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SCHEDULE: NOV 15-20, 2015

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An Extreme-Scale Implicit Solver for Complex PDEs: Highly Heterogeneous Flow in Earth’s Mantle

SESSION: ACM Gordon Bell Finalist II

EVENT TYPE: Awards Presentations, ACM Gordon Bell Finalists

EVENT TAG(S): Performance, HPC Beginner Friendly, Applications

TIME: 11:00AM - 11:30AM

SESSION CHAIR(S): Subhash Saini

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



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 0.5 million cores for severely nonlinear, ill-conditioned, heterogeneous and localized PDEs.

Chair/Author Details:

Subhash Saini (Chair) - NASA Ames Research Center|

Johann Rudi - The University of Texas at Austin

A. Cristiano I. Malossi - IBM Corporation

Tobin Isaac - The University of Texas at Austin

Georg Stadler - Courant Institute of Mathematical Sciences

Michael Gurnis - California Institute of Technology

Peter W. J. Staar - IBM Corporation

Yves Ineichen - IBM Corporation

Costas Bekas - IBM Corporation

Alessandro Curioni - IBM Corporation

Omar Ghattas - The University of Texas at Austin

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Paper provided by the ACM Digital Library

Paper also available from IEEE Computer Society