Low-constant parallel algorithms for finite element simulations using linear octrees

Hari Sundar, Rahul S. Sampath, Santi S. Adavani, Christos Davatzikos, George Biros

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

Abstract

In this article we propose parallel algorithms for the construction of conforming finite-element discretization on linear octrees. Existing octree-based discretizations scale to billions of elements, but the complexity constants can be high. In our approach we use several techniques to minimize overhead: a novel bottom-up tree-construction and 2:1 balance constraint enforcement; a Golomb-Rice encoding for compression by representing the octree and element connectivity as an Uniquely Decodable Code (UDC); overlapping communication and computation; and byte alignment for cache efficiency. The cost of applying the Laplacian is comparable to that of applying it using a direct indexing regular grid discretization with the same number of elements. Our algorithm has scaled up to four billion octants on 4096 processors on a Cray XT3 at the Pittsburgh Supercomputing Center. The overall tree construction time is under a minute in contrast to previous implementations that required several minutes; the evaluation of the discretization of a variable-coefficient Laplacian takes only a few seconds. (c) 2007 ACM.

Original languageEnglish (US)
Title of host publicationProceedings of the 2007 ACM/IEEE Conference on Supercomputing, SC'07
DOIs
StatePublished - Dec 1 2007
Event2007 ACM/IEEE Conference on Supercomputing, SC'07 - Reno, NV, United States
Duration: Nov 10 2007Nov 16 2007

Publication series

NameProceedings of the 2007 ACM/IEEE Conference on Supercomputing, SC'07

Other

Other2007 ACM/IEEE Conference on Supercomputing, SC'07
CountryUnited States
CityReno, NV
Period11/10/0711/16/07

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Software
  • Electrical and Electronic Engineering

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