Parameter identification in Helmholtz-type equations with a variable coefficient using a regularized DRBEM

The identification of the space-dependent coefficient in two-dimensional Helmholtz-type equations from a complete knowledge of the field modelled by these equations and its normal derivative on the boundary and additional internal measurements of the field is investigated. This problem is approached by combining a regularized dual reciprocity boundary element method (DRBEM) with a constrained non-linear minimisation technique. The optimal regularization parameter is chosen according to Morozov's discrepancy principle. The accuracy, convergence and stability of the proposed numerical method are carefully analysed and a sensitivity analysis with respect to the initial guess for the minimisation process is also performed. The numerical results obtained show that the combined regularized DRBEM-constrained non-linear minimisation technique is accurate, convergent, stable and robust.