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 present a solver for the 2D high-frequency Helmholtz equation inheterogeneous, constant density, acoustic media, with online parallelcomplexity that scales empirically as $\mathcal{O}(\frac{N}{P})$, where $N$ isthe number of volume unknowns, and $P$ is the number of processors, as long as$P = \mathcal{O}(N^{1/5})$. This sublinear scaling is achieved by domaindecomposition, not distributed linear algebra, and improves on the $P=\mathcal{O}(N^{1/8})$ scaling reported earlier in [L. Zepeda-N\'u\~nez and L.Demanet, J. Comput. Phys., 308 (2016), pp. 347-388 ]. The solver relies on atwo-level nested domain decomposition: a layered partition on the outer level,and a further decomposition of each layer in cells at the inner level. TheHelmholtz equation is reduced to a surface integral equation (SIE) posed at theinterfaces between layers, efficiently solved via a nested version of thepolarized traces preconditioner [L. Zepeda-N\'u\~nez and L. Demanet, J. Comput.Phys., 308 (2016), pp. 347-388.]. The favorable complexity is achieved via anefficient application of the integral operators involved in the SIE.

Nested domain decomposition with polarized traces for the 2D Helmholtz equation