Skip to main content
SpringerLink
Log in

Parallel decomposition of unstructured FEM-meshes

  • Conference paper
  • First Online:
Book cover Parallel Algorithms for Irregularly Structured Problems (IRREGULAR 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 980))

Abstract

We present a massively parallel algorithm for static and dynamic partitioning of unstructured FEM-meshes. The method consists of two parts. First a fast but inaccurate sequential clustering is determined which is used, together with a simple mapping heuristic, to map the mesh initially onto the processors of a massively parallel system. The second part of the method uses a massively parallel algorithm to remap and optimize the mesh decomposition taking several cost functions into account. It first calculates the amount of nodes that have to be migrated between pairs of clusters in order to obtain an optimal load balancing. In a second step, nodes to be migrated are chosen according to cost functions optimizing the amount and necessary communication and other measures which are important for the numerical solution method (like for example the aspect ratio of the resulting domains).

The parallel parts of the method are implemented in C under Parix to run on the Parsytec GCel systems. Results on up to 64 processors are presented and compared to those of other existing methods.

This work was partly supported by the DFG Sonderforschungsbereich 1511 “Massive Parallelität: Algorithmen, Entwurfsmethoden, Anwendungen”, by the Esprit Basic Research Action Nr. 7141 (ALCOM II) and the EC HC&M Project MAP.

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. P. Bastian: Parallel Adaptive Multigrid Methods. Tech. Rep., IWR Heidelberg 1993

    Google Scholar 

  2. G.E. Blelloch, A. Feldmann, O. Ghattas, J.R. Gilbert, G.L. Miller, D.R. O'Hallaron, E.J. Schwabe, J.R. Shewchuk, S.-H. Teng: Automated Parallel Solution of Unstructured PDE problems. CACM, to appear

    Google Scholar 

  3. S.H. Bokhari: On the Mapping Problem. IEEE TOC 30(3), 1981, pp. 207–214

    Google Scholar 

  4. N. Chrisochoides, C.E. Houstis, E.N. Houstis, S.K. Kortesis, J.R. Rice: Automatic Load Balanced Partitioning Strategies for PDE Computations. Proc. of ACM Int. Conf. on Supercomputing, 1989, pp. 99–107

    Google Scholar 

  5. R. Diekmann, R. Lüling, B. Monien, C. Spräner: A parallel local-search Algorithm for the k-Partitioning Problem. Proc. of the 28th Hawaii Int. Conference on System Sciences (HICSS '95), vol. 2, pp. 41–50 http://www.uni-paderborn.de/fachbereich/AG/monien/PERSONAL/diek.html

    Google Scholar 

  6. R. Diekmann, R. Lüling, A. Reinefeld: Distributed Combinatorial Optimization. Proc. of Sofsem'93, Czech Republik 1993, pp. 33–60

    Google Scholar 

  7. R. Diekmann, B. Monien, R. Preis: Using Helpful Sets to Improve Graph Bisections. Tech. Rep. tr-rf-94-008, CS-Dept., Univ. of Paderborn, 1994 To Appear in: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society 1995

    Google Scholar 

  8. C. Farhat: A Simple and Efficient Automatic FEM Domain Decomposer. Computers & Structures, Vol. 28(5), 1988, pp. 579–602

    Google Scholar 

  9. C. Farhat, H.D. Simon: TOP/DOMDEC — a Software Tool for Mesh Partitioning and Parallel Processing. Tech. Rep. RNR-93-011, NASA Ames 1993

    Google Scholar 

  10. T. Feder, D.H. Greene: Optimal Algorithms for Approximate Clustering. ACM Symp. on Theory of Computing (STOC), 1988

    Google Scholar 

  11. N. Floros, J. R. Reeve, J. Clinckemaillie, S. Vlachoutsis, G. Lonsdale: Comparative Efficiencies of Domain Decompositions. Tech. Rep. Univ. of Southampton, 1994

    Google Scholar 

  12. S.W. Hammond: Mapping Unstructured Grid Computations to Massively Parallel Computers. Tech. Rep. No. 92.14, RIACS, NASA Ames, June 1992

    Google Scholar 

  13. B. Hendrickson, R. Leland: The Chaco User's Guide. Technical Report SAND93-2339, Sandia National Laboratories, Nov. 1993

    Google Scholar 

  14. B. Hendrickson, R. Leland: An Improved Spectral Graph Partitioning Algorithm for Mapping Parallel Computations. SIAM J. on Scientific Computing, Vol. 16, No. 2, pp. 452–469, 1995.

    Article  Google Scholar 

  15. M.T. Jones, P.E. Plassmann: Parallel Algorithms for the Adaptive Refinement and Partitioning of Unstructured Meshes. Preprint, Argonne National Laboratory 1994

    Google Scholar 

  16. G. Karypis, V. Kumar: A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. Techn. Rep. 95-035, Dept. of Comp. Science, University of Minnesota, 1995.

    Google Scholar 

  17. H. van Lengen, J. Krome: Automatische Netzeinteilungsalgorithmen zum effektiven Einsatz der parallelen Substrukturtechnik. R. Flieger, R. Grebe (ed.): Parallele Datenverarbeitung aktuell: TAT '94 IOS Press, 1994, S. 327–336 (in German)

    Google Scholar 

  18. O.C. Martin, S.W. Otto: Partitioning of Unstructured Meshes for Load Balancing. Techn. Rep. CSE-94-017, Oregon Grad. Inst. of Science & Technology 1994.

    Google Scholar 

  19. B. Monien, R. Diekmann, R. Feldmann, R. Klasing, R. Lüling, K. Menzel, T. Römke, U.-P. Schroeder: Efficient Use of Parallel & Distributed Systems: From Theory to Practice. To appear in: J. van Leeuwen (ed.) Trends in Computer Science, Springer LNCS 1000, 1995.

    Google Scholar 

  20. C.-W. Ou, S. Ranka: Parallel Remapping Algorithms for Adaptive Problems. Tech. Rep. CRCP-TR94506, Rice University, 1994

    Google Scholar 

  21. A. Pothen, H.D. Simon, K.P. Liu: Partitioning Sparse Matrices with Eigenvectors of Graphs. SIAM J. on Matrix Analysis and Applications 11/3, 1990, pp. 430–452

    Article  Google Scholar 

  22. H.D. Simon: Partitioning of unstructured problems for parallel processing. Comput. Syst. Eng. 2, 1991, pp. 135–148

    Article  Google Scholar 

  23. S. Trewin: PUL-DM Prototype User Guide. Tech. Rep., Edinburgh Parallel Computing Center, 1993

    Google Scholar 

  24. C. Walshaw, M. Berzins: Dynamic Load-balancing for PDE solvers on apative unstructured meshes. Concurrency: Practice and Experience 7(1), 1995, pp. 17–28

    Google Scholar 

  25. C. Walshaw, M. Cross, M.G. Everett: A Parallelisable Algorithm for Optimising Unstructured Mesh Partitions. Math. Res. Rep., Univ. of Greenwich, London, 1995

    Google Scholar 

  26. R.D. Williams: Performance of Dynamic Load Balancing Algorithms for Unstructered Mesh Calculations. Concurrency 3, 1991, pp. 457–481

    Google Scholar 

  27. C. Xu, F. Lau: The Generalized Dimension Exchange Method for Load Balancing in k-ary n-cubes and Variants. J. Par. Distr. Comp. 24(1), 1995, pp. 72–85

    Article  Google Scholar 

  28. C. Xu, B. Monien, R. Lüling, F. Lau: An Analytical Comparison of Nearest Neighbor Algorithms for Load Balancing in Parallel Computers. Proc. of 9th International Parallel Processing Symposium (IPPS '95), 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Paderborn, Germany

    Ralf Diekmann, Derk Meyer & Burkhard Monien

Authors
  1. Ralf Diekmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Derk Meyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Burkhard Monien
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Afonso Ferreira José Rolim

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Diekmann, R., Meyer, D., Monien, B. (1995). Parallel decomposition of unstructured FEM-meshes. In: Ferreira, A., Rolim, J. (eds) Parallel Algorithms for Irregularly Structured Problems. IRREGULAR 1995. Lecture Notes in Computer Science, vol 980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60321-2_17

Download citation

  • DOI: https://doi.org/10.1007/3-540-60321-2_17

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60321-4

  • Online ISBN: 978-3-540-44915-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation