Skip to main content

Parallel Performance Model for Vertex Repositioning Algorithms and Application to Mesh Partitioning

  • Chapter
  • First Online:
Book cover 27th International Meshing Roundtable (IMR 2018)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 127))

Included in the following conference series:

Abstract

Many mesh optimization applications are based on vertex repositioning algorithms (VrPA). Since the time required for VrPA programs may be large and there is concurrency in processing mesh elements, parallelism has been used to improve performance. In this paper, we propose a performance model for parallel VrPA algorithms that are implemented on memory-distributed computers. This model is validated on two parallel computers and used in a quantitative analysis of performance scalability, load balancing and synchronization and communication overheads. We show that load imbalance and synchronization between boundary partitions are the major causes of the parallel bottlenecks. In order to diminish load imbalance, a new approach to mesh partitioning is proposed. This strategy reduces the imbalance in mesh element evaluations caused by multilevel k-way partitioning algorithms and consequently, improves the performance of parallel VrPA algorithms.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. K. Barker, N. Chrisochoides, Practical performance model for optimizing dynamic load balancing of adaptive applications, in Proceedings of the 19th IPDPS, 28.a-28.b (2005)

    Google Scholar 

  2. D. Benitez, J.M. Escobar, R. Montenegro, E. Rodriguez, Performance comparison and workload analysis of mesh untangling and smoothing algorithms, in Proceedings of the 27th International Meshing Roundtable (2018)

    Google Scholar 

  3. D. Bozdag, A. Gebremedhin, F. Manne, E. Boman, U. Catalyurek, A framework for scalable greedy coloring on distributed memory parallel computers. J. Parallel Distrib. Comput. 68(4), 515–535 (2008)

    Article  Google Scholar 

  4. M. Brewer, L. Diachin, P. Knupp, T. Leurent, D. Melander, The mesquite mesh quality improvement toolkit, in Proceedings of the 12th International Meshing Roundtable (2003), pp. 239–250

    Google Scholar 

  5. N. Chrisochoides, A survey of parallel mesh generation methods. Technical Report. SC-2005-09. Brown University (2005)

    Google Scholar 

  6. L. Diachin, P. Knupp, T. Munson, S. Shontz, A comparison of inexact Newton and coordinate descent mesh optimization techniques, in Proceedings of the 13th International Meshing Roundtable (2004), pp. 243–254

    Google Scholar 

  7. J.M. Escobar, E. Rodríguez, R. Montenegro, G. Montero, J.M. González-Yuste, Simultaneous untangling and smoothing of tetrahedral meshes. Comput. Methods Appl. Mech. Eng. 192, 2775–2787 (2003)

    Article  Google Scholar 

  8. L. Freitag, M.T. Jones, P.E. Plassmann, A parallel algorithm for mesh smoothing. SIAM J. Sci. Comput. 20(6), 2023–2040 (1999)

    Article  MathSciNet  Google Scholar 

  9. C. Geuzaine, J.F. Remacle, Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79(11), 1309–1331 (2009)

    Article  Google Scholar 

  10. W. Gropp, L.N. Olson, P. Samfass, Modeling MPI communication performance on SMP nodes, in Proceedings of the 23rd European MPI Users Group Meeting (2016)

    Google Scholar 

  11. G. Karypis, METIS (version 5.1.0) – A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-reducing Orderings of Sparse Matrices. University of Minnesota (2013)

    Google Scholar 

  12. P. Knupp, Updating meshes on deforming domains: an application of the target-matrix paradigm. Commun. Numer. Method Eng. 24, 467–476 (2007)

    Article  MathSciNet  Google Scholar 

  13. M. Mathis, D. Kerbyson, A general performance model of structured and unstructured mesh particle transport computations. J. Supercomput. 34, 181–199 (2005)

    Article  Google Scholar 

  14. R. Montenegro, J.M. Cascón, J.M. Escobar, E. Rodríguez, G. Montero, An automatic strategy for adaptive tetrahedral mesh generation. Appl. Numer. Math. 59(9), 2203–2217 (2009)

    Article  MathSciNet  Google Scholar 

  15. T. Panitanarak, S.M. Shontz, A parallel log barrier-based mesh warping algorithm for distributed memory machines. Eng. Comput. 34, 59–76 (2018)

    Article  Google Scholar 

  16. A. Sarje, S. Song, D. Jacobsen, K. Huck, J. Hollingsworth, A. Malony, S. Williams, L. Oliker, Parallel performance optimizations on unstructured mesh-based simulations. Procedia Comput. Sci. 51, 2016–2025 (2015)

    Article  Google Scholar 

  17. S.P. Sastry, S.M. Shontz, A parallel log-barrier method for mesh quality improvement and untangling. Eng. Comput. 30(4), 503–515 (2014)

    Article  Google Scholar 

  18. S.P. Sastry, S.M. Shontz, S.A. Vavasis, A log-barrier method for mesh quality improvement and untangling. Eng. Comput. 30(3), 315–329 (2014)

    Article  Google Scholar 

  19. R.B. Schnabel, Concurrent function evaluations in local and global optimization. CU-CS-345-86. Computer Science Technical Report. 332. University of Colorado, Boulder (1986)

    Google Scholar 

Download references

Acknowledgements

This work has been supported by Spanish Government, “Secretaría de Estado de Universidades e Investigación”, “Ministerio de Economía y Competitividad” and FEDER, grant contract: CTM2014-55014-C3-1-R. Cluster2 (TeideHPC) was provided by the “Instituto Tecnológico y de Energías Renovables, S.A.”. We thank to anonymous reviewers for their valuable comments and suggestions on this manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. Benitez .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Benitez, D., Escobar, J.M., Montenegro, R., Rodriguez, E. (2019). Parallel Performance Model for Vertex Repositioning Algorithms and Application to Mesh Partitioning. In: Roca, X., Loseille, A. (eds) 27th International Meshing Roundtable. IMR 2018. Lecture Notes in Computational Science and Engineering, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-030-13992-6_23

Download citation

Publish with us

Policies and ethics