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Quadrature-free discontinuous Galerkin method with code generation features for shallow water equations on automatically generated block-structured meshes

Title data

Faghih-Naini, Sara ; Aizinger, Vadym ; Kuckuk, Sebastian ; Zint, Daniel ; Grosso, Roberto ; Köstler, Harald:
Quadrature-free discontinuous Galerkin method with code generation features for shallow water equations on automatically generated block-structured meshes.
In: Advances in Water Resources. Vol. 138 (2020) . - No. 103552.
ISSN 1872-9657
DOI: https://doi.org/10.1016/j.advwatres.2020.103552

Official URL: Volltext

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

Although discretizations of the shallow water equations (SWE) based on the discontinuous Galerkin (DG) method are well established, their computational performance still generally lags behind that of the finite volume discretizations. In explicit and semi-implicit time stepping schemes commonly used in connection with the SWE models, the most computationally expensive parts of a DG algorithm are the element and edge integrals computed via loops over quadrature points. We propose a quadrature-free DG formulation for the SWE that replaces quadrature integrations by analytical evaluations. The method is implemented within the code generation framework of the ExaStencils project using the SymPy Python library. The new formulation uses block-structured triangular meshes automatically generated for a given number of blocks.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Local discontinuous Galerkin method (LDG); Shallow water equations; Quadrature-free formulation; Code generation domain specific languages (DSL; Python SymPy; Block-structured mesh
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: 16 Mar 2020 07:20
Last Modified: 16 Mar 2020 07:20
URI: https://eref.uni-bayreuth.de/id/eprint/54631