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Linearly scaling HDG: The hybridizable interior penalty method

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/
Document Type:Conference or Workshop Item (Speech)
Title:Linearly scaling HDG: The hybridizable interior penalty method
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Huismann, ImmoImmo.Huismann (at) dlr.deUNSPECIFIED
Stiller, Jörgjoerg.stiller (at) tu-dresden.deUNSPECIFIED
Fröhlich, Jochenjochen.froehlich (at) tu-dresden.deUNSPECIFIED
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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