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In the present work, we study and analyze an efficient iterative couplingmethod for a dimensionally heterogeneous problem . We consider the case of 2-DLaplace equation with non symmetric boundary conditions with a corresponding1-D Laplace equation. We will first show how to obtain the 1-D model from the2-D one by integration along one direction, by analogy with the link betweenshallow water equations and the Navier-Stokes system. Then, we will focus onthe design of an Schwarz-like iterative coupling method. We will discuss thechoice of boundary conditions at coupling interfaces. We will prove theconvergence of such algorithms and give some theoretical results related to thechoice of the location of the coupling interface, and the control of thedifference between a global 2-D reference solution and the 2-D coupled one.These theoretical results will be illustrated numerically.

Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem