Nabil Gmati ; Naouel Zrelli - 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 -
Numerical study of some iterative solvers for acoustics in unbounded domainsArticle

Authors: Nabil Gmati 1; Naouel Zrelli 1

  • 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.

Volume: Volume 4, 2006
Published on: August 20, 2006
Submitted on: February 17, 2006
Keywords: Transparent boundary conditions, domain decomposition, Helmholtz equation,conditions aux limites transparentes,décomposition de domaines,équation de Helmholtz,[INFO] Computer Science [cs],[MATH] Mathematics [math]

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