presented for Cauchy problems in smooth and piecewise smooth geometries, as well as simply and doubly connected domains. The accuracy, convergence and stability of the proposed numerical method with respect to various approximating functions, various DRBEM discretizations and various levels of noise added in the boundary data, respectively, are also analysed.