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

We pursue a low-wavenumber, second-order homogenized solution of thetime-harmonic wave equation at both low and high frequency in periodic mediawith a source term whose frequency resides inside a band gap. Considering thewave motion in an unbounded medium $\mathbb{R}^d$ ($d\geqslant1$), we first usethe (Floquet-)Bloch transform to formulate an equivalent variational problem ina bounded domain. By investigating the source term's projection onto certainperiodic functions, the second-order model can then be derived via asymptoticexpansion of the Bloch eigenfunction and the germane dispersion relationship.We establish the convergence of the second-order homogenized solution, and weinclude numerical examples to illustrate the convergence result.

A convergent low-wavenumber, high-frequency homogenization of the wave equation in periodic media with a source term