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

A family of effective equations for wave propagation in periodic media forarbitrary timescales $\mathcal{O}(\varepsilon^{-\alpha})$, where$\varepsilon\ll1$ is the period of the tensor describing the medium, isproposed. The well-posedness of the effective equations of the family isensured without requiring a regularization process as in previous models [A.Benoit and A. Gloria, arXiv:1701.08600, 2017], [G. Allaire, A. Lamacz, and J.Rauch, arXiv:1803.09455, 2018]. The effective solutions in the family areproved to be $\varepsilon$ close to the original wave in a norm equivalent tothe $L^\infty(0,\varepsilon^{-\alpha}T;L^2(\Omega))$ norm. In addition, anumerical procedure for the computation of the effective tensors of arbitraryorder is provided. In particular, we present a new relation between thecorrectors of arbitrary order, which allows to substantially reduce thecomputational cost of the effective tensors of arbitrary order. This relationis not limited to the effective equations presented in this paper and can beused to compute the effective tensors of alternative effective models.

Effective models and numerical homogenization for wave propagation in heterogeneous media on arbitrary timescales