Skip to Main content Skip to Navigation
Journal articles

Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation

Francis Collino 1 Patrick Joly 1 Matthieu Lecouvez 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this paper, we develop in a general framework a non overlapping Domain Decomposition Method that is proven to be well-posed and converges exponentially fast, provided that specific transmission operators are used. These operators are necessarily non local and we provide a class of such operators in the form of integral operators. To reduce the numerical cost of these integral operators, we show that a truncation process can be applied that preserves all the properties leading to an exponentially fast convergent method. A modal analysis is performed on a separable geometry to illustrate the theoretical properties of the method and we exhibit an optimization process to further reduce the convergence rate of the algorithm.
Document type :
Journal articles
Complete list of metadata

https://hal-cea.archives-ouvertes.fr/cea-03052206
Contributor : Flore Loyer <>
Submitted on : Tuesday, December 22, 2020 - 9:57:33 AM
Last modification on : Friday, January 15, 2021 - 3:07:02 AM

File

Collino.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Francis Collino, Patrick Joly, Matthieu Lecouvez. Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2020, 54 (3), pp.775-810. ⟨10.1051/m2an/2019050⟩. ⟨cea-03052206⟩

Share

Metrics

Record views

43

Files downloads

25