Skip to main content
SpringerLink
Log in

Quality balancing for parallel adaptive FEM

  • Regular Talks
  • Conference paper
  • First Online:
Solving Irregularly Structured Problems in Parallel (IRREGULAR 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1457))

Abstract

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.

This work is partly supported by the DFG-Sonderforschungsbereich 376 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen” and the EC ESPRIT Long Term Research Project 20244 (ALCOM-IT).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R.K. Ahuja, T.L. Magnanti, J.B. Orlin. Network Flows. Prentice Hall, 1993.

    Google Scholar 

  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. 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. J.E. Boillat. Load Balancing and Poisson Equation in a Graph. Concurrency-Practice and Experience 2(4), 289–313, 1990.

    Google Scholar 

  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. 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. 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. N. Chrisochoides et al. Automatic Load Balanced Partitioning Strategies for PDE Computations. ACM Int. Conf. on Supercomputing, 99–107, 1989.

    Google Scholar 

  9. G. Cybenko. Load Balancing for Distributed Memory Multiprocessors. J. of Parallel and Distributed Computing (7), 279–301, 1989.

    Google Scholar 

  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. R. Diekmann, D. Meyer, B. Monien. Parallel Decomposition of Unstructured FEMMeshes. Concurrency-Practice and Experience, 10(1), 53–72, 1998.

    Google Scholar 

  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. R. Diekmann, S. Muthukrishnan, M.V. Nayakkankuppam. Engineering Diffusive Load Balancing Algorithms... IRREGULAR, Springer LNCS 1253,111–122,1997.

    Google Scholar 

  14. R. Diekmann, R. Preis, F. Schlimbach, C. Walshaw. Aspect Ratio for' Mesh Partitioning. Euro-Par'98, Springer LNCS, 1998.

    Google Scholar 

  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. M.R. Garey, D.S. Johnson: Computers and Intractability. W.H. Freeman, 1979.

    Google Scholar 

  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. G. Horton. A multi-level diffusion method... Parallel Computing 19:209–218, 1993.

    Google Scholar 

  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. 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. M.T. Jones, P.E. Plassmann. Parallel Algorithms for Adaptive Mesh Refinement. SIAM J. Scientific Computing, 18, 686–708, 1997.

    Google Scholar 

  22. Jostle Documentation.

    Google Scholar 

  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. PadFEMDocumentation. http://www.uni-paderborn.de/cs/PadFEM/

    Google Scholar 

  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. F. Schlimbach. Load Balancing Heuristics Optimizing Subdomain Aspect Ratios for Adaptive Finite Element Simulations. MS-Thesis, Univ. Paderborn, 1998.

    Google Scholar 

  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. 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. 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. R. Verfürth. A Review of a posteriori Error Estimation and Adaptive MeshRefinement Techniques. John Wiley & Sons, Chichester, 1996.

    Google Scholar 

  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. 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. 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. O.C. Zienkiewicz. The finite element method. McGraw-Hill, 1989.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Paderborn, Fürstenallee 11, D-33102, Paderborn, Germany

    Ralf Diekmann & Frank Schlimbach

  2. School of Computing and Mathematical Sciences, The University of Greenwich, London, UK

    Chris Walshaw

Authors
  1. Ralf Diekmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frank Schlimbach
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chris Walshaw
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alfonso Ferreira José Rolim Horst Simon Shang-Hua Teng

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Diekmann, R., Schlimbach, F., Walshaw, C. (1998). Quality balancing for parallel adaptive FEM. In: Ferreira, A., Rolim, J., Simon, H., Teng, SH. (eds) Solving Irregularly Structured Problems in Parallel. IRREGULAR 1998. Lecture Notes in Computer Science, vol 1457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018537

Download citation

  • DOI: https://doi.org/10.1007/BFb0018537

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64809-3

  • Online ISBN: 978-3-540-68533-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation