Quadrature-free Discontinuous Galerkin Method for Shallow-water Equations

Titelangaben

Faghih-Naini, Sara ; Aizinger, Vadym ; Kuckuk, Sebastian ; Zint, Daniel ; Köstler, Harald ; Grosso, Roberto:
Quadrature-free Discontinuous Galerkin Method for Shallow-water Equations.
2019
Veranstaltung: 9th International Congress on Industrial and Applied Mathematics , 2019 July 15-19 , Valencia, Spain.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

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Abstract

The shallow water equations (SWE) are a commonly used model to study tsunamis, tides, and coastal ocean circulation. However, there exist various approaches to discretize and solve them efficiently. Which of them is best for a certain scenario is often not known and, in addition, depends heavily on the used HPC platform. From a simulation software perspective, this places a premium on the ability to adapt easily to different numerical methods and hardware architectures. One solution to this problem is to apply code generation techniques and to express methods and specific hardware-dependent implementations on different levels of abstraction. In this talk, we introduce a new quadrature-free discontinuous Galerkin (DG) formulation for the shallow water equation. Furthermore, we present parts of the toolchain for automated code generation and also demonstrate the convergence of our method for higher order DG discretizations. Finally, we show some simulation results on realistic computational grids.