Parallel geometric-algebraic multigrid on unstructured forests of octrees

  • Authors:

  • Hari Sundar;George Biros;Carsten Burstedde;Johann Rudi;Omar Ghattas;Georg Stadler

  • Affiliations:

  • The University of Texas at Austin, Austin, TX;The University of Texas at Austin, Austin, TX;The University of Texas at Austin, Austin, TX and Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany;The University of Texas at Austin, Austin, TX;The University of Texas at Austin, Austin, TX;The University of Texas at Austin, Austin, TX

  • Venue:
  • SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
  • Year:
  • 2012

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Abstract

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.