Advertisement

EdgePack: A Parallel Vertex and Node Reordering Package for Optimizing Edge-Based Computations in Unstructured Grids

  • Marcos Martins
  • Renato Elias
  • Alvaro Coutinho
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4395)

Abstract

A new and simple method is proposed to choose the best data configuration in terms of processing phase time according to previous probing of edge-based matrix-vector products for codes using iterative solvers in unstructured grid problems. This method is realized as a suite of routines named EdgePack, acting during both pre-solution and solution phase, based on data locality optimization techniques and variations of matrix-vector product algorithm. Results have been demonstrating the great flexibility and simplicity of this method, which is suitable for distributed memory platforms in which different data configurations can coexist.

Keywords

Unstructured Grid Iterative Solver Edge Connectivity Data Configuration Incompressible Fluid Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Burgess, D.A., Giles, M.B.: Renumbering unstructured grids to improve the performance of codes on hierarchical memory machines. Advances in Engineering Software 28, 189–201 (1997)CrossRefGoogle Scholar
  2. 2.
    Carey, G.F., Swift, S., McLey, R.T.: Maximizing sparse matrix-vector product performance on RISC based MIMD computers. Journal of Parallel and Distributed Computing 37, 146–158 (1996)CrossRefGoogle Scholar
  3. 3.
    Douglas, C.C., et al.: Cache Optimization for Structured and Unstructured Grid Multigrid. Electronic Transactions on Numerical Analysis 10, 21–40 (2000)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Gropp, W.D., et al.: Performance Modeling and Tuning of an Unstructured Mesh CFD Application. In: Proceedings of SC 2000, Dallas, Texas, United States, IEEE Computer Society Press, Los Alamitos (2000)Google Scholar
  5. 5.
    Löhner, R.: Renumbering Strategies for unstructured-grid solvers operating on shared-memory, cache-based parallel machines. Computer Methods in Applied Mechanics and Engineering 163, 95–109 (1998)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Oliker, L., et al.: Evaluation of cache-based superscalar and cacheless vector architectures for scientific computations. In: Proceedings of the 18th Annual International Conference on Supercomputing, Malo, France (2004)Google Scholar
  7. 7.
    Oliker, L., et al.: Parallel Conjugate Gradient: Effects of Ordering Strategies, Programming Paradigms, and Architectural Platforms. IEEE Transactions on Parallel and Distributed Systems 11(9), 931–940 (2000)CrossRefGoogle Scholar
  8. 8.
    Oliker, L., et al.: Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems. In: Rolim, J.D.P. (ed.) IPDPS-WS 2000. LNCS, vol. 1800, pp. 497–503. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Oliker, L., et al.: Effects of Ordering Strategies and Programming Paradigms on Sparse Matrix Computations. SIAM Review 44(3), 373–393 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Pinar, A., Heath, M.T.: Improving Performance of Sparse Matrix-Vector Multiplication, Conference on High Performance Networking and Computing. In: Proceedings of the 1999 ACM/IEEE Conference on Supercomputing (CDROM), Portland, Oregon, United States, IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  11. 11.
    Ribeiro, F.L.B., Coutinho, A.L.G.A.: Comparison between element, edge and compressed storage schemes for iterative solutions in finite element analyses. International Journal for Numerical Methods in Engineering 63(4), 569–588 (2005)CrossRefzbMATHGoogle Scholar
  12. 12.
    Vuduc, R., et al.: Performance Optimizations and Bounds for Sparse Matrix-Vector Multiply. In: Conference on High Performance Networking and Computing, Proceedings of the 2002 ACM/IEEE Conference on Supercomputing, Baltimore, Maryland, pp. 1–35. IEEE Computer Society Press, Los Alamitos (2002)Google Scholar
  13. 13.
    Peraire, J., Peiro, J., Morgan, K.: Multigrid solution of the 3d-compressible Euler equations on unstructured grids. Int. J. Num. Meth. Engrg. 36(6), 1029–1044 (1993)CrossRefzbMATHGoogle Scholar
  14. 14.
    Luo, H., Baum, J.D., Löhner, R.: Edge-based finite element scheme for the Euler equations. AIAA Journal 32(6), 1183–1190 (1994)zbMATHCrossRefGoogle Scholar
  15. 15.
    Coutinho, A.L.G.A., et al.: Edge-based finite element techniques for non-linear solid mechanics problems. Int. J. for Num. Meth. in Engrg. 50(9), 2053–2068 (2001)CrossRefzbMATHGoogle Scholar
  16. 16.
    Catabriga, L., Coutinho, A.L.G.A.: Implicit SUPG solution of Euler equations using edge-based data structures. Computer Methods in Applied Mechanics and Engineering 32, 3477–3490 (2002)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Martins, M.A.D., Alves, J.L.D., Coutinho, A.L.G.A.: Parallel Edged-Based Finite Techniques for Nonlinear Solid Mechanics. In: Palma, J.M.L.M., Dongarra, J.J., Hernández, V. (eds.) VECPAR 2000. LNCS, vol. 1981, pp. 506–518. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Elias, R.N., Martins, M.A.D., Coutinho, A.L.G.A.: Parallel Edge-Based Inexact Newton Solution of Steady Incompressible 3D Navier-Stokes Equations. In: Cunha, J.C., Medeiros, P.D. (eds.) Euro-Par 2005. LNCS, vol. 3648, pp. 1237–1245. Springer, Heidelberg (2005)Google Scholar
  19. 19.
    Coutinho, A.L.G.A., et al.: Performance comparison of data reordering algorithms for sparse matrix-vector multiplication in edge-based unstructured grid computations. Int. J. Num. Meth. Engng, acceptedGoogle Scholar
  20. 20.
    Karypis, G., Kumar, V.: Metis 4.0: Unstructured Graph Partitioning and Sparse Matrix Ordering System. Technical report, Department of Computer Science, University of Minnesota, Minneapolis (1998), http://www.users.cs.umn.edu/~karypis/metis
  21. 21.
    Löhner, R., Galle, M.: Minimization of indirect addressing for edge-based field solvers. Communications in Numerical Methods in Engineering 18, 335–343 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  22. 22.
    Löhner, R.: Some useful renumbering strategies for unstructured grids. International Journal for Numerical Methods in Engineering 36, 3259–3270 (1993)CrossRefzbMATHGoogle Scholar
  23. 23.
    Sydenstricker, R.M., et al.: Edge-Based Interface Elements for Solution of Three-Dimensional Geomechanical Problems. In: Palma, J.M.L.M., et al. (eds.) VECPAR 2002. LNCS, vol. 2565, pp. 53–64. Springer, Heidelberg (2003)Google Scholar
  24. 24.
    Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. In: Proc. ACM Nat. Conf., pp. 157–172. ACM Press, New York (1969)Google Scholar
  25. 25.
    Barth, T.J.: Numerical Aspects of Computing Viscous High Reynolds Number Flows on Unstructured Meshes. In: AIAA, 29th Aerospace Sciences Meeting, AIAA 91-0721, Reno, Nevada, January 7-10, 1991, pp. 91–721 (1991)Google Scholar
  26. 26.
    Löhner, R.: Edges, Stars, Superedges and Chains. Comp. Meth. Appl. Mech. Eng. 111, 255–263 (1994)CrossRefzbMATHGoogle Scholar
  27. 27.
    Kalro, V., Tezduyar, T.E.: Parallel 3D Computation of Unsteady Flows around Circular Cylinders. Parallel Computing 23, 1235–1248 (1997)CrossRefMathSciNetzbMATHGoogle Scholar
  28. 28.
    Williamson, C.H.K.: Defining a Universal and Continuous Strouhal-Reynolds Number Relationship for the Laminar Vortex Shedding of a Circular Cylinder. Phys. Fluids 31, 2742–2744 (1988)CrossRefGoogle Scholar
  29. 29.
    Baranyi, L.: Computation of Unsteady Momentum and Heat Transfer from a Fixed Circular Cylinder in Laminar Flow. Journal of Computational and Applied Mechanics 4(1), 13–25 (2003)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Marcos Martins
    • 1
  • Renato Elias
    • 1
  • Alvaro Coutinho
    • 1
  1. 1.Center for Parallel Computations and Department of Civil Engineering, Federal University of Rio de Janeiro, P. O. Box 68506, RJ 21945-970 – Rio de JaneiroBrazil

Personalised recommendations