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 consider a numerical method to solve scattering problemswith multi-periodic layers with different periodicities. The main tool appliedin this paper is the Bloch transform. With this method, the problem is writteninto an equivalent coupled family of quasi-periodic problems. As the Blochtransform is only defined for one fixed period, the inhomogeneous layer withanother period is simply treated as a non-periodic one. First, we approximatethe refractive index by a periodic one where its period is an integer multipleof the fixed period, and it is decomposed by finite number of quasi-periodicfunctions. Then the coupled system is reduced into a simplified formulation. Aconvergent finite element method is proposed for the numerical solution, andthe numerical method has been applied to several numerical experiments. At theend of this paper, relative errors of the numerical solutions will be shown toillustrate the convergence of the numerical algorithm.

Numerical methods for scattering problems from multi-layers with different periodicities