Optimized Schwarz Methods for circular flat interfaces and geometric heterogeneous coupled problems
Thursday 2nd March 2017
Gigante, G.; Vergara, C.
In this work, we focus on the Optimized Schwarz Method for circular flat interfaces and geometric heterogeneous coupling. In the first case, we pro- vide a convergence analysis for the diffusion-reaction problem and jumping coefficients and we apply the general optimization procedure developed in Gigante and Vergara, Numer. Math., 131(2), 369–404, 2015. In the numer- ical simulations, we discuss how to choose the range of frequencies in the optimization and the influence of the Finite Element and projection errors on the convergence. In the second case, we consider the coupling between a three-dimensional and a one-dimensional diffusion-reaction problem and we develop a new optimization procedure. The numerical results highlight the suitability of the theoretical findings.