SCHEDULE: NOV 10-16, 2012
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Parallel Geometric-Algebraic Multigrid on Unstructured Forests of Octrees
SESSION: Fast Algorithms
EVENT TYPE: Papers
TIME: 11:00AM - 11:30AM
SESSION CHAIR: Torsten Hoefler
AUTHOR(S):Hari Sundar, George Biros, Carsten Burstedde, Johann Rudi, Omar Ghattas, Georg Stadler
We present a parallel multigrid method for solving variable-coefficient elliptic partial differential equations on arbitrary geometries using highly adapted meshes. Our method is designed for meshes that are built from an unstructured hexahedral macro mesh, in which each macro element is adaptively refined as an octree. This forest-of-octrees approach enables us to generate meshes for complex geometries with arbitrary levels of local refinement. We use geometric multigrid (GMG) for each of the octrees and algebraic multigrid (AMG) as the coarse grid solver. We designed our GMG sweeps to entirely avoid collectives, thus minimizing communication cost. We present weak and strong scaling results for the 3D variable-coefficient Poisson problem that demonstrate high parallel scalability. As a highlight, the largest problem we solve is on a non-uniform mesh with 100 billion unknowns on 262,144 cores of NCCS's Cray XK6 ``Jaguar''; in this solve we sustain 272 TFlops/s.
Torsten Hoefler (Chair) - ETH Zurich
Hari Sundar - University of Texas at Austin
George Biros - University of Texas at Austin
Carsten Burstedde - University of Texas at Austin
Johann Rudi - University of Texas at Austin
Omar Ghattas - University of Texas at Austin
Georg Stadler - University of Texas at Austin