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hyper.deal: An Efficient, Matrix-free Finite-element Library for High-dimensional Partial Differential Equations
Tech Univ Munich, Inst Computat Mech, Dept Mech Engn, Boltzmannstr 15, D-85748 Garching, Germany.;Helmholtz Zentrum Hereon, Inst Mat Syst Modeling, Max Planck Str 1, D-21502 Geesthacht, Germany..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis. Max Planck Inst Plasma Phys, Boltzmannstr 2, D-85748 Garching, Germany.;Tech Univ Munich, Dept Math, Boltzmannstr 3, D-85748 Garching, Germany..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Computational Science. Tech Univ Munich, Inst Computat Mech, Dept Mech Engn, Boltzmannstr 15, D-85748 Garching, Germany..
2021 (English)In: ACM Transactions on Mathematical Software, ISSN 0098-3500, E-ISSN 1557-7295, Vol. 47, no 4, p. 1-34, article id 33Article in journal (Refereed) Published
Abstract [en]

This work presents the efficient, matrix-free finite-element library hyper deal for solving partial differential equations in two up to six dimensions with high-order discontinuous Galerkin methods. It builds upon the low-dimensional finite-element library deal. II to create complex low-dimensional meshes and to operate on them individually. These meshes are combined via a tensor product on the fly, and the library provides new special-purpose highly optimized matrix-free functions exploiting domain decomposition as well as shared memory via MPI-3.0 features. Both node-level performance analyses and strong/weak-scaling studies on up to 147,456 CPU cores confirm the efficiency of the implementation. Results obtained with the library hyper . deal are reported for high-dimensional advection problems and for the solution of the Vlasov-Poisson equation in up to six-dimensional phase space.

Place, publisher, year, edition, pages
ASSOC COMPUTING MACHINERY Association for Computing Machinery (ACM), 2021. Vol. 47, no 4, p. 1-34, article id 33
Keywords [en]
Matrix-free operator evaluation, discontinuous Galerkin methods, high-dimensional, high-order, Vlasov-Poisson equation, MPI-3.0 shared memory
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-457641DOI: 10.1145/3469720ISI: 000703370900004OAI: oai:DiVA.org:uu-457641DiVA, id: diva2:1607518
Funder
German Research Foundation (DFG), KO5206/1-1German Research Foundation (DFG), KR4661/2-1eSSENCE - An eScience CollaborationAvailable from: 2021-11-01 Created: 2021-11-01 Last updated: 2024-01-15Bibliographically approved

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Kormann, KatharinaKronbichler, Martin

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