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Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities
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SYSNO ASEP 0556736 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities Author(s) Dostál, Z. (CZ)
Horák, David (UGN-S) SAI, ORCID
Kružík, Jakub (UGN-S)
Brzobohatý, T. (CZ)
Vlach, O. (CZ)Number of authors 5 Source Title Numerical Algorithms. - : Springer - ISSN 1017-1398
Roč. 91, č. 2 (2022), s. 773-801Number of pages 29 s. Publication form Online - E Language eng - English Country NL - Netherlands Keywords domain decomposition ; variational inequality ; scalability ; massively parallel algorithms ; hybrid TFETI-DP Subject RIV BA - General Mathematics OECD category Applied mathematics R&D Projects LQ1602 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) GA19-11441S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support UGN-S - RVO:68145535 UT WOS 000784390700002 EID SCOPUS 85128280893 DOI 10.1007/s11075-022-01281-3 Annotation The unpreconditioned hybrid domain decomposition method was recently shown to be a competitive solver for linear elliptic PDE problems discretized by structured grids. Here, we plug H-TFETI-DP (hybrid total finite element tearing and interconnecting dual primal) method into the solution of huge boundary elliptic variational inequalities. We decompose the domain into subdomains that are discretized and then interconnected partly by Lagrange multipliers and partly by edge averages. After eliminating the primal variables, we get a quadratic programming problem with a well-conditioned Hessian and bound and equality constraints that is effectively solvable by specialized algorithms. We prove that the procedure enjoys optimal, i.e., asymptotically linear complexity. The analysis uses recently established bounds on the spectrum of the Schur complements of the clusters interconnected by edge/face averages. The results extend the scope of scalability of massively parallel algorithms for the solution of variational inequalities and show the outstanding efficiency of the H-TFETI-DP coarse grid split between the primal and dual variables. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2023 Electronic address https://link.springer.com/content/pdf/10.1007/s11075-022-01281-3.pdf
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