Skip to main content
SpringerLink
Log in

Parallel hydrodynamic finite element model with an N-Best refining partition scheme

  • Geology
  • Published:
Chinese Journal of Oceanology and Limnology Aims and scope Submit manuscript

Abstract

We enhance a robust parallel finite element model for coasts and estuaries cases with the use of N-Best refinement algorithms, in multilevel partitioning scheme. Graph partitioning is an important step to construct the parallel model, in which computation speed is a big concern. The partitioning strategy includes the division of the research domain into several semi-equal-sized sub-domains, minimizing the sum weight of edges between different sub-domains. Multilevel schemes for graph partitioning are divided into three phases: coarsening, partitioning, and uncoarsening. In the uncoarsening phase, many refinement algorithms have been proposed previously, such as KL, Greedy, and Boundary refinements. In this study, we propose an N-Best refinement algorithm and show its advantages in our case study of Xiamen Bay. Compared with original partitioning algorithm in previous models, the N-Best algorithm can speed up the computation by 1.9 times, and the simulation results are in a good match with the in-situ data.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson E. 1988. Parallel implementation of preconditioned conjugate gradient methods for solving sparse systems of linear equations. Technical Report 805, Centre for Supercomputing Research and Development, University Illinois, Urbana, IL.

    Google Scholar 

  • Aykanat C, Özgüner F, Ercal F, Sadayappan P. 1988. Iterative algorithms for solution of large sparse systems of linear equations on hypercubes. IEEE Transactions on Computers, 37(12): 1 554–1 567.

    Article  Google Scholar 

  • Barnard S T, Simon H D. 1993. A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. In: Sincovec R F, Keyes D E, Leuze M R, Petzold L R, Reed D E eds. Proceedings of the 6th SIAM Conference on Parallel Processing for Scientific Computing. Society for Industrial and Applied Mathematics. Philadelphia, United State. p.711–718.

  • Baños R, Gil C, Ortega J, Montoya F G. 2004. A parallel multilevel metaheuristic for graph partitioning. Journal of Heuristics, 10(3): 315–336.

    Article  Google Scholar 

  • Berger M J, Bokhari S H. 1987. A partitioning strategy for nonuniform problems on multiprocessors. IEEE Transactions on Computers, 36(5): 570–580.

    Article  Google Scholar 

  • Bui T, Jones C. 1993. A heuristic for reducing fill in sparse matrix factorization. Proceedings of the 6th SIAM Conference on Parallel Processing for Scientific Computing. In: Sincovec R F, Keyes D E, Leuze M R, Petzold L R, Reed D E eds. Proceedings of the 6th SIAM Conference on Parallel Processing for Scientific Computing. Society for Industrial and Applied Mathematics. Philadelphia, United State. p. 445–452.

  • Ciarlet J P, Lamour F. 1996. On the validity of a front-oriented approach to partitioning large sparse graphs with a connectivity constraint. Numerical Algorithms, 12: 193–214.

    Article  Google Scholar 

  • Cong J, Smith M L. 1993. A parallel bottom-up clustering algorithm with applications to circuit partitioning in VLSI design. In: Dunlop A E (Chairman). Proceedings of the 30th International Conference on Design Automation. Dallas, Texas, United States. p. 755–760.

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

    Article  Google Scholar 

  • Fiduccia C M, Mattheyses R M. 1982. A linear-time heuristic for improving network partitions. Proceedings of 19th IEEE Design Automation Conference. In: Friendenson R A, Breiland J R, Thompson T J eds. IEEE Press, Piscataway, NJ, USA. p.175–181.

    Google Scholar 

  • Geohring T, Saad Y. 1994. Heuristic algorithms for automatic graph partitioning. Technical report UMSI-94-29, Department of Computer Science, University of Minnesota, Minneapolis.

    Google Scholar 

  • George A, Liu J W. 1981. Computer solution of large sparse positive definite systems. Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  • Hendrickson B, Leland R. 1995a. The Chaco User’s Guide, Version 2.0. Technical Report SAND95-2344, Sandia Natl. Lab., Albuquerque, NM, 87185.

    Google Scholar 

  • Hendrickson B, Leland R. 1995b. An improved spectral graph partitioning algorithm for mapping parallel computations. SIAM Journal of Scientific Computing, 16(2): 452–469.

    Article  Google Scholar 

  • Hendrickson B, Leland R. 1995c. A multilevel algorithm for partitioning graphs. Proceedings of Supercomputing. p. 626–657.

  • Hsieh S H, Paulino G H, Abel J F. 1995. Recursive spectral algorithms for automatic domain partitioning in parallel finite element analysis. Computer Methods in Applied Mechanics and Engineering, 121(1): 137–162.

    Article  Google Scholar 

  • Jiang Y W, Wai O W H, Li Y S. 2003. 3D parallel estuary model for cohesive sediment transport in large tidal flats. Coastal Sediments’ 03, Fifth International Symposium on Coastal Engineering and Science of Coastal Sediment Processes. Florida. ISTP. ISBN: 981-238-422-7.

  • Jiang Y W, Wai O W H. 2005. Drying-wetting approach for 3D finite element sigma coordinate model for estuaries with large tidal flats. Advances in Water Resources, 28(8): 779–792.

    Article  Google Scholar 

  • Jones M T, Plassman P E. 1994. Parallel algorithms for the adaptive refinement and partitioning of unstructured meshes. Proceedings of the Scalable High Performance Computing Conference. p. 478–485.

  • Kamath C, Sameh A H. 1984. The preconditioned conjugate gradient algorithm on a multiprocessor. In: Vichnevetsky R, Stepleman R S eds. Advances in Computer Methods for Partial Differential Equations, New York, IMACS.

    Google Scholar 

  • Karypis G, Kumar V. 1995a. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1): 359–392.

    Article  Google Scholar 

  • Karypis G, Kumar V. 1995b. METIS: Unstructured graph partitioning and sparse matrix ordering system. Technical Report, Department of Computer Science, University of Minnesota.

  • Karypis G, Kumar V. 1996. Parallel multilevel graph partitioning. Proceedings of the 10th International Parallel Processing Symposium. p. 314–319.

  • Karypis G, Kumar V. 1998. A parallel algorithm for multilevel graph partitioning and sparse matrix ordering. Journal of Parallel and Distributed Computing, 48(1): 71–95.

    Article  Google Scholar 

  • Kernighan B W, Lin S. 1970. An efficient heuristic procedure for partitioning graphs. The Bell System Technical Journal, 49(2): 291–308.

    Google Scholar 

  • Kim S K, Chronopoulos A. 1991. A class of Lanczos-like algorithms implemented on parallel computers. Parallel Computing, 17: 763–778.

    Article  Google Scholar 

  • Lu Q M, Wai O W H. 1998. An efficient operator splitting scheme for three-dimensional hydrodynamic computations. International Journal for Numerical Methods in Fluids, 26(7): 771–789.

    Article  Google Scholar 

  • Pellegrini F. 1996. SCOTCH 3.1 User’s Guide. Technical Report 1137-96, LaBRI., University Bordeaux, France.

    Google Scholar 

  • Pothen A, Simon H D, Liou K P. 1990. Partitioning sparse matrices with eigenvectors of graphs. SIAM Journal on Matrix Analysis and Applications, 11(3): 430–452.

    Article  Google Scholar 

  • Pothen A, Simon H D, Wang L. 1992. Towards a fast implementation of spectral nested dissection. In: Werner Robert ed. Proceedings of the 1992 ACM/IEEE Conference on Supercomputing. Minneapolis, Minnesota, United States. p.42–51.

  • Preis R, Diekmann R. 1996. The PARTY Partitioning-Library, User Guide-Version 1.1. Technical Report Tr-rsfb-96-024, University of Paderborn, Paderborn, Germany.

    Google Scholar 

  • Saad Y, Schultz M H. 1985. Parallel implementations of preconditioned conjugate gradient methods. Technical Report, Yale University, Department of Computer Science.

  • Schloegel K, Karypis G, Kumar V. 2001. Wavefront diffusion and LMSR: algorithms for dynamic repartitioning of adaptive meshes. IEEE Transactions on Parallel and Distributed Systems, 12(5): 451–466.

    Article  Google Scholar 

  • Wai O W H, Lu Q M. 2000. An efficient parallel model for coastal transport process simulation. Advances in Water Resources, 23(7): 747–764.

    Article  Google Scholar 

  • Wai O W H, Chen Y, Li Y S. 2004a. A 3-D wave-current driven coastal sediment transport model. Coastal Engineering Journal, 46(4): 385–424.

    Article  Google Scholar 

  • Wai O W H, Wang C H, Li Y S, Li X D. 2004b. The formation mechanisms of turbidity maximum in the Pearl River estuary, China. Marine Pollution Bulletin, 48(5): 441–448.

    Article  Google Scholar 

  • Walshaw C, Cross M, Everett M. 1999. Mesh partitioning and load-balancing for distributed memory parallel systems. In: Topping B H V ed. Proceedings Parallel and Distributed Computing for Computational Mechanics: Systems and Tools, Saxe-Coburg Publications, Edinburgh. p. 110–123.

  • Wang W Q, Zhang Y H, Huang Z Q. 2000. Characteristics of salinity front in Jiulongjiang Estuary Xiamen Harbour. Journal of Oceanography in Taiwan Strait, 19(1): 82–88. (in Chinese with English abstract).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Xiamen University, Xiamen, 361005, China

    Zhenchang Zhang  (张振昌) & Changle Zhou  (周昌乐)

  2. State Key Laboratory of Marine Environmental Science (Xiamen University), Xiamen, 361005, China

    Huasheng Hong  (洪华生) & Yuwu Jiang  (江毓武)

  3. Department of Civil and Structural Engineering, the Hong Kong Polytechnic University, Hong Kong, China

    Onyx Winghong Wai

Authors
  1. Zhenchang Zhang  (张振昌)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huasheng Hong  (洪华生)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Onyx Winghong Wai
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuwu Jiang  (江毓武)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Changle Zhou  (周昌乐)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuwu Jiang  (江毓武).

Additional information

Supported by the National Natural Science Foundation of China (Nos. 40406005, 41076001, 40440420596)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Z., Hong, H., Wai, O.W. et al. Parallel hydrodynamic finite element model with an N-Best refining partition scheme. Chin. J. Ocean. Limnol. 28, 1340–1349 (2010). https://doi.org/10.1007/s00343-010-9937-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00343-010-9937-x

Keyword

Search

Navigation