Quality balancing for parallel adaptive FEM

  • Ralf Diekmann
  • Frank Schlimbach
  • Chris Walshaw
Regular Talks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1457)


We present a dynamic distributed load balancing algorithm for parallel, adaptive finite element simulations using preconditioned conjugate gradient solvers based on domain-decomposition. The load balancer is designed to maintain good partition aspect ratios. It can calculate a balancing flow using different versions of diffusion and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. We show how to use information from the second step to guide the first. Experimental results using Bramble's preconditioner and comparisons to existing state-ot-the-art load balancers show the benefits of the construction.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R.K. Ahuja, T.L. Magnanti, J.B. Orlin. Network Flows. Prentice Hall, 1993.Google Scholar
  2. 2.
    S. Blazy, W. Borchers, U. Dralle. Parallelization methods for a characteristic's pressure correction scheme. Notes on Numerical Fluid Mechanics, 1995.Google Scholar
  3. 3.
    S. Blazy et al. Parallel Adaptive PCG. In: B.H.V. Topping (ed). Advances in Computational Mechanics... Civil-Comp Press, Edinburgh, 1998.Google Scholar
  4. 4.
    J.E. Boillat. Load Balancing and Poisson Equation in a Graph. Concurrency-Practice and Experience 2(4), 289–313, 1990.Google Scholar
  5. 5.
    J.H. Bramble, J.E. Pasciac, A.H. Schatz. The construction of preconditioners for elliptic problems by substructuring L+IL, Math. Comp., 47+49, 1986+87.Google Scholar
  6. 6.
    T.N. Bui, S. Chaudhuri, F.T. Leighton, M. Sisper. Graph Bisection Algorithms with Good Average Case Behaviour. Combinatorica 7(2), 171–191, 1987.Google Scholar
  7. 7.
    M. Burghardt, L. Laemmer, U. Meissner. Parallel adaptive Mesh Generation. EuroConf. Par. Comp. in Computat. Mech., Civil-Comp Press, Edinburgh, 45–52, 1997.Google Scholar
  8. 8.
    N. Chrisochoides et al. Automatic Load Balanced Partitioning Strategies for PDE Computations. ACM Int. Conf. on Supercomputing, 99–107, 1989.Google Scholar
  9. 9.
    G. Cybenko. Load Balancing for Distributed Memory Multiprocessors. J. of Parallel and Distributed Computing (7), 279–301, 1989.Google Scholar
  10. 10.
    R. Diekmann, A. Frommer, B. Monien. Nearest Neighbor Load Balancing on Graphs. 6th Europ. Symp. on Algorithms (ESA), Springer LNCS, 1998.Google Scholar
  11. 11.
    R. Diekmann, D. Meyer, B. Monien. Parallel Decomposition of Unstructured FEMMeshes. Concurrency-Practice and Experience, 10(1), 53–72, 1998.Google Scholar
  12. 12.
    R. Diekmann, B. Monien, R. Preis. Load Balancing Strategies for Distributed Memory Machines. Techn. Rep. tr-rsfb-96-050, CS-Dept., Univ. of Paderborn, 1997.Google Scholar
  13. 13.
    R. Diekmann, S. Muthukrishnan, M.V. Nayakkankuppam. Engineering Diffusive Load Balancing Algorithms... IRREGULAR, Springer LNCS 1253,111–122,1997.Google Scholar
  14. 14.
    R. Diekmann, R. Preis, F. Schlimbach, C. Walshaw. Aspect Ratio for' Mesh Partitioning. Euro-Par'98, Springer LNCS, 1998.Google Scholar
  15. 15.
    C. Farhat, N. Maman, G. Brown. Mesh Partitioning for Implicit Computations via Iterative Domain Decomposition:... J. Numer. Meth. Engrg., 38:989–1000, 1995.Google Scholar
  16. 16.
    M.R. Garey, D.S. Johnson: Computers and Intractability. W.H. Freeman, 1979.Google Scholar
  17. 17.
    B. Ghosh, S. Muthukrishnan, M.H. Schultz. First and Second Order Diffusive Methods for Rapid, Coarse, Distributed Load Balancing. ACM-SPAA, 72–81, 1996.Google Scholar
  18. 18.
    G. Horton. A multi-level diffusion method... Parallel Computing 19:209–218, 1993.Google Scholar
  19. 19.
    Y.F. Hu, R.J. Blake. An optimal dynmic load balancing algorithm. Techn. Rep. DL-P-95-011, Daresbury Lab., UK, 1995 (to appear in CPE).Google Scholar
  20. 20.
    M.T. Jones, P.E. Plassmann. Parallel Algorithms for the Adaptive Refinement and Partitioning of Unstructured Meshes. Proc. IEEE HPCC, 478–485, 1994.Google Scholar
  21. 21.
    M.T. Jones, P.E. Plassmann. Parallel Algorithms for Adaptive Mesh Refinement. SIAM J. Scientific Computing, 18, 686–708, 1997.Google Scholar
  22. 22.
    Jostle Documentation.Google Scholar
  23. 23.
    L. Oliker, R. Biswas. Efficient Load Balancing and Data Remapping for Adaptive Grid Calculations. Proc. 9th ACM SPAA, 33–42, 1997.Google Scholar
  24. 24.
    PadFEMDocumentation. http://www.uni-paderborn.de/cs/PadFEM/Google Scholar
  25. 25.
    K. Schloegel, G. Karypis, and V. Kumar. Multilevel Diffusion Schemes for Repartitioning of Adaptive Meshes. J. Par. Dist. Comput., 47(2):109–124, 1997.Google Scholar
  26. 26.
    F. Schlimbach. Load Balancing Heuristics Optimizing Subdomain Aspect Ratios for Adaptive Finite Element Simulations. MS-Thesis, Univ. Paderborn, 1998.Google Scholar
  27. 27.
    N. Touheed, P.K. Jimack. Parallel Dynamic Load-Balancing for Adaptive Distributed Memory PDE Solvers. 8th SIAM Conf. Par. Proc. for Sc. Computing, 1997.Google Scholar
  28. 28.
    D. Vanderstraeten, R. Keunings, C. Farhat. Beyond Conventional Mesh Partitioning Algorithms... 6th SIAM Conf. Par. Proc. for Sc. Computing, 611–614, 1995.Google Scholar
  29. 29.
    D. Vanderstraeten, C. Farhat, P.S. Chen, R. Keunings, O. Zone. A Retrofit Based Methodology for the Fast Generation and Optimization of Large-Scale Mesh Partitions:... Comput. Methods Appl. Mech. Engrg., 133:25–45, 1996.Google Scholar
  30. 30.
    R. Verfürth. A Review of a posteriori Error Estimation and Adaptive MeshRefinement Techniques. John Wiley & Sons, Chichester, 1996.Google Scholar
  31. 31.
    C. Walshaw, M. Cross. Mesh Partitioning: A Multilevel Balancing and Refinement Algorithm. Tech. Rep. 98/IM/35, University of Greenwich, London, 1998.Google Scholar
  32. 32.
    C. Walshaw, M. Cross, and M. Everett. A Localised Algorithm for Optimising Unstructured Mesh Partitions. Int. J. Supercomputer Appl., 9(4):280–295, 1995.Google Scholar
  33. 33.
    C. Walshaw, M. Cross, and M. Everett. Parallel Dynamic Graph Partitioning for Adaptive Unstructured Meshes. J. Par. Dist. Comput., 47(2):102–108, 1997.Google Scholar
  34. 34.
    O.C. Zienkiewicz. The finite element method. McGraw-Hill, 1989.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Ralf Diekmann
    • 1
  • Frank Schlimbach
    • 1
  • Chris Walshaw
    • 2
  1. 1.Department of Computer ScienceUniversity of PaderbornPaderbornGermany
  2. 2.School of Computing and Mathematical SciencesThe University of GreenwichLondonUK

Personalised recommendations