Communications in Mathematical Sciences
Volume 13 (2015)
An optimization-based, heterogeneous to homogeneous coupling method
Pages: 1639 – 1648
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.
global-local method, multiscale analysis, homogenization, heterogeneous multiscale method, domain decomposition
2010 Mathematics Subject Classification
49J20, 65N30, 74Q05