We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.
- Helmholtz equation
- inverse problem
- Cauchy problem
- alternating iterative algorithms
- relaxation procedure
- boundary element method
Johansson, B. T., & Marin, L. (2009). Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation. Computers Materials and Continua, 13(2), 153-190. https://doi.org/10.3970/cmc.2009.013.153