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Interface control domain decomposition methods for heterogeneous problems

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journal contribution
posted on 11.09.2015 by Marco Discacciati, Paola Gervasio, Alfio Quarteroni
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

International Journal for Numerical Methods in Fluids

Volume

76

Issue

8

Pages

471 - 496

Citation

DISCACCIATI, M., GERVASIO, P. and QUARTERONI, A., 2014. Interface control domain decomposition methods for heterogeneous problems. International Journal for Numerical Methods in Fluids, 76 (8), pp. 471 - 496.

Publisher

© John Wiley & Sons, Ltd.

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2014

Notes

This is the peer reviewed version of the following article: DISCACCIATI, M., GERVASIO, P. and QUARTERONI, A., 2014. Interface control domain decomposition methods for heterogeneous problems. International Journal for Numerical Methods in Fluids, 76 (8), pp. 471 - 496, which has been published in final form at http://dx.doi.org/10.1002/fld.3942 This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

ISSN

1097-0363

Language

en

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