A Quasi-Optimal Non-Overlapping Domain Decomposition Algorithm for the Helmholtz Equation

Yassine Boubendir; Xavier Antoine; Christophe Geuzaine

hal-00573550, version 1

A Quasi-Optimal Non-Overlapping Domain Decomposition Algorithm for the Helmholtz Equation

Yassine Boubendir () ¹, Xavier Antoine () ^2, 3, Christophe Geuzaine () ⁴

Journal of Computational Physics 213, 2 (2012) 262-280

Abstract: This paper presents a new non-overlapping domain decomposition method for the Helmholtz equation, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of transmission conditions and a suitable approximation of the Dirichlet to Neumann operator. A convergence theorem of the algorithm is established and numerical results validating the new approach are presented in both two and three dimensions.

1: Department of Mathematical Sciences [Newark, NJ] (NJIT)
State University of New Jersey
2: Institut Elie Cartan Nancy (IECN)
CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
3: CORIDA (INRIA Nancy - Grand Est / IECN / LMAM)
INRIA – CNRS : UMR7502 – Université de Lorraine
4: Applied and Computational Electromagnetics (ACE)
Université de Liège – Institut Montefiore - Département d'Electricité, Electronique et Informatique (Liège) – Fonds de la Recherche Scientifique [FNRS]

hal-00573550, version 1
http://hal.archives-ouvertes.fr/hal-00573550
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From: Xavier Antoine <>
Submitted on: Friday, 4 March 2011 13:28:00
Updated on: Wednesday, 21 November 2012 15:28:30

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