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Code Generation for quadrature-free Discontinuous Galerkin Discretizations of the Shallow-water Equations

Title data

Faghih-Naini, Sara ; Aizinger, Vadym ; Kuckuk, Sebastian ; Zint, Daniel ; Köstler, Harald ; Grosso, Roberto:
Code Generation for quadrature-free Discontinuous Galerkin Discretizations of the Shallow-water Equations.
2021
Event: Platform for Advanced Scientific Computing (PASC) Conference 2021 , 05.-09. July 2020 , Online-Conference.
(Conference item: Conference , Poster )

Project information

Project title:
Project's official titleProject's id
Performance optimized software strategies for unstructured-mesh applications in ocean modelingNo information

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

The discontinuous Galerkin (DG) methods are already well-established in nearly all areas of computational and geophysical fluid dynamics. Their strengths include the ability to use high-order approximation spaces, robustness for problems with shocks and discontinuities, natural support of h- and p-adaptivity, and many other features. However, comparatively high computational costs of DG discretizations can only be partially offset by efficient parallel scaling. For hyperbolic systems discretized in time by an explicit Runge-Kutta method, the most computationally expensive parts of a DG algorithm are the element and edge integrals computed via loops over quadrature points. We present a new quadrature-free DG formulation for the nonlinear shallow-water equations that replaces quadrature integrations by analytical evaluations. In order to be able to employ the quadrature-free methodology to operators with fraction-type nonlinearities, we propose a mixed (re-)formulation of the equation system. The numerical scheme has been successfully implemented within the ExaStencils code generation framework using a specialized Python front end based on the SymPy library.

Further data

Item Type: Conference item (Poster)
Refereed: No
Additional notes: Best Poster Award
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Scientific Computing
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Numerics of Partial Differential Equations
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Numerics of Partial Differential Equations > Professor Numerics of Partial Differential Equations - Univ.-Prof. Dr. Vadym Aizinger
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Research Institutions > Research Centres > Forschungszentrum für Wissenschaftliches Rechnen an der Universität Bayreuth - HPC-Forschungszentrum
Result of work at the UBT: Yes
DDC Subjects: 000 Computer Science, information, general works
000 Computer Science, information, general works > 004 Computer science
500 Science
500 Science > 500 Natural sciences
500 Science > 510 Mathematics
500 Science > 550 Earth sciences, geology
600 Technology, medicine, applied sciences
600 Technology, medicine, applied sciences > 600 Technology
Date Deposited: 15 Jul 2021 10:20
Last Modified: 15 Jul 2021 10:20
URI: https://eref.uni-bayreuth.de/id/eprint/66549