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Journal Articles ESAIM: Mathematical Modelling and Numerical Analysis Year : 2020

Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation

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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.
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Dates and versions

cea-03052206 , version 1 (22-12-2020)

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