Interface control domain decomposition methods for heterogeneous problems |
| |
Authors: | Marco Discacciati Paola Gervasio Alfio Quarteroni |
| |
Institution: | 1. Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III (MA3), Universitat Politècnica de Catalunya (UPC BarcelonaTech), Campus Nord UPC ‐ C2, E‐08034 Barcelona, Spain;2. DICATAM, Università degli Studi di Brescia, via Branze 38, I‐25123 Brescia, Italy;3. Chair of Modelling and Scientific Computing, CMCS‐MATHICSE, Ecole Polytechnique Fédérale de Lausanne, Station 8, CH‐1015 Lausanne, Switzerland and MOX, Politecnico di Milano, P.zza Leonardo da Vinci 32, I‐20133 Milano, Italy |
| |
Abstract: | This paper is concerned with the solution of heterogeneous problems by the interface control domain decomposition (ICDD) method, a strategy introduced for the solution of partial differential equations in computational domains partitioned into subdomains that overlap. After reformulating the original boundary value problem by introducing new additional control variables, the unknown traces of the solution at internal subdomain interfaces; the latter are determined by requiring that the (a priori) independent solutions in each subdomain undergo the minimization of a suitable cost functional. We provide an abstract formulation for coupled heterogeneous problems and a general theorem of well‐posedness for the associated ICDD problem. Then, we illustrate and validate an efficient algorithm based on the solution of the Schur‐complement system restricted solely to the interface control variables by considering two kinds of heterogeneous boundary value problems: the coupling between pure advection and advection–diffusion equations and the coupling between Stokes and Darcy equations. In the latter case, we also compare the ICDD method with a classical approach based on the Beavers–Joseph–Saffman conditions. Copyright © 2014 John Wiley & Sons, Ltd. |
| |
Keywords: | heterogeneous problems domain decomposition methods ICDD method advection– diffusion Stokes– Darcy coupling hp‐finite elements |
|
|