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An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in earth's mantle

Rudi, Johann and Malossi, A. Cristiano I. and Isaac, Tobin and Stadler, Georg and Gurnis, Michael and Staar, Peter W. J. and Ineichen, Yves and Bekas, Costas and Curioni, Alessandro and Ghattas, Omar (2015) An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in earth's mantle. In: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis. Association for Computing Machinery , New York, NY, Art. No. 5. ISBN 978-1-4503-3723-6.

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Mantle convection is the fundamental physical process within earth's interior responsible for the thermal and geological evolution of the planet, including plate tectonics. The mantle is modeled as a viscous, incompressible, non-Newtonian fluid. The wide range of spatial scales, extreme variability and anisotropy in material properties, and severely nonlinear rheology have made global mantle convection modeling with realistic parameters prohibitive. Here we present a new implicit solver that exhibits optimal algorithmic performance and is capable of extreme scaling for hard PDE problems, such as mantle convection. To maximize accuracy and minimize runtime, the solver incorporates a number of advances, including aggressive multi-octree adaptivity, mixed continuous-discontinuous discretization, arbitrarily-high-order accuracy, hybrid spectral/geometric/algebraic multigrid, and novel Schur-complement preconditioning. These features present enormous challenges for extreme scalability. We demonstrate that---contrary to conventional wisdom---algorithmically optimal implicit solvers can be designed that scale out to 1.5 million cores for severely nonlinear, ill-conditioned, heterogeneous, and anisotropic PDEs.

Item Type:Book Section
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Gurnis, Michael0000-0003-1704-597X
Additional Information:© 2015 is held by the owner/author(s). Publication rights licensed to ACM. We wish to acknowledge the contributions of W. Scott Futral (LLNL) and Roy Musselman (IBM), who were instrumental in helping us achieve the scaling results on Sequoia. Their contributions came after SC’s July deadline for finalizing the author list had passed, but they should be regarded as co-authors. We wish to offer our deepest thanks to Lawrence Livermore National Laboratory, Jülich Supercomputing Center, RPI Center for Computational Innovation, and Texas Advanced Computing Center for granting us the computing resources required to prove the pioneering nature of this work. This research was partially supported by NSF grants CMMI-1028889 and ARC- 0941678 and DOE grants DE-FC02-13ER26128 and DEFG02- 09ER25914 as well as the EU FP7 EXA2GREEN and NANOSTREAMS projects. We also thank Carsten Burstedde for his dedicated work on the p4est library.
Group:Seismological Laboratory
Funding AgencyGrant Number
Department of Energy (DOE)DE-FC02-13ER26128
Department of Energy (DOE)DE-FG02-09ER25914
European Union (EU) FP7EXA2GREEN
European Union (EU) FP7NANOSTREAMS
Record Number:CaltechAUTHORS:20151123-153422845
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62346
Deposited By: Tony Diaz
Deposited On:23 Nov 2015 23:44
Last Modified:10 Nov 2021 23:01

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