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.

Linked References

  1. R. Lohner, “Adaptive remeshing for transient problems,” Computer Methods in Applied Mechanics and Engineering, vol. 75, p. 195, 1989. View at Google Scholar
  2. M. J. Berger and J. Oliger, “Adaptive mesh refinement for shock hydrodynamics,” Journal of Computational Physics, vol. 53, p. 484, 1984. View at Google Scholar
  3. M. J. Berger and P. Collela, “Local adaptive mesh refinement for shock hydrodynamics,” Journal of Computational Physics, vol. 82, p. 64, 1989. View at Google Scholar
  4. M. J. Berger and R. J. LeVeque, “An adaptive Cartesian mesh algorithm for the Euler equations in arbitrary geometries,” AIAA Paper 89-1930-CP, 1989. View at Google Scholar
  5. J. J. Quirk, “An alternative to unstructured grids for computing gas dynamic flows around arbitrary complex two-dimensional bodies,” Computers and Fluids, vol. 23, p. 125, 1994. View at Google Scholar
  6. P. MacNeice, K. M. Olson, C. Mobary, R. DeFainchtein, and C. Packer, “PARAMESH: a parallel adaptive mesh refinement community toolkit,” Computer Physics Communications, vol. 126, p. 330, 2000. View at Google Scholar
  7. M. Parashar, J. C. Browne, C. Edwards, and K. Klimkowsky, “A computational infrastructure for parallel adaptive methods,” in Proceedings of the 4th U.S. Congress on Computational Mechanics: Symposium on Parallel Adaptive Method, San Francisco, Calif, USA, 1997.
  8. C. A. Rendleman, V. E. Beckner, M. Lijewski, W. Y Crutchfield, and J. B. Bell, “Parallelization of structured, hierarchical adaptive mesh refinement algorithms,” Computing and Visualization in Science, vol. 3, p. 147, 2000. View at Google Scholar
  9. A. M. Khokhlov, “Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations,” Journal of Computational Physics, vol. 143, no. 2, pp. 519–543, 1998. View at Publisher · View at Google Scholar
  10. P. Diener, N. Jansen, A. Khokhlov, and I. Novikov, “Adaptive mesh refinement approach to the construction of initial data for black hole collisions,” Classical and Quantum Gravity, vol. 17, p. 435, 2000. View at Publisher · View at Google Scholar
  11. T. Ogawa, T. Ohta, R. Matsumoto, K. Yamashita, and M. Den, “Hydrodynamical simulations using a fully threaded tree,” Progress of Theoretical Physics, vol. 138, p. 654, 2000. View at Google Scholar
  12. S. Popinet, “Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries,” Journal of Computational Physics, vol. 190, p. 572, 2003. View at Publisher · View at Google Scholar
  13. M. J. Aftosmis, M. J. Berger, and G. Adomavicius, “A parallel Cartesian approach for external aerodynamics of vehicles with complex geometry,” in Proceedings of the Thermal and Fluids Analysis Workshop, NASA Marshall Spaceflight Center, Huntsville, Ala, USA, 1999.
  14. P. C. Campbell, K. D. Devine, J. E. Flaherty, L. G. Gervasio, and J. D. Teresco, “Dynamic octree load balancing using space-filling curves,” Tech. Rep. CS-03-01, Williams College Department of Computer Science, 2003. View at Google Scholar
  15. J. K. Lawder and P. J. H. King, “Using state diagrams for Hilbert curve mappings,” International Journal of Computer Mathematics, vol. 78, p. 327, 2001. View at Publisher · View at Google Scholar
  16. J. R. Pilkington and S. B. Baden, “Partitioning with spacefilling curves,” Tech. Rep. CS94-349, CSE, 1994. View at Google Scholar
  17. H. Ji, F.-S. Lien, and E. Yee, “An efficient second-order accurate cut-cell method for solving the variable coefficient Poisson equation with jump conditions on irregular domains,” International Journal of Numerical Methods in Fluids, vol. 52, p. 723, 2006. View at Google Scholar
  18. T. J. Barth and D. C. Jersperson, “The design and application of upwind schemes on unstructured meshes,” AIAA Paper 89-0366, 1989. View at Google Scholar
  19. T. J. Barth, “A 3-D upwind Euler solver for unstructured meshes,” AIAA Paper 91-1548, 1991. View at Google Scholar
  20. J. E. Jones and S. F. McCormick, “Parallel multigrid methods,” in Parallel Numerical Algorithms, D. Keyes, A. Sameh, and V. Venkatakrishnan, Eds., vol. 4, pp. 203–224, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997. View at Google Scholar
  21. J. H. Bramble, J. E. Pasciak, and J. Xu, “Parallel multilevel preconditioners,” Mathematics of Computation, vol. 55, p. 1, 1990. View at Publisher · View at Google Scholar
  22. The Shared Hierarchical Academic Research Computing Network,