[2110.11211] A dimension-oblivious domain decomposition method based on space-filling curves Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2110.11211 (math) [Submitted on 21 Oct 2021 ( v1 ), last revised 10 Aug 2022 (this version, v3)] Title: A dimension-oblivious domain decomposition method based on space-filling curves Authors: Michael Griebel , Marc Alexander Schweitzer , Lukas Troska View a PDF of the paper titled A dimension-oblivious domain decomposition method based on space-filling curves, by Michael Griebel and 2 other authors View PDF HTML (experimental) Abstract: In this paper we present an algebraic dimension-oblivious two-level domain decomposition solver for discretizations of elliptic partial differential equations. The proposed parallel solver is based on a space-filling curve partitioning approach that is applicable to any discretization, i.e. it directly operates on the assembled matrix equations. Moreover, it allows for the effective use of arbitrary processor numbers independent of the dimension of the underlying partial differential equation while maintaining optimal convergence behavior. This is the core property required to attain a sparse grid based combination method with extreme scalability which can utilize exascale parallel systems efficiently. Moreover, this approach provides a basis for the development of a fault-tolerant solver for the numerical treatment of high-dimensional problems. To achieve the required data redundancy we are therefore concerned with large overlaps of our domain decomposition which we construct via space-filling curves. In this paper, we propose our space-filling curve based domain decomposition solver and present its convergence properties and scaling behavior. The results of numerical experiments clearly show that our approach provides optimal convergence and scaling behavior in arbitrary dimension utilizing arbitrary processor numbers. Comments: 28 pages, 11 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:2103.03315 Subjects: Numerical Analysis (math.NA) MSC classes: 65F50, 65Y05, 65M55, 65N55 Cite as: arXiv:2110.11211 [math.NA] (or arXiv:2110.11211v3 [math.NA] for this version) https://doi.org/10.48550/arXiv.2110.11211 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1137/21M1454481 Focus to learn more DOI(s) linking to related resources Submission history From: Michael Griebel [ view email ] [v1] Thu, 21 Oct 2021 15:35:21 UTC (961 KB) [v2] Wed, 20 Apr 2022 16:38:57 UTC (1,516 KB) [v3] Wed, 10 Aug 2022 20:09:51 UTC (4,051 KB) Full-text links: Access Paper: View a PDF of the paper titled A dimension-oblivious domain decomposition method based on space-filling curves, by Michael Griebel and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2021-10 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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