Exponentially convergent non overlapping domain decomposition methods for the Helmholtz equation
2020 ◽
Vol 54
(3)
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pp. 775-810
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Keyword(s):
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.
2019 ◽
Vol 57
(3)
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pp. 1411-1444
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2009 ◽
Vol 4
(1)
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pp. 1-26
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