Hybrid Parallel Multigrid Methods for Geodynamical Simulations
Even on modern supercomputer architectures, Earth mantle simulations are so compute intensive that they are considered grand challenge applications. The dominating roadblocks in this branch of Geophysics are model complexity and uncertainty in parameters
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bstract Even on modern supercomputer architectures, Earth mantle simulations are so compute intensive that they are considered grand challenge applications. The dominating roadblocks in this branch of Geophysics are model complexity and uncertainty in parameters and data, e.g., rheology and seismically imaged mantle heterogeneity, as well as the enormous space and time scales that must be resolved in the computational models. This article reports on a massively parallel all-at-once multigrid solver for the Stokes system as it arises in mantle convection models. The solver employs the hierarchical hybrid grids framework and demonstrates that a system with coupled velocity components and with more than a trillion (1:7 1012) degrees of freedom can be solved in about 1,000 s using 40,960 compute cores of JUQUEEN. The simulation framework is used to investigate the influence of asthenosphere thickness and viscosity on upper mantle velocities in a static scenario. Additionally, results for a time-dependent simulation with a time-variable temperature-dependent viscosity model are presented.
S. Bauer • H.-P. Bunge • M. Mohr • J. Weismüller Department of Earth and Environmental Sciences, Ludwig-Maximilians-Universität München, München, Germany e-mail: [email protected] D. Drzisga • M. Huber • L. John () • C. Waluga • B. Wohlmuth Institute for Numerical Mathematics, Technische Universität München, München, Germany e-mail: [email protected] B. Gmeiner • U. Rüde Department of Computer Science 10, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany H. Stengel • G. Wellein • M. Wittmann Erlangen Regional Computing Center (RRZE), Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany © Springer International Publishing Switzerland 2016 H.-J. Bungartz et al. (eds.), Software for Exascale Computing – SPPEXA 2013-2015, Lecture Notes in Computational Science and Engineering 113, DOI 10.1007/978-3-319-40528-5_10
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1 Introduction The surface of our planet is shaped by processes deep beneath our feet. For a better understanding of these physical phenomena, simulations with high resolution are essential. The solid Earth’s mantle extends from some tens of kilometers below the surface down to the core-mantle boundary at about 3,490 km depth. On geologic time scales, the mantle behaves like a highly viscous convecting fluid with one complete overturn taking about 100 million years [14]. It is this motion that is finally responsible for plate tectonics, mountain and ocean building, volcanism, and the accumulation of stresses leading to earthquakes. Convection itself is driven by internal heating, resulting from the decay of radioactive rocks in the mantle, by heat flux from the Earth’s core, and by secular cooling. Due to the enormous length scales advection predominates heat transport through the planet over heat conduction. The governing equations for mantle convection are formulations for the balance of forces and the conservation of mass and energy. While the general structure of
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