BEGIN:VCALENDAR PRODID:-//Microsoft Corporation//Outlook MIMEDIR//EN VERSION:1.0 BEGIN:VEVENT DTSTART:20121114T180000Z DTEND:20121114T183000Z LOCATION:255-BC DESCRIPTION;ENCODING=QUOTED-PRINTABLE: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=0Ause 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. =0AWe 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. SUMMARY:Parallel Geometric-Algebraic Multigrid on Unstructured Forests of Octrees PRIORITY:3 END:VEVENT END:VCALENDAR BEGIN:VCALENDAR PRODID:-//Microsoft Corporation//Outlook MIMEDIR//EN VERSION:1.0 BEGIN:VEVENT DTSTART:20121114T180000Z DTEND:20121114T183000Z LOCATION:255-BC DESCRIPTION;ENCODING=QUOTED-PRINTABLE: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=0Ause 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. =0AWe 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. SUMMARY:Parallel Geometric-Algebraic Multigrid on Unstructured Forests of Octrees PRIORITY:3 END:VEVENT END:VCALENDAR