Domain-decomposed parallelization of B-spline based s-version of the finite element method via generalized graph abstraction

[2606.21142] Domain-decomposed parallelization of B-spline based s-version of the finite element method via generalized graph abstraction Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2606.21142 (math) [Submitted on 19 Jun 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Domain-decomposed parallelization of B-spline based s-version of the finite element method via generalized graph abstraction Authors: Nozomi Magome , Naoki Morita , Shigeki Kaneko , Naoto Mitsume View a PDF of the paper titled Domain-decomposed parallelization of B-spline based s-version of the finite element method via generalized graph abstraction, by Nozomi Magome and 3 other authors View PDF HTML (experimental) Abstract: The s-version of the finite element method (SFEM) enables locally high-resolution analysis by superimposing independently defined finite element meshes. However, domain-decomposed parallelization is nontrivial because complex interactions arise among degrees of freedom distributed over multiple meshes. In this study, we propose a method for constructing a graph structure that uniformly represents interactions among computational points, including both intra- and inter-mesh interactions, based on the overlap of basis-function supports. We apply the proposed graph representation to the B-spline based SFEM (BSFEM), a high-accuracy SFEM formulation previously proposed by the authors. The resulting graph partition enables the consistent assignment of degrees of freedom and elements to processes and the construction of the MPI communication structure, thereby realizing domain-decomposition-based distributed-memory parallelization of BSFEM. To the best of the authors' knowledge, this BSFEM implementation constitutes the first domain-decomposition-based distributed-memory parallelization of an SFEM-based method. Furthermore, as an example demonstrating the utility of the proposed graph representation, we apply cost-weighted graph partitioning in which the matrix-generation costs specific to BSFEM are incorporated into node weights, and demonstrate effective static load balancing that accounts for the nonuniform matrix-generation workload. Comments: 27 pages, 15 figures Subjects: Numerical Analysis (math.NA) ACM classes: G.1.0 Cite as: arXiv:2606.21142 [math.NA] (or arXiv:2606.21142v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2606.21142 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nozomi Magome [ view email ] [v1] Fri, 19 Jun 2026 06:28:12 UTC (9,545 KB) [v2] Sat, 15 Aug 2026 10:47:15 UTC (9,523 KB) Full-text links: Access Paper: View a PDF of the paper titled Domain-decomposed parallelization of B-spline based s-version of the finite element method via generalized graph abstraction, by Nozomi Magome and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2026-06 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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