Quasi Optimal Interface Conditions in Domain Decomposition Methods. Application to Problems with Extreme Contrasts in the Coefficients. Optimized Interface Conditions in Domain Decomposition Methods. Application to Problems with Extreme Contrasts in the Coefficients

Interface conditions are crucial in domain decomposition methods and their design has been the subject of many works. We propose in this paper a novel approach where only one or two real parameters have to be chosen for the entire interface. The method relies on van der Sluis’ result on a quasi optimal diagonal preconditioner for a symmetric positive definite matrix, see [35]. It is then possible to design Robin interface conditions using only one real parameter for the entire interface. By adding a second real parameter and more general interface conditions, it is possible to take into account highly heterogeneous media. Numerical results are given. ∗CNRS, UMR 7641, CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France