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Robin-Dirichlet algorithms for the Cauchy problem for the Helmholtz equation
- Publication Year :
- 2018
-
Abstract
- 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. Mazya does not converge for large wavenumbers k in the Helmholtz equation. Here, we present some simple modifications of the algorithm which may restore the convergence. They consist of the replacement of the Neumann-Dirichlet iterations by the Robin-Dirichlet ones which repairs the convergence for less than the first Dirichlet-Laplacian eigenvalue. In order to treat large wavenumbers, we present an algorithm based on iterative solution of Robin-Dirichlet boundary value problems in a sufficiently narrow border strip. Numerical implementations obtained using the finite difference method are presented. The numerical results illustrate that the algorithms suggested in this paper, produce convergent iterative sequences.<br />Funding Agencies|Swedish International Development Cooperation Agency (Sida); University of Rwanda (UR) [51160027-02, 51160059-02]
Details
- Database :
- OAIster
- Notes :
- Berntsson, Fredrik, Kozlov, Vladimir, Mpinganzima, Lydie, Turesson, Bengt-Ove
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1234556793
- Document Type :
- Electronic Resource
- Full Text :
- https://doi.org/10.1080.17415977.2017.1380639