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Multirate time stepping for accelerating explicit discontinuous Galerkin computations with application to geophysical flows
Seny, B.; Lambrechts, J.; Comblen, R.; Legat, V.; Remacle, J.-F. (2013). Multirate time stepping for accelerating explicit discontinuous Galerkin computations with application to geophysical flows. Int. J. Numer. Methods Fluids 71(1): 41-64. dx.doi.org/10.1002/fld.3646
In: International Journal for Numerical Methods in Fluids. Wiley Interscience: Chichester; New York. ISSN 0271-2091, more
Peer reviewed article  

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Keyword
    Marine
Author keywords
    discontinuous Galerkin; high performance computing; multirate timestepping; explicit Runge-Kutta; shallow water equations; Great BarrierReef

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Abstract
    This paper presents multirate explicit time-stepping schemes for solving partial differential equations with discontinuous Galerkin elements in the framework of Large-scale marine flows. It addresses the variability of the local stable time steps by gathering the mesh elements in appropriate groups. The real challenge is to develop methods exhibiting mass conservation and consistency. Two multirate approaches, based on standard explicit RungeKutta methods, are analyzed. They are well suited and optimized for the discontinuous Galerkin framework. The significant speedups observed for the hydrodynamic application of the Great Barrier Reef confirm the theoretical expectations.

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