| Issue |
ESAIM: M2AN
Volume 54, Number 3, May-June 2020
|
|
|---|---|---|
| Page(s) | 775 - 810 | |
| DOI | https://doi.org/10.1051/m2an/2019050 | |
| Published online | 01 April 2020 | |
Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation
1
Laboratoire Poems, UMR 7231 CNRS/INRIA/ENSTA ParisTech, ENSTA ParisTech, 828, Boulevard des Maréchaux, 91762 Palaiseau, France
2
CEA-Cesta, 15 Avenue des Sablières, 33114 Le Barp, France
* Corresponding author: matthieu.lecouvez@gmail.com
Received:
22
December
2018
Accepted:
30
June
2019
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.
Mathematics Subject Classification: 65N55 / 65N12 / 58G15 / 31A10 / 35P15
Key words: Domain decomposition methods / exponentially fast convergent methods / integral operators / norms of fractional order Sobolev spaces / pseudo-differential operators
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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