Large-scale simulation of mantle convection based on a new matrix-free approach

Bauer S, Huber M, Ghelichkhan S, Mohr M, Rüde U, Wohlmuth BI (2019)


Publication Type: Journal article

Publication year: 2019

Journal

Publisher: Elsevier

Book Volume: 31

Pages Range: 60--76

URI: https://www.sciencedirect.com/science/article/pii/S1877750318309840#!

DOI: 10.1016/j.jocs.2018.12.006

Abstract

In this paper, we report on a two-scale approach for efficient matrix-free finite element simulations. It is an extended version of our previous conference publication [1]. The proposed method is based on surrogate element matrices constructed by low order polynomial approximations. It is applied to a Stokes-type PDE system with variable viscosity as is a key component in mantle convection models. We set the ground for a rigorous performance analysis inspired by the concept of parallel textbook multigrid efficiency and study the weak scaling behavior on SuperMUC, a peta-scale supercomputer system. For a complex geodynamical model, we achieve, on up to 47 250 compute cores, a parallel efficiency of 93% for application of the discrete operator and 83% for a complete Uzawa V-cycle including the coarse grid solve. Our largest simulation uses a trillion (O (10 12)) degrees of freedom for a global mesh resolution …


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APA:

Bauer, S., Huber, M., Ghelichkhan, S., Mohr, M., Rüde, U., & Wohlmuth, B.I. (2019). Large-scale simulation of mantle convection based on a new matrix-free approach. Journal of Computational Science, 31, 60--76. https://dx.doi.org/10.1016/j.jocs.2018.12.006

MLA:

Bauer, Simon, et al. "Large-scale simulation of mantle convection based on a new matrix-free approach." Journal of Computational Science 31 (2019): 60--76.

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