Skip to main content
SpringerLink
Log in

Partitioning and Dynamic Load Balancing for the Numerical Solution of Partial Differential Equations

  • Conference paper
Numerical Solution of Partial Differential Equations on Parallel Computers

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 51))

Summary

In parallel simulations, partitioning and load-balancing algorithms compute the distribution of application data and work to processors. The effectiveness of this distribution greatly influences the performance of a parallel simulation. Decompositions that balance processor loads while keeping the application’s communication costs low are preferred. Although a wide variety of partitioning and load-balancing algorithms have been developed, their effectiveness depends on the characteristics of the application using them. In this chapter, we review several partitioning algorithms, along with their strengths and weaknesses for various PDE applications. We also discuss current efforts toward improving partitioning algorithms for future applications and architectures.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Adjerid, J. E. Flaherty, P. Moore, and Y. Wang. High-order adaptive methods for parabolic systems. Physica-D, 60:94–111, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  2. S. Aluru and F. Sevilgen. Parallel domain decomposition and load balancing using space-filling curves. In Proc. International Conference on High-Performance Computing, pages 230–235, 1997.

    Google Scholar 

  3. R. E. Bank and M. J. Holst. A new paradigm for parallel adaptive meshing algorithms. SIAM J. Scien. Comput., 22:1411–1443, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  4. K. J. Barker and N. P. Chrisochoides. An evaluation of a framework for the dynamic load balancing of highly adaptive and irregular parallel applications. In Proc. Supercomputing 2003, Phoenix, 2003.

    Google Scholar 

  5. S. T. Barnard. PMRSB: parallel multilevel recursive spectral bisection. In F. Baker and J. Wehmer, editors, Proc. Supercomputing’ 95, San Diego, December 1995.

    Google Scholar 

  6. S. T. Barnard and H. D. Simon. Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. Concurrency: Practice and Experience, 6(2):101–117, 1994.

    Google Scholar 

  7. J. J. Bartholdi and L. K. Platzman. An O(n log n) travelling salesman heuristic based on spacefilling curves. Operation Research Letters, 1(4):121–125, September 1982.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. C. Bauer. Efficient Solution Procedures for Adaptive Finite Element Methods — Applications to Elliptic Problems. PhD thesis, State University of New York at Buffalo, 2002.

    Google Scholar 

  9. M. J. Berger and S. H. Bokhari. A partitioning strategy for nonuniform problems on multiprocessors. IEEE Trans. Computers, 36:570–580, 1987.

    Google Scholar 

  10. M. Berzins. A new metric for dynamic load balancing. Appl. Math. Modelling, 25:141–151, 2000.

    Article  MATH  Google Scholar 

  11. T. Bially. Space-filling curves: their generation and their application to band reduction. IEEE Trans. Inform. Theory, IT-15:658–664, Nov. 1969.

    Article  Google Scholar 

  12. E. Boman, K. Devine, R. Heaphy, B. Hendrickson, M. Heroux, and R. Preis. LDRD report: Parallel repartitioning for optimal solver performance. Technical Report SAND2004-0365, Sandia National Laboratories, Albuquerque, NM, February 2004.

    Google Scholar 

  13. E. Boman, K. Devine, R. Heaphy, B. Hendrickson, W. F. Mitchell, M. S. John, and C. Vaughan. Zoltan: Data-management services for parallel applications. URL: http://www.cs.sandia.gov/Zoltan.

    Google Scholar 

  14. C. L. Bottasso, J. E. Flaherty, C. Özturan, M. S. Shephard, B. K. Szymanski, J. D. Teresco, and L. H. Ziantz. The quality of partitions produced by an iterative load balancer. In B. K. Szymanski and B. Sinharoy, editors, Proc. Third Workshop on Languages, Compilers, and Runtime Systems, pages 265–277, Troy, 1996.

    Google Scholar 

  15. T. Bui and C. Jones. A heuristic for reducing fill in sparse matrix factorization”. In Proc. 6th SIAM Conf. Parallel Processing for Scientific Computing, pages 445–452. SIAM, 1993.

    Google Scholar 

  16. A. Caldwell, A. Kahng, and J. Markov. Design and implementation of move-based heuristics for VLSI partitioning. ACM J. Experimental Algs., 5, 2000.

    Google Scholar 

  17. P. M. Campbell, K. D. Devine, J. E. Flaherty, L. G. Gervasio, and J. D. Teresco. Dynamic octree load balancing using space-filling curves. Technical Report CS-03-01, Williams College Department of Computer Science, 2003.

    Google Scholar 

  18. F. Cao, J. R. Gilbert, and S.-H. Teng. Partitioning meshes with lines and planes. Technical Report CSL-96-01, Xerox PARC, 1996. ftp://parcftp.xerox.com/pub/gilbert/index.html.

    Google Scholar 

  19. U. Catalyurek and C. Aykanat. Decomposing irregularly sparse matrices for parallel matrix-vector multiplications. Lecture Notes in Computer Science, 1117:75–86, 1996.

    Article  MathSciNet  Google Scholar 

  20. U. Catalyurek and C. Aykanat. Hypergraph-partitioning based decomposition for parallel sparse-matrix vector multiplication. IEEE Trans. Parallel Dist. Systems, 10(7):673–693, 1999.

    Article  Google Scholar 

  21. C. Chang, T. Kurc, A. Sussman, U. Catalyurek, and J. Saltz. A hypergraph-based workload partitioning strategy for parallel data aggregation. In Proc. of 11th SIAM Conf. Parallel Processing for Scientific Computing. SIAM, March 2001.

    Google Scholar 

  22. S. Chatterjee, A. R. Lebeck, P. K. Patnala, and M. Thottethodi. Recursive array layouts and fast parallel matrix multiplication. In ACM Symposium on Parallel Algorithms and Architectures, pages 222–231, 1999.

    Google Scholar 

  23. C.-K. Cheng and Y.-C. A. Wei. An improved two-way partitioning algorithm with stable performance. IEEE Trans. Computer Aided Design, 10(12):1502–1511, 1991.

    Article  Google Scholar 

  24. G. Cybenko. Dynamic load balancing for distributed memory multiprocessors. J. Parallel Distrib. Comput., 7:279–301, 1989.

    Article  Google Scholar 

  25. L. Dagum. Automatic partitioning of unstructured grids into connected components. In Proc. Supercomputing Conference 1993, pages 94–101, Los Alamitos, 1993. IEEE, Computer Society Press.

    Google Scholar 

  26. H. L. de Cougny, K. D. Devine, J. E. Flaherty, R. M. Loy, C. Özturan, and M. S. Shephard. Load balancing for the parallel adaptive solution of partial differential equations. Appl. Numer. Math., 16:157–182, 1994.

    Article  MathSciNet  Google Scholar 

  27. K. D. Devine, E. G. Boman, R. T. Heaphy, B. A. Hendrickson, J. D. Teresco, J. Faik, J. E. Flaherty, and L. G. Gervasio. New challenges in dynamic load balancing. Appl. Numer. Math., 52(2–3):133–152, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  28. K. D. Devine and J. E. Flaherty. Parallel adaptive hp-refinement techniques for conservation laws. Appl. Numer. Math., 20:367–386, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  29. K. D. Devine, B. A. Hendrickson, E. Boman, M. St. John, and C. Vaughan. Zoltan: A Dynamic Load Balancing Library for Parallel Applications; User’s Guide. Sandia National Laboratories, Albuquerque, NM, 1999. Tech. Report SAND99-1377. Opensource software distributed at http://www.cs.sandia.gov/Zoltan.

    Google Scholar 

  30. R. Diekmann, D. Meyer, and B. Monien. Parallel decomposition of unstructured femmeshes. In Proc. Parallel Algorithms for Irregularly Structured Problems, pages 199–216. Springer LNCS 980, 1995.

    Google Scholar 

  31. R. Diekmann, B. Monien, and R. Preis. Load balancing strategies for distributed memory machines. In B. Topping, editor, Parallel and Distributed Processing for Computational Mechanics: Systems and Tools, pages 124–157, Edinburgh, 1999. Saxe-Coburg.

    Google Scholar 

  32. R. Diekmann, R. Preis, F. Schlimbach, and C. Walshaw. Shape-optimized mesh partitioning and load balancing for parallel adaptive fem. Parallel Comput., 26(12):1555–1581, 2000.

    Article  MATH  Google Scholar 

  33. H. C. Edwards. A Parallel Infrastructure for Scalable Adaptive Finite Element Methods and its Application to Least Squares C? Collocation. PhD thesis, The University of Texas at Austin, May 1997.

    Google Scholar 

  34. R. Enbody, R. Purdy, and C. Severance. Dynamic load balancing. In Proc. 7th SIAM Conference on Parallel Processing for Scientific Computing, pages 645–646. SIAM, February 1995.

    Google Scholar 

  35. J. Faik, L. G. Gervasio, J. E. Flaherty, J. Chang, J. D. Teresco, E. G. Boman, and K. D. Devine. A model for resource-aware load balancing on heterogeneous clusters. Technical Report CS-04-03, Williams College Department of Computer Science, 2004. Presented at Cluster’ 04.

    Google Scholar 

  36. C. Farhat. A simple and efficient automatic FEM domain decomposer. Computers and Structures, 28(5):579–602, 1988.

    Article  Google Scholar 

  37. C. Farhat, S. Lanteri, and H. D. Simon. TOP/DOMDEC: a software tool for mesh partitioning and parallel processing. Comp. Sys. Engng., 6(1):13–26, 1995.

    Article  Google Scholar 

  38. C. Farhat and M. Lesoinne. Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics. Int. J. Numer. Meth. Engng., 36:745–764, 1993.

    Article  MATH  Google Scholar 

  39. C. M. Fiduccia and R. M. Mattheyses. A linear time heuristic for improving network partitions. In Proc. 19th IEEE Design Automation Conference, pages 175–181. IEEE, 1982.

    Google Scholar 

  40. J. E. Flaherty, M. Dindar, R. M. Loy, M. S. Shephard, B. K. Szymanski, J. D. Teresco, and L. H. Ziantz. An adaptive and parallel framework for partial differential equations. In D. F. Griffiths, D. J. Higham, and G. A. Watson, editors, Numerical Analysis 1997 (Proc. 17th Dundee Biennial Conf.), number 380 in Pitman Research Notes in Mathematics Series, pages 74–90. Addison Wesley Longman, 1998.

    Google Scholar 

  41. J. E. Flaherty, R. M. Loy, C. Özturan, M. S. Shephard, B. K. Szymanski, J. D. Teresco, and L. H. Ziantz. Parallel structures and dynamic load balancing for adaptive finite element computation. Appl. Numer. Math., 26:241–263, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  42. J. E. Flaherty, R. M. Loy, M. S. Shephard, B. K. Szymanski, J. D. Teresco, and L. H. Ziantz. Adaptive local refinement with octree load-balancing for the parallel solution of three-dimensional conservation laws. J. Parallel Distrib. Comput., 47:139–152, 1997.

    Article  Google Scholar 

  43. J. E. Flaherty, R. M. Loy, M. S. Shephard, B. K. Szymanski, J. D. Teresco, and L. H. Ziantz. Predictive load balancing for parallel adaptive finite element computation. In H. R. Arabnia, editor, Proc. PDPTA’ 97, volume I, pages 460–469, 1997.

    Google Scholar 

  44. J. E. Flaherty, R. M. Loy, M. S. Shephard, and J. D. Teresco. Software for the parallel adaptive solution of conservation laws by discontinuous Galerkin methods. In B. Cockburn, G. Karniadakis, and S.-W. Shu, editors, Discontinous Galerkin Methods Theory, Computation and Applications, volume 11 of Lecture Notes in Compuational Science and Engineering, pages 113–124. Springer, 2000.

    Google Scholar 

  45. J. Garbers, H. J. Promel, and A. Steger. Finding clusters in VLSI circuits. In Proc. IEEE Intl. Conf. on Computer Aided Design, pages 520–523, 1990.

    Google Scholar 

  46. M. Garey, D. Johnson, and L. Stockmeyer. Some simplified NP-complete graph problems. Theoretical Computer Science, 1(3):237–267, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  47. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, 1979.

    Google Scholar 

  48. L. Hagen and A. Kahng. Fast spectral methofs for ratio cut partitioning and clustering. In Proc. IEEE Intl. Conf. on Computer Aided Design, pages 10–13, 1991.

    Google Scholar 

  49. L. Hagen and A. Kahng. A new approach to effective circuit clustering. In Proc. IEEE Intl. Conf. on Computer Aided Design, pages 422–427, 1992.

    Google Scholar 

  50. B. Hendrickson. Graph partitioning and parallel solvers: Has the emperor no clothes? In Proc. Irregular’98, volume 1457 of Lecture Notes in Computer Science, pages 218–225. Springer-Verlag, 1998.

    Google Scholar 

  51. B. Hendrickson and K. Devine. Dynamic load balancing in computational mechanics. Comput. Methods Appl. Mech. Engrg., 184(2–4):485–500, 2000.

    Article  MATH  Google Scholar 

  52. B. Hendrickson and T. G. Kolda. Graph partitioning models for parallel computing. Parallel Comput., 26:1519–1534, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  53. B. Hendrickson and R. Leland. The Chaco user’s guide, version 2.0. Technical Report SAND94-2692, Sandia National Laboratories, Albuquerque, 1994. Open-source software distributed at http://www.cs.sandia.gov/~bahendr/chaco.html.

    Google Scholar 

  54. B. Hendrickson and R. Leland. An improved spectral graph partitioning algorithm for mapping parallel computations. SIAM J. Scien. Comput., 16(2):452–469, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  55. B. Hendrickson and R. Leland. A multilevel algorithm for partitioning graphs. In Proc. Supercomputing’ 95, 1995.

    Google Scholar 

  56. G. Horton. A multi-level diffusion method for dynamic load balancing. Parallel Comput., 19:209–218, 1993.

    Article  MATH  Google Scholar 

  57. S.-H. Hsieh, G. H. Paulino, and J. F. Abel. Evaluation of automatic domain partitioning algorithms for parallel finite element analysis. Structural Engineering Report 94-2, School of Civil and Environmental Engineering, Cornell University, Ithaca, 1994.

    Google Scholar 

  58. Y. F. Hu and R. J. Blake. An optimal dynamic load balancing algorithm. Preprint DLP-95-011, Daresbury Laboratory, Warrington, WA4 4AD, UK, 1995.

    Google Scholar 

  59. Y. F. Hu, R. J. Blake, and D. R. Emerson. An optimal migration algorithm for dynamic load balancing. Concurrency: Practice and Experience, 10:467–483, 1998.

    Article  MATH  Google Scholar 

  60. H. V. Jagadish. Linear clustering of objects with multiple attributes. In Proc. ACM SIGMOD, pages 332–342, 1990.

    Google Scholar 

  61. M. T. Jones and P. E. Plassmann. Computational results for parallel unstructured mesh computations. Comp. Sys. Engng., 5(4–6):297–309, 1994.

    Article  Google Scholar 

  62. L. V. Kale and S. Krishnan. CHARM++: A portable concurrent object oriented system based on C++. ACM SIGPLAN notices, 28(10):91–128, 1993.

    Article  Google Scholar 

  63. G. Karypis, R. Aggarwal, V. Kumar, and S. Shekhar. Multilevel hypergraph partitioning: application in VLSI domain. In Proc. 34th conf. Design automation, pages 526–529. ACM, 1997.

    Google Scholar 

  64. G. Karypis and V. Kumar. Metis: Unstructured graph partitioning and sparse matrix ordering system. Tech. Report, University of Minnesota, Department of Computer Science, Minneapolis, MN, 1995. Open-source software distributed at http://www-users.cs.umn.edu/~karypis/metis.

    Google Scholar 

  65. G. Karypis and V. Kumar. Multilevel algorithms for multiconstraint graph paritioning. Technical Report 98-019, Department of Computer Science, University of Minnesota, 1998.

    Google Scholar 

  66. G. Karypis and V. Kumar. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Scien. Comput., 20(1), 1999.

    Google Scholar 

  67. G. Karypis and V. Kumar. Parallel multivelel k-way partitioning scheme for irregular graphs. SIAM Review, 41(2):278–300, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  68. G. Karypis, K. Schloegel, and V. Kumar. ParMetis Parallel Graph Partitioning and Sparse Matrix Ordering Library, Version 3.1. University of Minnesota Department of Computer Science and Engineering, and Army HPC Research Center, Minneapolis, 2003. Open-source software distributed at http://www-users.cs.umn.edu/~karypis/metis.

    Google Scholar 

  69. B. Kernighan and S. Lin. An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal, 29:291–307, 1970.

    Google Scholar 

  70. E. Leiss and H. Reddy. Distributed load balancing: design and performance analysis. W. M. Kuck Research Computation Laboratory, 5:205–270, 1989.

    Google Scholar 

  71. R. M. Loy. Adaptive Local Refinement with Octree Load-Balancing for the Parallel Solution of Three-Dimensional Conservation Laws. PhD thesis, Computer Science Dept., Rensselaer Polytechnic Institute, Troy, 1998.

    Google Scholar 

  72. B. Maerten, D. Roose, A. Basermann, J. Fingberg, and G. Lonsdale. DRAMA: A library for parallel dynamic load balancing of finite element applications. In Proc. Ninth SIAM Conference on Parallel Processing for Scientific Computing, San Antonio, 1999. Library distributed under license agreement from http://www.ccrl-nece.de/~drama/drama.html.

    Google Scholar 

  73. T. Minyard and Y. Kallinderis. Octree partitioning of hybrid grids for parallel adaptive viscous flow simulations. Int. J. Numer. Meth. Fluids, 26:57–78, 1998.

    Article  MATH  Google Scholar 

  74. T. Minyard and Y. Kallinderis. Parallel load balancing for dynamic execution environments. Comput. Methods Appl. Mech. Engrg., 189(4):1295–1309, 2000.

    Article  MATH  Google Scholar 

  75. T. Minyard, Y. Kallinderis, and K. Schulz. Parallel load balancing for dynamic execution environments. In Proc. 34th Aerospace Sciences Meeting and Exhibit, number 96-0295, Reno, 1996.

    Google Scholar 

  76. W. F. Mitchell. Refinement tree based partitioning for adaptive grids. In Proc. Seventh SIAM Conf. on Parallel Processing for Scientific Computing, pages 587–592. SIAM, 1995.

    Google Scholar 

  77. W. F. Mitchell. The full domain partition approach to distributing adaptive grids. Appl. Numer. Math., 26:265–275, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  78. W. F. Mitchell. The refinement-tree partition for parallel solution of partial differential equations. NIST Journal of Research, 103(4):405–414, 1998.

    Google Scholar 

  79. B. Moon, H. V. Jagadish, C. Faloutsos, and J. H. Saltz. Analysis of the clustering properties of the Hilbert spacefilling curve. IEEE Trans. Knowledge and Data Engng., 13(1):124–141, January/February 2001.

    Article  Google Scholar 

  80. G. M. Morton. A computer oriented geodetic data base and a new technique in file sequencing. Technical report, IBM Ltd., March 1966.

    Google Scholar 

  81. J. T. Oden, A. Patra, and Y. Feng. Domain decomposition for adaptive hp finite element methods. In Proc. Seventh Intl. Conf. Domain Decomposition Methods, State College, Pennsylvania, October 1993.

    Google Scholar 

  82. L. Oliker and R. Biswas. PLUM: Parallel load balancing for adaptive unstructured meshes. J. Parallel Distrib. Comput., 51(2):150–177, 1998.

    Article  Google Scholar 

  83. L. Oliker, R. Biswas, and R. C. Strawn. Parallel implementaion of an adaptive scheme for 3D unstructured grids on the SP2. In Proc. 3rd International Workshop on Parallel Algorithms for Irregularly Structured Problems, Santa Barbara, 1996.

    Google Scholar 

  84. J. A. Orenstein. Spatial query processing in an object-oriented database system. In Proc. ACM SIGMOD, pages 326–336, May 1986.

    Google Scholar 

  85. M. Ozdal and C. Aykanat. Hypergraph models and algorithms for data-pattern based clustering. Data Mining and Knowledge Discovery, 9:29–57, 2004.

    Article  MathSciNet  Google Scholar 

  86. C. Özturan. Distributed Environment and Load Balancing for Adaptive Unstructured Meshes. PhD thesis, Computer Science Dept., Rensselaer Polytechnic Institute, Troy, 1995.

    Google Scholar 

  87. M. Parashar and J. C. Browne. On partitioning dynamic adaptive grid hierarchies. In Proc. 29th Annual Hawaii International Conference on System Sciences, volume 1, pages 604–613, Jan. 1996.

    Google Scholar 

  88. M. Parashar, J. C. Browne, C. Edwards, and K. Klimkowski. A common data management infrastructure for adaptive algorithms for PDE solutions. In Proc. SC97, San Jose, CA, 1997.

    Google Scholar 

  89. A. Patra and J. T. Oden. Problem decomposition for adaptive hp finite element methods. Comp. Sys. Engng., 6(2):97–109, 1995.

    Article  Google Scholar 

  90. E. A. Patrick, D. R. Anderson, and F. K. Brechtel. Mapping multidimensional space to one dimension for computer output display. IEEE Trans. Computers, C-17(10):949–953, October 1968.

    Google Scholar 

  91. G. Peano. Sur une courbe, qui remplit toute une aire plane. Mathematische Annalen, 36:157–160, 1890.

    Article  MATH  MathSciNet  Google Scholar 

  92. F. Pellegrini. SCOTCH 3.1 User’s guide. Technical Report 1137-96, LaBRI, Université Bordeaux I, August 1996. Library available at http://www.labri.fr/Perso/~pelegrin/scotch/.

    Google Scholar 

  93. F. Pellegrini and J. Roman. Experimental analysis of the dual recursive bipartitioning algorithm for static mapping. Technical Report 1038-96, Université Bordeaux I, 1996.

    Google Scholar 

  94. J. R. Pilkington and S. B. Baden. Dynamic partitioning of non-uniform structured workloads with spacefilling curves. IEEE Trans. on Parallel and Distributed Systems, 7(3):288–300, 1996.

    Article  Google Scholar 

  95. A. Pinar and B. Hendrickson. Graph partitioning for complex objectives. In Proc. 15th Int’l Parallel and Distributed Processing Symp. (I PDPS), San Francisco, CA, April 2001.

    Google Scholar 

  96. S. Plimpton, S. Attaway, B. Hendrickson, J. Swegle, C. Vaughan, and D. Gardner. Transient dynamics simulations: Parallel algorithms for contact detection and smoothed particle hydrodynamics. J. Parallel Distrib. Comput., 50:104–122, 1998.

    Article  MATH  Google Scholar 

  97. A. Pothen, H. Simon, and K.-P. Liou. Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Mat. Anal. Appl., 11(3):430–452, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  98. R. Preis and R. Diekmann. PARTY–a software library for graph partitioning. In B. Topping, editor, Advances in Computational Mechanics with Parallel and Distributed Processing, pages 63–71. CIVIL-COMP PRESS, 1997. Library distributed under free research and academic license at http://wwwcs.upb.de/fachbereich/AG/monien/RESEARCH/PART/party.html.

    Google Scholar 

  99. H. Sagan. Space-Filling Curves. Springer-Verlag, 1994.

    Google Scholar 

  100. K. Schloegel, G. Karypis, and V. Kumar. Multilevel diffusion schemes for repartitioning of adaptive meshes. J. Parallel Distrib. Comput., 47(2):109–124, 1997.

    Article  Google Scholar 

  101. K. Schloegel, G. Karypis, and V. Kumar. A new algorithm for multi-objective graph partitioning. Tech. Report 99-003, University of Minnesota, Department of Computer Science and Army HPC Center, Minneapolis, 1999.

    Google Scholar 

  102. K. Schloegel, G. Karypis, and V. Kumar. A unified algorithm for load-balancing adaptive scientific simulations. In Proc. Supercomputing, Dallas, 2000.

    Google Scholar 

  103. K. Schloegel, G. Karypis, and V. Kumar. Wavefront diffusion and LMSR: Algorithms for dynamic repartitioning of adaptive meshes. IEEE Trans. Parallel Distrib. Syst., 12(5):451–466, 2001.

    Article  Google Scholar 

  104. K. Schloegel, G. Karypis, and V. Kumar. Parallel static and dynamic multiconstraint graph partitioning. Concurrency and Computation — Practice and Experience, 14(3):219–240, 2002.

    Article  MATH  Google Scholar 

  105. M. S. Shephard, S. Dey, and J. E. Flaherty. A straightforward structure to construct shape functions for variable p-order meshes. Comp. Meth. in Appl. Mech. and Engng., 147:209–233, 1997.

    Article  MATH  Google Scholar 

  106. M._S. Shephard, J. E. Flaherty, H. L. de Cougny, C. Özturan, C. L. Bottasso, and M. W. Beall. Parallel automated adaptive procedures for unstructured meshes. In Parallel Computing in CFD, number R-807, pages 6.1–6.49. Agard, Neuilly-Sur-Seine, 1995.

    Google Scholar 

  107. H. D. Simon. Partitioning of unstructured problems for parallel processing. Comp. Sys. Engng., 2:135–148, 1991.

    Article  Google Scholar 

  108. S. Sinha and M. Parashar. Adaptive system partitioning of AMR applications on heterogeneous clusters. Cluster Computing, 5(4):343–352, October 2002.

    Article  Google Scholar 

  109. A. Sohn and H. Simon. S-HARP: A scalable parallel dynamic partitioner for adaptive mesh-based computations. In Proc. Supercomputing’ 98, Orlando, 1998.

    Google Scholar 

  110. J. Steensland. Vampire homepage. http://user.it.uu.se/~johans/research/vampire/vampire1.html, 2000. Open-source software distributed at http://user.it.uu.se/~johans/research/vampire/download.html.

    Google Scholar 

  111. J. Steensland, S. Chandra, and M. Parashar. An application-centric characterization of domain-based SFC partitioners for parallel SAMR. IEEE Trans. Parallel and Distrib. Syst., 13(12):1275–1289, 2002.

    Article  Google Scholar 

  112. J. Steensland, S. Söderberg, and M. Thuné. A comparison of partitioning schemes for blockwise parallel SAMR algorithms. In Proc. 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia, volume 1947 of Lecture Notes in Computer Science, pages 160–169, London, 2000. Springer-Verlag.

    Google Scholar 

  113. V. E. Taylor and B. Nour-Omid. A study of the factorization fill-in for a parallel implementation of the finite element method. Int. J. Numer. Meth. Engng., 37:3809–3823, 1994.

    Article  MATH  Google Scholar 

  114. J. D. Teresco, J. Faik, and J. E. Flaherty. Hierarchical partitioning and dynamic load balancing for scientific computation. Technical Report CS-04-04, Williams College Department of Computer Science, 2004. To appear in the Proceedings of PARA’04.

    Google Scholar 

  115. J. D. Teresco and L. P. Ungar. A comparison of Zoltan dynamic load balancers for adaptive computation. Technical Report CS-03-02, Williams College Department of Computer Science, 2003. Presented at COMPLAS’ 03.

    Google Scholar 

  116. A. Trifunovic and W. J. Knottenbelt. Towards a parallel disk-based algorithm for multilevel k-way hypergraph partitioning. In Proc. 18th International Parallel and Distributed Processing Symposium (IPDPS’04), page 236b, Santa Fe, 2004.

    Google Scholar 

  117. R. Van Driessche and D. Roose. An improved spectral bisection algorithm and its application to dynamic load balancing. Parallel Comput., 21:29–48, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  118. D. Vanderstraeten, C. Farhat, P. Chen, R. Keunings, and O. Ozone. A retrofit based methodology for the fast generation and optimization of large-scale mesh partitions: beyond the minimum interface size criterion. Comput. Methods Appl. Mech. Engrg., 133:25–45, 1996.

    Article  MATH  Google Scholar 

  119. B. Vastenhouw and R. H. Bisseling. A two-dimensional data distribution method for parallel sparse matrix-vector multiplication. Preprint 1238, Dept. of Mathematics, Utrecht University, May 2002.

    Google Scholar 

  120. C. Walshaw. The Parallel JOSTLE Library User’s Guide, Version 3.0. University of Greenwich, London, UK, 2002. Library distributed under free research and academic license at http://staffweb.cms.gre.ac.uk/~c.walshaw/jostle/.

    Google Scholar 

  121. C. Walshaw and M. Cross. Multilevel Mesh Partitioning for Heterogeneous Communication Networks. Tech. Rep. 00/IM/57, Comp. Math. Sci., Univ. Greenwich, London SE10 9LS, UK, March 2000.

    Google Scholar 

  122. C. Walshaw and M. Cross. Multilevel Mesh Partitioning for Heterogeneous Communication Networks. Future Generation Comput. Syst., 17(5):601–623, 2001. (Originally published as Univ. Greenwich Tech. Rep. 00/IM/57).

    Article  Google Scholar 

  123. C. Walshaw and M. Cross. Dynamic mesh partitioning and load-balancing for parallel computational mechanics codes. In B. H. V. Topping, editor, Computational Mechanics Using High Performance Computing, pages 79–94. Saxe-Coburg Publications, Stirling, 2002. (Invited Chapter, Proc. Parallel & Distributed Computing for Computational Mechanics, Weimar, Germany, 1999).

    Google Scholar 

  124. C. Walshaw, M. Cross, and M. Everett. A localized algorithm for optimizing unstructured mesh partitions. Intl. J. of Supercomputer Applications, 9(4):280–295, 1995.

    Article  Google Scholar 

  125. C. Walshaw, M. Cross, and M. Everett. Parallel dynamic graph-partitioning for unstructured meshes. J. Parallel Distrib. Comput., 47(2):102–108, 1997.

    Article  Google Scholar 

  126. C. Walshaw, M. Cross, and K. McManus. Multiphase mesh partitioning. Appl. Math. Modelling, 25(2):123–140, 2000. (Originally published as Univ. Greenwich Tech. Rep. 99/IM/51).

    Article  MATH  Google Scholar 

  127. M._S. Warren and J. K. Salmon. A parallel hashed oct-tree n-body algorithm. In Proc. Supercomputing’ 93, pages 12–21. IEEE Computer Society, 1993.

    Google Scholar 

  128. J. Watts. A practical approach to dynamic load balancing. Master’s Thesis, October 1995.

    Google Scholar 

  129. J. Watts, M. Rieffel, and S. Taylor. A load balancing technique for multiphase computations. In Proc. High Performance Computing’ 97, pages 15–20. Society for Computer Simulation, 1997.

    Google Scholar 

  130. S. Wheat. A Fine Grained Data Migration Approach to Application Load Balancing on MP MIMD Machines. PhD thesis, University of New Mexico, Department of Computer Science, Albuquerque, 1992.

    Google Scholar 

  131. S. Wheat, K. Devine, and A. MacCabe. Experience with automatic, dynamic load balancing and adaptive finite element computation. In H. El-Rewini and B. Shriver, editors, Proc. 27th Hawaii International Conference on System Sciences, pages 463–472, Kihei, 1994.

    Google Scholar 

  132. M. Willebeek-LeMair and A. Reeves. Strategies for dynamic load balancing on highly parallel computers. IEEE Parallel and Distrib. Sys., 4(9):979–993, 1993.

    Article  Google Scholar 

  133. R. Wolski, N. T. Spring, and J. Hayes. The Network Weather Service: A distributed resource performance forecasting service for metacomputing. Future Generation Comput. Syst., 15(5–6):757–768, October 1999.

    Article  Google Scholar 

  134. C. Xu, F. Lau, and R. Diekmann. Decentralized remapping of data parallel applications in distributed memory multiprocessors. Tech. Rep. tr-rsfb-96-021, Dept. of Computer Science, University of Paderborn, Paderborn, Germany, Sept. 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Williams College, Williamstown, MA, 01267, USA

    James D. Teresco

  2. Discrete Algorithms and Mathematics Department, Sandia National Laboratories, Albuquerque, NM, 87185, USA

    Karen D. Devine

  3. Department of Computer Science, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Joseph E. Flaherty

Authors
  1. James D. Teresco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karen D. Devine
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joseph E. Flaherty
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Simula Research Laboratory, P.O. Box 134, 1325, Lysaker, Fornebu, Norway

    Are Magnus Bruaset  & Aslak Tveito  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Teresco, J.D., Devine, K.D., Flaherty, J.E. (2006). Partitioning and Dynamic Load Balancing for the Numerical Solution of Partial Differential Equations. In: Bruaset, A.M., Tveito, A. (eds) Numerical Solution of Partial Differential Equations on Parallel Computers. Lecture Notes in Computational Science and Engineering, vol 51. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31619-1_2

Download citation

Publish with us

Policies and ethics

Search

Navigation