Algorithm re-design and code generation for performance improvements of a discontinuous Galerkin shallow water model on CPUs, GPUs, FPGAs and heterogeneous systems

Titelangaben

Faghih-Naini, Sara ; Aizinger, Vadym ; Kuckuk, Sebastian ; Angersbach, Richard ; Alt, Christoph ; Kenter, Tobias ; Köstler, Harald:
Algorithm re-design and code generation for performance improvements of a discontinuous Galerkin shallow water model on CPUs, GPUs, FPGAs and heterogeneous systems.
2023
Veranstaltung: European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) 2023 , 4.-8. September 2023 , Lisbon, Portugal.
(Veranstaltungsbeitrag: Kongress/Konferenz/Symposium/Tagung , Vortrag )

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Abstract

Heterogeneous architectures and accelerator hardware have become a clear trend in current high-performance computing environments.
In this talk, we present new numerical, algorithmic, and computational technologies with the potential to be incorporated into future ocean and atmospheric models after successful evaluation. First, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free discontinuous Galerkin method for the shallow water equations [1]. Our new approach separates the computations of lower-order degrees of freedom from the rest of the discretization, which lets us overlap computations of the lower-order and the higher-order DG solution components. We use automatic code generation [2] to optimize the kernel distribution between the CPU and GPU, achieving significant performance improvements.
Furthermore, we present a new approach to port shallow water simulations to FPGAs based on the same code generation framework in combination with a template-based stencil processing library that provides FPGA-specific optimizations for a streaming execution model [3].


[1] S. Faghih-Naini, V. Aizinger, S. Kuckuk, R. Angersbach and H. Köstler, p-adaptive discontinuous Galerkin method for the shallow water equations on heterogeneous computing architectures. Submitted to Transactions on Mathematical Software, 2023.

[2] S. Faghih-Naini, S. Kuckuk, V. Aizinger, D. Zint, R. Grosso, and H. Köstler, Quadrature-free discontinuous Galerkin method with code generation features for shallow water equations on automatically generated block-structured meshes. Advances in Water Resources 138 (2020), p. 103552.

[3] C. Alt, T. Kenter, S. Faghih-Naini, J. Faj, J.-O. Opdenhövel, C. Plessl, V. Aizinger, J. Hönig and H. Köstler. Shallow Water DG Simulations on FPGAs: Design and Comparison of a Novel Code Generation Pipeline. Accepted at ISC High Performance, 2023.