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

Johann Rudi, A. Cristiano I. Malossi, Tobin Isaac, Georg Stadler, Michael Gurnis, Peter W.J. Staar, Yves Ineichen, Costas Bekas, Alessandro Curioni, Omar Ghattas

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publicationProceedings of SC 2015
Subtitle of host publicationThe International Conference for High Performance Computing, Networking, Storage and Analysis
PublisherIEEE Computer Society
ISBN (Electronic)9781450337236
DOIs
StatePublished - Nov 15 2015
EventInternational Conference for High Performance Computing, Networking, Storage and Analysis, SC 2015 - Austin, United States
Duration: Nov 15 2015Nov 20 2015

Publication series

NameInternational Conference for High Performance Computing, Networking, Storage and Analysis, SC
Volume15-20-November-2015
ISSN (Print)2167-4329
ISSN (Electronic)2167-4337

Other

OtherInternational Conference for High Performance Computing, Networking, Storage and Analysis, SC 2015
CountryUnited States
CityAustin
Period11/15/1511/20/15

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Software

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