Robin–Dirichlet algorithms for the Cauchy problem for the Helmholtz equation
2014 (English)Manuscript (preprint) (Other academic)
The Cauchy problem for the Helmholtz equation is considered. It was demonstrated in a previous paper by the authors that the alternating algorithm suggested by V.A. Kozlov and V.G. Maz’ya does not converge for large wavenumbers in the Helmholtz equation. We prove here that if we alternate Robin and Dirichlet boundary conditions instead of Neumann and Dirichlet boundary conditions, then the algorithm will converge. We present also another algorithm based on the same idea, which converges for large wavenumbers. Numerical implementations obtained using the finite difference method are presented. Numerical results illustrate that the algorithms suggested in this paper, produce a convergent iterative sequences.
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IdentifiersURN: urn:nbn:se:liu:diva-105876OAI: oai:DiVA.org:liu-105876DiVA: diva2:711803