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Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine

Dumbser, Michael; Fambri, Francesco; Tavelli, Maruizio; Bader, Michael; Weinzierl, Tobias

Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine Thumbnail


Authors

Michael Dumbser

Francesco Fambri

Maruizio Tavelli

Michael Bader



Abstract

In this paper we discuss a new and very efficient implementation of high order accurate arbitrary high order schemes using derivatives discontinuous Galerkin (ADER-DG) finite element schemes on modern massively parallel supercomputers. The numerical methods apply to a very broad class of nonlinear systems of hyperbolic partial differential equations. ADER-DG schemes are by construction communication-avoiding and cache-blocking, and are furthermore very well-suited for vectorization, and so they appear to be a good candidate for the future generation of exascale supercomputers. We introduce the numerical algorithm and show some applications to a set of hyperbolic equations with increasing levels of complexity, ranging from the compressible Euler equations over the equations of linear elasticity and the unified Godunov-Peshkov-Romenski (GPR) model of continuum mechanics to general relativistic magnetohydrodynamics (GRMHD) and the Einstein field equations of general relativity. We present strong scaling results of the new ADER-DG schemes up to 180,000 CPU cores. To our knowledge, these are the largest runs ever carried out with high order ADER-DG schemes for nonlinear hyperbolic PDE systems. We also provide a detailed performance comparison with traditional Runge-Kutta DG schemes

Citation

Dumbser, M., Fambri, F., Tavelli, M., Bader, M., & Weinzierl, T. (2018). Efficient Implementation of ADER Discontinuous Galerkin Schemes for a Scalable Hyperbolic PDE Engine. Axioms, 7(3), Article 63. https://doi.org/10.3390/axioms7030063

Journal Article Type Article
Acceptance Date Aug 22, 2018
Online Publication Date Sep 1, 2018
Publication Date Sep 1, 2018
Deposit Date May 21, 2018
Publicly Available Date Sep 20, 2018
Journal Axioms
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 7
Issue 3
Article Number 63
DOI https://doi.org/10.3390/axioms7030063
Related Public URLs https://arxiv.org/abs/1808.03788

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