English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we develop an iterative scheme to construct multiscale basisfunctions within the framework of the Constraint Energy Minimizing GeneralizedMultiscale Finite Element Method (CEM-GMsFEM) for the mixed formulation. Theiterative procedure starts with the construction of an energy minimizingsnapshot space that can be used for approximating the solution of the modelproblem. A spectral decomposition is then performed on the snapshot space toform global multiscale space. Under this setting, each global multiscale basisfunction can be split into a non-decaying and a decaying parts. Thenon-decaying part of a global basis is localized and it is fixed during theiteration. Then, one can approximate the decaying part via a modifiedRichardson scheme with an appropriately defined preconditioner. Using this setof iterative-based multiscale basis functions, first-order convergence withrespect to the coarse mesh size can be shown if sufficiently many times ofiterations with regularization parameter being in an appropriate range areperformed. Numerical results are presented to illustrate the effectiveness andefficiency of the proposed computational multiscale method.

Iterative Oversampling Technique for Constraint Energy Minimizing Generalized Multiscale Finite Element Method in the Mixed Formulation