Parallel geometric-algebraic multigrid on unstructured forests of octrees

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 hexa-hedral 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.

Original languageEnglish (US)
Title of host publication2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012
DOIs
StatePublished - 2012
Event2012 24th International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012 - Salt Lake City, UT, United States
Duration: Nov 10 2012Nov 16 2012

Other

Other2012 24th International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012
CountryUnited States
CitySalt Lake City, UT
Period11/10/1211/16/12

Fingerprint

Macros
Geometry
Partial differential equations
Scalability
Communication
Costs

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture
  • Software

Cite this

Sundar, H., Biros, G., Burstedde, C., Rudi, J., Ghattas, O., & Stadler, G. (2012). Parallel geometric-algebraic multigrid on unstructured forests of octrees. In 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012 [6468484] https://doi.org/10.1109/SC.2012.91

Parallel geometric-algebraic multigrid on unstructured forests of octrees. / Sundar, Hari; Biros, George; Burstedde, Carsten; Rudi, Johann; Ghattas, Omar; Stadler, Georg.

2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012. 2012. 6468484.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Sundar, H, Biros, G, Burstedde, C, Rudi, J, Ghattas, O & Stadler, G 2012, Parallel geometric-algebraic multigrid on unstructured forests of octrees. in 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012., 6468484, 2012 24th International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012, Salt Lake City, UT, United States, 11/10/12. https://doi.org/10.1109/SC.2012.91
Sundar H, Biros G, Burstedde C, Rudi J, Ghattas O, Stadler G. Parallel geometric-algebraic multigrid on unstructured forests of octrees. In 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012. 2012. 6468484 https://doi.org/10.1109/SC.2012.91
Sundar, Hari ; Biros, George ; Burstedde, Carsten ; Rudi, Johann ; Ghattas, Omar ; Stadler, Georg. / Parallel geometric-algebraic multigrid on unstructured forests of octrees. 2012 International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2012. 2012.
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