Communications in Mathematical Sciences

Volume 13 (2015)

Number 6

An optimization-based, heterogeneous to homogeneous coupling method

Pages: 1639 – 1648

(Fast Communication)

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n6.a13

Authors

Assyr Abdulle (ANMC, Section de Mathématiques, École Polytechnique Fédérale de Lausanne, Switzerland)

Orane Jecker (ANMC, Section de Mathématiques, École Polytechnique Fédérale de Lausanne, Switzerland)

Abstract

An optimization-based algorithm is proposed for solving elliptic problems with highly oscillatory coefficients that do not exhibit scale separation in a subregion of the physical domain. The given method, written as a constrained minimization problem, couples a numerical homogenization method in the subregion of the physical domain with scale separation with a fine scale solver in subregions without scale separation. The unknown boundary conditions of both problems in the overlap region are determined by minimizing the discrepancy of the corresponding solutions in this overlap.

Keywords

global-local method, multiscale analysis, homogenization, heterogeneous multiscale method, domain decomposition

2010 Mathematics Subject Classification

49J20, 65N30, 74Q05

Published 13 May 2015