Section: New Results

A Schwarz coupling method for dimensionally heterogeneous problem

Participant : Antoine Rousseau.

We study and analyze in [10] an efficient iterative coupling method for a dimensionally heterogeneous problem. We consider the case of 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D Laplace equation. We first show how to obtain the 1-D model from the 2-D one by integration along one direction, by analogy with the link between shallow water equations and the Navier-Stokes system. Then, we focus on the design of an Schwarz-like iterative coupling method. We discuss the choice of boundary conditions at coupling interfaces. We prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and the control of the difference between a global 2-D reference solution and the 2-D coupled one. These theoretical results are illustrated numerically.