Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation


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.

Publication DOI:
Divisions: Engineering & Applied Sciences > Mathematics
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Uncontrolled Keywords: Helmholtz equation,inverse problem,Cauchy problem,alternating iterative algorithms,relaxation procedure,boundary element method
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Related URLs: ... 09.013.153.html (Publisher URL)
PURE Output Type: Article
Published Date: 2009
Authors: Johansson, B. Tomas (ORCID Profile 0000-0001-9066-7922)
Marin, Liviu


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