Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation. (English) Zbl 1062.78015

Marin, L.; Elliott, L.; Heggs, P. J.; Ingham, D. B.; Lesnic, D.; Wen, X.

Int. J. Numer. Methods Eng. 60, No. 11, 1933-1947 (2004).

The interior Cauchy problem for the Helmholtz equation is solved numerically. It is shown that, for problems which possess a solution, the classical Tikhonov’s regularization method works equally well, or even better, than more sophisticated methods.

Reviewer: D. Lesnic (Leeds)

MSC:

78M15

Boundary element methods applied to problems in optics and electromagnetic theory

Keywords:

Boundary element method; Cauchy problem; Helmholtz equation; regularization; inverse problem