Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 246491, 24 pages
Research Article

Parallel Adaptive Mesh Refinement Combined with Additive Multigrid for the Efficient Solution of the Poisson Equation

1Waterloo CFD Engineering Consulting Inc., Waterloo, ON, Canada N2T 2N7
2Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1
3Hazard Protection Section, Defence R&D Canada, Suffield, P.O. Box 4000 Stn Main, Medicine Hat, AB, Canada T1A 8K6

Received 6 October 2011; Accepted 9 November 2011

Academic Editors: A.-C. Lee and A. Stathopoulos

Copyright © 2012 Her Majesty the Queen in Right of Canada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Three different speed-up methods (viz., additive multigrid method, adaptive mesh refinement (AMR), and parallelization) have been combined in order to provide a highly efficient parallel solver for the Poisson equation. Rather than using an ordinary tree data structure to organize the information on the adaptive Cartesian mesh, a modified form of the fully threaded tree (FTT) data structure is used. The Hilbert space-filling curve (SFC) approach has been adopted for dynamic grid partitioning (resulting in a partitioning that is near optimal with respect to load balancing on a parallel computational platform). Finally, an additive multigrid method (BPX preconditioner), which itself is parallelizable to a certain extent, has been used to solve the linear equation system arising from the discretization. Our numerical experiments show that the proposed parallel AMR algorithm based on the FTT data structure, Hilbert SFC for grid partitioning, and additive multigrid method is highly efficient.