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Robin-Dirichlet algorithms for the Cauchy problem for the Helmholtz equation.
- Source :
-
Inverse Problems in Science & Engineering . Jul2018, Vol. 26 Issue 7, p1062-1078. 17p. - 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. Maz’ya does not converge for large wavenumbers <italic>k</italic> 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 <inline-graphic></inline-graphic> 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17415977
- Volume :
- 26
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Inverse Problems in Science & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 128765822
- Full Text :
- https://doi.org/10.1080/17415977.2017.1380639