Open this publication in new window or tab >>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
Association for Computing Machinery (ACM)ASSOC COMPUTING MACHINERY, 2021
Keywords
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:nbn:se:uu:diva-457641 (URN)10.1145/3469720 (DOI)000703370900004 ()
Funder
German Research Foundation (DFG), KO5206/1-1German Research Foundation (DFG), KR4661/2-1eSSENCE - An eScience Collaboration
2021-11-012021-11-012024-01-15Bibliographically approved