A Parallelisable Algorithm for Partitioning Unstructured Meshes

  • C. Walshaw
  • M. Cross
  • M. Everett
  • S. Johnson


A new method is described for solving the graph-partitioning problem which arises in mapping unstructured mesh calculations to parallel computers. The method, encapsulated in a software tool, JOSTLE, employs a combination of techniques including the Greedy algorithm to give an initial partition together with some powerful optimisation heuristics. A clustering technique is additionally employed to speed up the whole process. The resulting partitioning method is designed to work efficiently in parallel as well as sequentially and can be applied to both static and dynamically refined meshes. Experiments, on graphs with up to a million nodes, indicate that the JOSTLE procedure is up to an order of magnitude faster than existing state-of-the-art techniques such as Multilevel Recursive Spectral Bisection.


Parallel Machine Edge Weight Unstructured Mesh Initial Partition Processor Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. T. Barnard and H. D. Simon. A Fast Multilevel Implementation of Recursive Spectral Bisection for Partitioning Unstructured Problems. Con-currency: Practice and Experience, 6 (2): 101–117, 1994.CrossRefGoogle Scholar
  2. [2]
    D. P. Bertsekas and J. N. Tsitsiklis. Parallel and Distributed Computation: Numerical Methods. Prentice Hall, Englewood Cliffs, NJ, 1989.zbMATHGoogle Scholar
  3. [3]
    G. Cybenko. Dynamic load balancing for distributed memory multiprocessors. J. Par. Dist. Comput., 7: 279–301, 1989.CrossRefGoogle Scholar
  4. [4]
    C. Farhat. A Simple and Efficient Automatic FEM Domain Decomposer. Comp. and Struct., 28: 579–602, 1988.CrossRefGoogle Scholar
  5. [5]
    C. Farhat and H. D. Simon. TOP/DOMDEC — a Software Tool for Mesh Partitioning and Parallel Processing. Tech. Rep. RNR-93–011, NASA Ames, Moffat Field, CA., 1993.Google Scholar
  6. [6]
    C. M. Fiduccia and R. M. Mattheyses. A Linear Time Heuristic for Improving Network Partitions. In Proc. 19th IEEE Design Automation Conf., pages 175–181, IEEE, 1982.Google Scholar
  7. [7]
    B. Hendrickson and R. Leland. Multidimensional Spectral Load Balancing. Tech. Rep. SAND 93–0074, Sandia National Labs, Albuquerque, NM., 1992.Google Scholar
  8. [8]
    B. Hendrickson and R. Leland. A Multilevel Algorithm for Partitioning Graphs. Tech. Rep. SAND 93–1301, Sandia National Labs, Albuquerque, NM., 1993.Google Scholar
  9. [9]
    B. W. Jones. Mapping Unstructured Mesh Codes onto Local Memory Parallel Architectures. PhD thesis, School of Maths., University of Greenwich, London SE18 6PF, UK, 1994.Google Scholar
  10. [10]
    B. W. Kernighan and S. Lin. An Efficient Heuristic for Partitioning Graphs. Bell Systems Tech. J., 49: 291–308, 1970.zbMATHGoogle Scholar
  11. [11]
    S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220: 671–680, 1983.MathSciNetzbMATHCrossRefGoogle Scholar
  12. [12]
    P. Lawrence. Mesh Generation by Domain Bisection. PhD thesis, School of Maths., University of Greenwich, London SE18 6PF, UK, 1994.Google Scholar
  13. [13]
    R. Lohner, R. Ramamurti, and D. Martin. A Parallelizable Load Balancing Algorithm. AIAA-93–0061, 1993.Google Scholar
  14. [14]
    K. McManus, M. Cross, and S. Johnson. Integrated Flow and Stress using an Unstructured Mesh on Distributed Memory Parallel Systems. (submitted for the Proceedings, Parallel Computational Fluid Dynamics ‘84), University of Greenwich, London, SE18 6PF, UK, 1994.Google Scholar
  15. [15]
    J. Savage and M. Wloka. Parallelism in Graph Partitioning. J. Par. Dist. Comput., 13: 257–272, 1991.MathSciNetCrossRefGoogle Scholar
  16. [16]
    N. G. Shivaratri, P. Krueger, and M. Singhal. Load distributing for locally distributed systems. IEEE Comput., 25 (12): 33–44, 1992.CrossRefGoogle Scholar
  17. [17]
    J. Song. A partially asynchronous and iterative algorithm for distributed load balancing. Parallel Comput., 20: 853–868, 1994.MathSciNetCrossRefGoogle Scholar
  18. [18]
    P. R. Suaris and G. Kedem. An Algorithm for Quadrisection and Its Application to Standard Cell Placement. IEEE Trans. Circuits and Systems, 35 (3): 294–303, 1988.CrossRefGoogle Scholar
  19. D. Vanderstraeten and R. Kennings. Optimized Partitioning of Unstructured Finite Element Meshes. CESAME Tech. Rep. 93.32 (accepted by Int. J. Num. Meth. Engng.),1993.Google Scholar
  20. [20]
    C. Walshaw and M. Cross. A Parallelisable Algorithm for Optimising Unstructured Mesh Partitions. (submitted for publication), 1994.Google Scholar
  21. [21]
    C. Walshaw, M. Cross, S. Johnson, and M. Everett. JOSTLE: Partitioning of Unstructured Meshes for Massively Parallel Machines. (submitted for the Proceedings, Parallel CFD’94), 1994.Google Scholar
  22. [22]
    C. Walshaw, M. Cross, S. Johnson, and M. Everett. Mapping Unstructured Meshes to Parallel Machine Topologies. (in preparation ), 1994.Google Scholar
  23. [23]
    C. H. Walshaw and M. Berzins. Dynamic Load-Balancing For PDE Solvers On Adaptive Unstructured Meshes. (accepted by Concurrency: Practice and Experience), 1993.Google Scholar
  24. [24]
    R. D. Williams. Performance of dynamic load balancing algorithms for unstructured mesh calculations. Concurrency: Practice F5 Experience, 3: 457–481, 1991.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • C. Walshaw
    • 1
  • M. Cross
    • 1
  • M. Everett
    • 1
  • S. Johnson
    • 1
  1. 1.School of Mathematics, Statistics & Scientific ComputingUniversity of GreenwichLondonUK

Personalised recommendations