Parallel geometric-algebraic multigrid on unstructured forests of octrees

Hari Sundar, George Biros, Carsten Burstedde, Johann Rudi, Omar Ghattas, Georg Stadler
2012 2012 International Conference for High Performance Computing, Networking, Storage and Analysis  
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
more » ... ctrees 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 variablecoefficient 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.
doi:10.1109/sc.2012.91 dblp:conf/sc/SundarBBRGS12 fatcat:o67eaqhs2vcbblgfr2ulonkp7m