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A time dependent approach for removing the cell boundary error in elliptic homogenization problems
Uppsala University, Sweden.ORCID iD: 0000-0003-4481-0964
KTH, Stockholm.
2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 314, p. 206-227Article in journal (Refereed) Published
Abstract [en]

This paper concerns the cell-boundary error present in multiscale algorithms for elliptic homogenization problems. Typical multiscale methods have two essential components: a macro 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(ε/η) error in the computation, where ε is the size of the microscopic variations in the media and η 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 ε/η in the periodic setting. Additionally, we present numerical evidence showing that the method improves the O(ε/η) error to O(ε) in general non-periodic media.

Place, publisher, year, edition, pages
2016. Vol. 314, p. 206-227
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-45328DOI: 10.1016/j.jcp.2016.03.009OAI: oai:DiVA.org:mdh-45328DiVA, id: diva2:1355421
Available from: 2019-09-27 Created: 2019-09-27 Last updated: 2019-10-11Bibliographically approved

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Arjmand, Doghonay

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