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

This paper presents efficient data structures for the implementation ofmatrix-free finite element methods on block-structured, hybrid tetrahedralgrids. It provides a complete categorization of all geometric sub-objects thatemerge from the regular refinement of the unstructured, tetrahedral coarse gridand describes efficient iteration patterns and analytical linearizationfunctions for the mapping of coefficients to memory addresses. This foundationenables the implementation of fast, extreme-scalable, matrix-free, iterativesolvers, and in particular geometric multigrid methods by design. Theirapplication to the variable-coefficient Stokes system subject to an enrichedGalerkin discretization and to the curl-curl problem discretized withN\'ed\'elec edge elements showcases the flexibility of the implementation.Eventually, the solution of a curl-curl problem with $1.6 \cdot 10^{11}$ (morethan one hundred billion) unknowns on more than $32000$ processes with amatrix-free full multigrid solver demonstrates its extreme-scalability.

Fundamental Data Structures for Matrix-Free Finite Elements on Hybrid Tetrahedral Grids