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

The paper describes a sparse direct solver for the linear systems that arisefrom the discretization of an elliptic PDE on a two dimensional domain. Thesolver is designed to reduce communication costs and perform well on GPUs; ituses a two-level framework, which is easier to implement and optimize thantraditional multi-frontal schemes based on hierarchical nested dissectionorderings. The scheme decomposes the domain into thin subdomains, or "slabs".Within each slab, a local factorization is executed that exploits the geometryof the local domain. A global factorization is then obtained through the LUfactorization of a block-tridiagonal reduced coefficient matrix. The solver hascomplexity $O(N^{5/3})$ for the factorization step, and $O(N^{7/6})$ for eachsolve once the factorization is completed.  The solver described is compatible with a range of different localdiscretizations, and numerical experiments demonstrate its performance forregular discretizations of rectangular and curved geometries. The techniquebecomes particularly efficient when combined with very high-order convergentmulti-domain spectral collocation schemes. With this discretization, aHelmholtz problem on a domain of size $1000 \lambda \times 1000 \lambda$ (forwhich $N=100 \mbox{M}$) is solved in 15 minutes to 6 correct digits on ahigh-powered desktop with GPU acceleration.

SlabLU: A Two-Level Sparse Direct Solver for Elliptic PDEs