Huismann, Immo and Stiller, Jörg and Fröhlich, Jochen (2021) Linearly scaling HDG: The hybridizable interior penalty method. International Conference on Spectral and High Order Methods, 12.-16.07.2021, Wien, Österreich.
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Abstract
For elliptic equations in three dimensions, the runtime of discontinuous Galerkin methods typically scales with O(p^4 n_e) , where p is the polynomial degree and n_e the number of elements and structure exploitation via tensor-product bases is assumed. For local discontinuous Galerkin methods that allow for hybridization, the authors were able to linearize the runtime, i.e. to create a solver that scales with O(p^3 n_e) = O (n_DOF), where n_DOF are the total number of degrees of freedom. This contribution extends the developed techniques to the hybridizable interior penalty method, first deriving a linearly scaling elliptic operator, thereafter a linearly scaling block smoothers and, lastly, combining both into a linearly scaling multigrid method, i.e. O(p^3 n_e) = O (n_DOF). Runtime tests confirm that the solver requires a similar amount of runtime per degree of freedom as low-order solvers, enabling high-order simulations that are as cheap as low-order simulations.
Item URL in elib: | https://elib.dlr.de/144614/ | ||||||||||||
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Document Type: | Conference or Workshop Item (Speech) | ||||||||||||
Title: | Linearly scaling HDG: The hybridizable interior penalty method | ||||||||||||
Authors: |
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Date: | 2021 | ||||||||||||
Refereed publication: | No | ||||||||||||
Open Access: | No | ||||||||||||
Gold Open Access: | No | ||||||||||||
In SCOPUS: | No | ||||||||||||
In ISI Web of Science: | No | ||||||||||||
Status: | Published | ||||||||||||
Keywords: | Discontinuous Galerkin, Substructuring Hybridizable Discontinuous Galerkin, elliptic equations, multigrid | ||||||||||||
Event Title: | International Conference on Spectral and High Order Methods | ||||||||||||
Event Location: | Wien, Österreich | ||||||||||||
Event Type: | international Conference | ||||||||||||
Event Dates: | 12.-16.07.2021 | ||||||||||||
HGF - Research field: | Aeronautics, Space and Transport | ||||||||||||
HGF - Program: | Aeronautics | ||||||||||||
HGF - Program Themes: | Efficient Vehicle | ||||||||||||
DLR - Research area: | Aeronautics | ||||||||||||
DLR - Program: | L EV - Efficient Vehicle | ||||||||||||
DLR - Research theme (Project): | L - Digital Technologies | ||||||||||||
Location: | Dresden | ||||||||||||
Institutes and Institutions: | Institute of Software Methods for Product Virtualization > High Perfomance Computing | ||||||||||||
Deposited By: | Huismann, Immo | ||||||||||||
Deposited On: | 18 Oct 2021 13:06 | ||||||||||||
Last Modified: | 18 Oct 2021 13:06 |
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