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.

No abstract

Electromagnetism / ÉlectromagnétismeQuasi-local transmission conditions for non-overlapping domain decomposition methods for the Helmholtz equation Conditions de transmission quasi-locales pour des méthodes de décomposition de domaine appliquées à l'équation de Helmholtz

No abstract