A Quadrature-free p-adaptive Discontinuous Galerkin Formulation for Shallow-water Equations with Code Generation Features

Titelangaben

Faghih-Naini, Sara ; Kuckuk, Sebastian ; Zint, Daniel ; Aizinger, Vadym ; Köstler, Harald ; Grosso, Roberto:
A Quadrature-free p-adaptive Discontinuous Galerkin Formulation for Shallow-water Equations with Code Generation Features.
2020
Veranstaltung: Modeling and Simulation of Transport Phenomena , 12.-15. Okt. 2020 , Treis-Karden, Deutschland.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

Weitere URLs

Abstract

In nearly all areas of computational and geophysical fluid dynamics, discontinuous Galerkin methods are an acknowledged numerical tool. This is not only due to their ability to use high-order approximation spaces, their robustness for problems with shocks but also due to their natural support for h- and p-adaptivity. However, they need substantially more degrees of freedom than the continuous finite elements resulting in a computational performance handicap that can only be partially offset by efficient parallel scaling. In this talk, we present a new quadrature-free formulation for the nonlinear shallow-water equations (SWE), in which quadrature integrations are replaced by analytical integral evaluations. If used in combination with hierarchical bases, this formulation allows to elegantly separate discrete equations for different polynomial orders.We exploit this feature of our scheme to design a special type of p-adaptive discretization. The method is implemented within the ExaStencils code generation framework. We explain the whole code generation toolchain based on the multi-layered domain-specific language (DSL) ExaSlang. The workflow starts with the mapping of the discrete formulation to our Python frontend GHODDESS which then is passed to the ExaStencils compiler that in its turn produces an optimized stand-alone C++ code. Our framework utilizes block-structured meshes that are generated using an initial unstructured mesh of the computational domain. This approach allows to exploit performance enhancements connected to regular discretization stencils without sacrificing the capability to accurately capture the geometry and the topography of coastal domains. Comparisons to a quadrature-based DG code and to unstructured meshes demonstrate considerable performance improvement of the new approach while achieving comparable accuracy and stability.