Balancing Domain Decomposition by Constraints Algorithms for Curl-Conforming Spaces of Arbitrary Order

Stefano Zampini, Panayot Vassilevski, Veselin Dobrev, Tzanio Kolev

Research output: Chapter in Book/Report/Conference proceedingChapter

6 Scopus citations

Abstract

We construct Balancing Domain Decomposition by Constraints methods for the linear systems arising from arbitrary order, finite element discretizations of the H(curl) model problem in three-dimensions. Numerical results confirm that the proposed algorithm is quasi-optimal in the coarse-to-fine mesh ratio, and poly-logarithmic in the polynomial order of the curl-conforming discretization space. Additional numerical experiments, including higher-order geometries, upscaled finite elements, and adaptive coarse spaces, prove the robustness of our algorithm. A scalable three-level extension is presented, and it is validated with large scale experiments using up to 16,384 subdomains and almost a billion of degrees of freedom.
Original languageEnglish (US)
Title of host publicationDomain Decomposition Methods in Science and Engineering XXIV
PublisherSpringer Nature
Pages103-116
Number of pages14
ISBN (Print)9783319938721
DOIs
StatePublished - Jan 5 2019

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