Combining hardware, software, and numerical methodologies to improve computational performance of a discontinuous Galerkin shallow water model

Titelangaben

Faghih-Naini, Sara ; Kuckuk, Sebastian ; Zint, Daniel ; Aizinger, Vadym ; Köstler, Harald ; Grosso, Roberto ; Kenter, Tobias ; Shambhu, Adesh:
Combining hardware, software, and numerical methodologies to improve computational performance of a discontinuous Galerkin shallow water model.
2021
Veranstaltung: SIAM Conference on Mathematical & Computational Issues in the Geosciences (GS21) , 21.-24. June 2021 , Online-Conference.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

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Abstract

Recent trends in computer technology on the way to exascale computing allow for more realistic simulations of ocean and climate. However, since easy performance gains are mostly a thing of the past, in order to improve the performance of simulation codes, the focus has to be put on developing efficient numerical methods and exploiting specific features of underlying hardware. This talk presents two projects based on a discontinuous Galerkin (DG) model for the shallow water equations (SWE) aiming to realize these concepts.
First, we present a new quadrature-free DG formulation of the nonlinear SWE. If used together with a hierarchical basis, our new formulation allows to elegantly separate the discrete equations for different polynomial orders. We exploit this when designing a p-adaptive algorithm which can be distributed among several CPUs and GPUs in order to reduce computational cost. The method is implemented within the ExaStencils code generation framework that is based on the domain-specific language ExaSlang and emits an optimized C++ code. Within our work, it is extended by the Python fronted GHODDESS responsible for mapping the DG scheme to ExaSlang.
Furthermore, we present the first field-programmable gate array (FPGA) implementation of a SWE model based on the DG method that, following an Algorithm-Hardware-Co-design approach, introduces algorithmic changes into the numerical scheme contributing to strong scaling improvements of two to three orders of magnitude.