TU Darmstadt / ULB / TUprints

A matrix‐free macro‐element variant of the hybridized discontinuous Galerkin method

Badrkhani, Vahid ; Hiemstra, René R. ; Mika, Michał ; Schillinger, Dominik (2024)
A matrix‐free macro‐element variant of the hybridized discontinuous Galerkin method.
In: International Journal for Numerical Methods in Engineering, 2023, 124 (20)
doi: 10.26083/tuprints-00024660
Article, Secondary publication, Publisher's Version

[img] Text
Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

Download (5MB)
Item Type: Article
Type of entry: Secondary publication
Title: A matrix‐free macro‐element variant of the hybridized discontinuous Galerkin method
Language: English
Date: 23 January 2024
Place of Publication: Darmstadt
Year of primary publication: 2023
Place of primary 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: 10.26083/tuprints-00024660
Corresponding Links:
Origin: Secondary publication DeepGreen

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
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-246606
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 > Mechanics > Numerical Mechanics
Date Deposited: 23 Jan 2024 13:36
Last Modified: 06 Feb 2024 08:05
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/24660
PPN: 515256366
Actions (login required)
View Item View Item