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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We present and analyze a pollution-free Petrov-Galerkin multiscale finiteelement method for the Helmholtz problem with large wave number $\kappa$ as avariant of [Peterseim, ArXiv:1411.1944, 2014]. We use standard continuous $Q_1$finite elements at a coarse discretization scale $H$ as trial functions,whereas the test functions are computed as the solutions of local problems at afiner scale $h$. The diameter of the support of the test functions behaves like$mH$ for some oversampling parameter $m$. Provided $m$ is of the order of$\log(\kappa)$ and $h$ is sufficiently small, the resulting method is stableand quasi-optimal in the regime where $H$ is proportional to $\kappa^{-1}$. Inhomogeneous (or more general periodic) media, the fine scale test functionsdepend only on local mesh-configurations. Therefore, the seemingly high costfor the computation of the test functions can be drastically reduced onstructured meshes. We present numerical experiments in two and three spacedimensions.

Stable Multiscale Petrov-Galerkin Finite Element Method for High Frequency Acoustic Scattering