A Time Dependent Approach for Removing the Cell Boundary Error in Elliptic Homogenization Problems
(English)Manuscript (preprint) (Other academic)
This paper concerns the cell-boundary error present in multiscale algorithms for elliptichomogenization problems. Typical multiscale methods have two essential components: amacro and a micro model. The micro model is used to upscale parameter values which are missing in the macro model. To solve the micro model, boundary conditions are required on the boundary of the microscopic domain. Imposing a naive boundary condition leads to O(e/eta) error in the computation, where e is the size of the microscopic variations in the media and eta is the size of the micro-domain. The removal of this error in modern multiscale algorithms still remains an important open problem. In this paper, we present a time-dependent approach which is general in terms of dimension. We provide a theorem which shows that we have arbitrarily high order convergence rates in terms of e/eta in theperiodic setting. Additionally, we present numerical evidence showing that the method improves the O(e/eta) error to O(e) in general non-periodic media.
IdentifiersURN: urn:nbn:se:kth:diva-129241OAI: oai:DiVA.org:kth-129241DiVA: diva2:651107
FunderSwedish e‐Science Research Center, 649031
QC 201309242013-09-242013-09-242015-02-17Bibliographically approved