## 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 title Project's id Performance optimized software strategies for unstructured-mesh applications in ocean modeling No 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.