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Optimized Transmission Conditions for Domain Decomposition Methods and Helmholtz Equation. Application to Higher Order Finite Element Methods

Francis Collino 1 Marc Duruflé 2, 3 P Joly 4 Matthieu Lecouvez 5
2 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
4 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
CNRS - Centre National de la Recherche Scientifique : UMR7231, UMA - Unité de Mathématiques Appliquées, Inria Saclay - Ile de France
Abstract : Domain decomposition methods for solving Helmholtz equation are considered. Such methods rely on transmission conditions set on the interfaces between subdomains. The convergence of the iterative algorithm used to solve the associated linear system depends on these transmission conditions. Optimized transmission conditions (such as proposed in [1]) usually rely on transparent boundary conditions or local operators that are an approximation of the exact transparent boundary condition. In this talk, non-local optimized transmission conditions based on Riesz potentials as detailed in [2] are studied. The non-local operators can be replaced by quasi-local operators, and the obtained rate of convergence is independent of the mesh size. These conditions are applied to higher order finite element methods.
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https://hal.archives-ouvertes.fr/hal-01110763
Contributor : Marc Duruflé <>
Submitted on : Wednesday, January 28, 2015 - 9:02:08 PM
Last modification on : Thursday, March 5, 2020 - 7:22:58 PM

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Francis Collino, Marc Duruflé, P Joly, Matthieu Lecouvez. Optimized Transmission Conditions for Domain Decomposition Methods and Helmholtz Equation. Application to Higher Order Finite Element Methods. International Conference on Spectral and High Order Methods 2014, Jun 2014, Salt Lake City, United States. ⟨hal-01110763⟩

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