Nabil Gmati ; Naouel Zrelli
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Numerical study of some iterative solvers for acoustics in unbounded domains
arima:1849 -
Revue Africaine de Recherche en Informatique et Mathématiques Appliquées,
August 20, 2006,
Volume 4, 2006
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https://doi.org/10.46298/arima.1849
Numerical study of some iterative solvers for acoustics in unbounded domains
Authors: Nabil Gmati 1; Naouel Zrelli 1
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Nabil Gmati;Naouel Zrelli
1 Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l'Ingénieur [Tunis]
The aim of this paper is to study some iterative methods, based on the domain decomposition approach to solve the acoustic harmonic wave propagation in an unbounded domain. We describe how our methodology applies to semi-infinite closed guides and to acoustic scattering problems. In both cases, we use some well-known transparent boundary conditions by imposing on a fictitious boundary a boundary condition by the means of a Fourier expansion. For numerical purposes, we propose an original algorithm based on a fixed-point technique applied to the problem set in the truncated domain. We will interprate this method as a domain decomposition solver which allows to state convergence results. The improvement brought by this method is a consequence of the sparsity presentation of the finite matrix system which is decomposed only once.