A Parallel Adaptive Multilevel Method Using the Full Domain Partition

William F. Mitchell

Applied and Computational Mathematics Division
Bldg 820 Rm 365
NIST
Gaithersburg, MD 20899-0001


Abstract

Adaptive multilevel methods combine multigrid iteration with adaptive refinement to produce fast O(N) solutions on sequential computers. The efficient use of these methods on parallel computers is currently a research topic. Recently the Full Domain Partition (FUDOP) was introduced to distribute adaptive grids over the processors of a distributed memory architecture such that multigrid maintains optimal convergence rates with only two communication steps per cycle. With FUDOP each processor receives a partition of the grid plus the minimum number of extra grid elements to cover the full domain. When considered level by level, FUDOP can be interpreted as domain decomposition with overlapping subdomains on each level. The Extended Full Domain Partition, FUDOP(k), adds additional grid elements to guarantee k levels of overlap on each multigrid level. In this talk the Extended Full Domain Partition will be defined, a multigrid algorithm using FUDOP(k) will be described, and experimental results will be presented.