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
Article, Bibliographie
This is the latest version of this item.
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2023 |
| Creators: | Badrkhani, Vahid ; Hiemstra, René R. ; Mika, Michał ; Schillinger, Dominik |
| Type of entry: | Bibliographie |
| Title: | A matrix‐free macro‐element variant of the hybridized discontinuous Galerkin method |
| Language: | English |
| Date: | 2023 |
| Place of Publication: | Chichester |
| Publisher: | John Wiley & Sons |
| Journal or Publication Title: | International Journal for Numerical Methods in Engineering |
| Volume of the journal: | 124 |
| Issue Number: | 20 |
| DOI: | 10.1002/nme.7320 |
| Corresponding Links: | |
| 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. |
| Uncontrolled Keywords: | domain decomposition, hybridized discontinuous Galerkin method, load balancing, local adaptive refinement, macro‐elements, matrix‐free, scalability |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics 600 Technology, medicine, applied sciences > 624 Civil engineering and environmental protection engineering |
| Divisions: | 13 Department of Civil and Environmental Engineering Sciences 13 Department of Civil and Environmental Engineering Sciences > Mechanics 13 Department of Civil and Environmental Engineering Sciences > Mechanics > Numerical Mechanics |
| Date Deposited: | 24 Jan 2024 07:53 |
| Last Modified: | 24 Jan 2024 14:57 |
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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) [Currently Displayed]
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