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, 2021-07-12 - 2021-07-16, 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 Start Date: | 12 July 2021 | ||||||||||||||||
Event End Date: | 16 July 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: | 24 Apr 2024 20:43 |
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