Badrkhani, Vahid ; Hiemstra, René R. ; Mika, Michał ; Schillinger, Dominik (2023)
A matrix‐free macro‐element variant of the hybridized discontinuous Galerkin method.
In: International Journal for Numerical Methods in Engineering, 124 (20)
doi: 10.1002/nme.7320
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
We investigate a macro‐element variant of the hybridized discontinuous Galerkin (HDG) method, using patches of standard simplicial elements that can have non‐matching interfaces. Coupled via the HDG technique, our method enables local refinement by uniform simplicial subdivision of each macro‐element. By enforcing one spatial discretization for all macro‐elements, we arrive at local problems per macro‐element that are embarrassingly parallel, yet well balanced. Therefore, our macro‐element variant scales efficiently to n‐node clusters and can be tailored to available hardware by adjusting the local problem size to the capacity of a single node, while still using moderate polynomial orders such as quadratics or cubics. Increasing the local problem size means simultaneously decreasing, in relative terms, the global problem size, hence effectively limiting the proliferation of degrees of freedom. The global problem is solved via a matrix‐free iterative technique that also heavily relies on macro‐element local operations. We investigate and discuss the advantages and limitations of the macro‐element HDG method via an advection‐diffusion model problem.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Badrkhani, Vahid ; Hiemstra, René R. ; Mika, Michał ; Schillinger, Dominik |
| Art des Eintrags: | Bibliographie |
| Titel: | A matrix‐free macro‐element variant of the hybridized discontinuous Galerkin method |
| Sprache: | Englisch |
| Publikationsjahr: | 2023 |
| Ort: | Chichester |
| Verlag: | John Wiley & Sons |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | International Journal for Numerical Methods in Engineering |
| Jahrgang/Volume einer Zeitschrift: | 124 |
| (Heft-)Nummer: | 20 |
| DOI: | 10.1002/nme.7320 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | We investigate a macro‐element variant of the hybridized discontinuous Galerkin (HDG) method, using patches of standard simplicial elements that can have non‐matching interfaces. Coupled via the HDG technique, our method enables local refinement by uniform simplicial subdivision of each macro‐element. By enforcing one spatial discretization for all macro‐elements, we arrive at local problems per macro‐element that are embarrassingly parallel, yet well balanced. Therefore, our macro‐element variant scales efficiently to n‐node clusters and can be tailored to available hardware by adjusting the local problem size to the capacity of a single node, while still using moderate polynomial orders such as quadratics or cubics. Increasing the local problem size means simultaneously decreasing, in relative terms, the global problem size, hence effectively limiting the proliferation of degrees of freedom. The global problem is solved via a matrix‐free iterative technique that also heavily relies on macro‐element local operations. We investigate and discuss the advantages and limitations of the macro‐element HDG method via an advection‐diffusion model problem. |
| Freie Schlagworte: | domain decomposition, hybridized discontinuous Galerkin method, load balancing, local adaptive refinement, macro‐elements, matrix‐free, scalability |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 624 Ingenieurbau und Umwelttechnik |
| Fachbereich(e)/-gebiet(e): | 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Numerische Mechanik |
| Hinterlegungsdatum: | 24 Jan 2024 07:53 |
| Letzte Änderung: | 24 Jan 2024 14:57 |
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| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
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A matrix‐free macro‐element variant of the hybridized discontinuous Galerkin method. (deposited 23 Jan 2024 13:36)
- A matrix‐free macro‐element variant of the hybridized discontinuous Galerkin method. (deposited 24 Jan 2024 07:53) [Gegenwärtig angezeigt]
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