Computers and Concrete

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An optimized mesh partitioning in FEM based on element search technique

  • Shiralinezhad, V. (Department of Civil Engineering, Shahed University) ;
  • Moslemi, H. (Department of Civil Engineering, Shahed University)
  • Received : 2018.12.06
  • Accepted : 2019.04.09
  • Published : 2019.05.25
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Abstract

The substructuring technique is one of the efficient methods for reducing computational effort and memory usage in the finite element method, especially in large-scale structures. Proper mesh partitioning plays a key role in the efficiency of the technique. In this study, new algorithms are proposed for mesh partitioning based on an element search technique. The computational cost function is optimized by aligning each element of the structure to a proper substructure. The genetic algorithm is employed to minimize the boundary nodes of the substructures. Since the boundary nodes have a vital performance on the mesh partitioning, different strategies are proposed for the few number of substructures and higher number ones. The mesh partitioning is optimized considering both computational and memory requirements. The efficiency and robustness of the proposed algorithms is demonstrated in numerous examples for different size of substructures.

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References

  1. Ansari, S.U., Hussain, M., Mazhar, S., Manzoor, T., Siddiqui, K.J., Abid, M. and Jamal, H. (2017), "Mesh partitioning and efficient equation solving techniques by distributed finite element methods: A survey", Arch. Comput. Meth. Eng., 26(1), 1-16. https://doi.org/10.1007/s11831-017-9227-2.
  2. Badia, S. and Verdugo, F. (2018), "Robust and scalable domain decomposition solvers for unfitted finite element methods", J. Comput. Appl. Math., 344, 740-759. https://doi.org/10.1016/j.cam.2017.09.034.
  3. Bahreininejad, A. and Hesamfar, P. (2006), "Subdomain generation using emergent ant colony optimization", Comput. Struct., 84, 1719-1728. https://doi.org/10.1016/j.compstruc.2006.06.002.
  4. Barnard, S.T., Pothen, A. and Simon, H. (1995), "A spectral algorithm for envelope reduction of sparse matrices", Numer. Lin. Algebra Appl., 2, 317-334. https://doi.org/10.1002/nla.1680020402.
  5. Diekmann, R., Preis, R., Schlimbach, F. and Walshaw, C. (2000), "Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM", Parallel Comput., 2, 1555-1581. https://doi.org/10.1016/S0167-8191(00)00043-0.
  6. Farhat, C. and Lesoinne, M. (1993), "Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics", Int. J. Numer. Meth. Eng., 36, 745-764. https://doi.org/10.1002/nme.1620360503.
  7. Fu, L., Litvinov, S., Hu, X.Y. and Adams, N.A. (2017), "A novel partitioning method for block-structured adaptive meshes", J. Comput. Phys., 341, 447-473. https://doi.org/10.1016/j.jcp.2016.11.016
  8. Garey, M.R. and Johnson, D.S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman W.H. and Company, NY.
  9. Hussain, M., Abid, M., Ahmad, M. and Hussain, F. (2013), "A parallel 2D stabilized finite element method for darcy flow on distributed systems", World Appl. Sci. J., 27, 1119-1125. DOI:10.5829/idosi.wasj.2013.27.09.15177.
  10. Jordi, A., Georgas, N. and Blumberg, A. (2017), "A parallel domain decomposition algorithm for coastal ocean circulation models based on integer linear programming", Ocean Dyn., 67, 639-649. https://doi.org/10.1007/s10236-017-1049-0.
  11. Kaveh, A. and Bondarabady, H.A.R. (2003), "A hybrid graphgenetic method for domain decomposition", Finite Elem. Anal. Des., 39, 1237-1247. https://doi.org/10.1016/S0168-874X(02)00192-0.
  12. Kaveh, A. and Mahdavi, V.R. (2015), "Optimal domain decomposition using Colliding Bodies Optimization and kmedian method", Finite Elem. Anal. Des., 98, 41-49. https://doi.org/10.1016/j.finel.2015.01.010.
  13. Kaveh, A. and Shojaee, S. (2008), "Optimal domain decomposition via p-median methodology using ACO and hybrid ACGA", Finite Elem. Anal. Des., 44, 505-512. https://doi.org/10.1016/j.finel.2008.01.005.
  14. Khan, A.I. and Topping, B.H.V. (1993), "Subdomain generation for parallel finite element analysis", Comput. Syst. Eng., 4, 473-488. https://doi.org/10.1016/0956-0521(93)90015-O.
  15. Korosec, P., Silc, J. and Robic, B. (2004), "Solving the meshpartitioning problem with an ant-colony algorithm", Parallel Comput., 30, 785-801. https://doi.org/10.1016/j.parco.2003.12.016.
  16. Marot, C., Pellerin, J. and Remacle, J.F. (2019), "One machine, one minute, three billion tetrahedra", Int. J. Numer. Meth. Eng., 117, 967-990. https://doi.org/10.1002/nme.5987.
  17. Mehrdoost, Z. and Bahrainian, S.S. (2016), "A multilevel tabu search algorithm for balanced partitioning of unstructured grids", Int. J. Numer. Meth. Eng., 105, 678-692. https://doi.org/10.1002/nme.5003.
  18. Mohan Rao, A.R. (2008), "A mesh partitioning algorithm for generation of shape optimized submeshes using evolutionary computing", Pollack Periodica, 3, 91-103. https://doi.org/10.1556/Pollack.3.2008.3.8.
  19. Mohan Rao, A.R. (2009), "Distributed evolutionary multiobjective mesh-partitioning algorithm for parallel finite element computations", Comput. Struct., 87, 1461-1473. https://doi.org/10.1016/j.compstruc.2009.05.006.
  20. Mohan Rao, A.R. (2009), "Parallel mesh-partitioning algorithms for generating shape optimised partitions using evolutionary computing", Adv. Eng. Softw., 40, 141-157. https://doi.org/10.1016/j.advengsoft.2008.03.017.
  21. Mohan Rao, A.R., Appa Rao, T.V.S.R. and Dattaguru, B. (2002), "Automatic decomposition of unstructured meshes employing genetic algorithms for parallel FEM computationss", Struct. Eng. Mech., 14, 625-647. https://doi.org/10.12989/sem.2002.14.6.625.
  22. Mohan Rao, A.R., Appa Rao, T.V.S.R. and Dattaguru, B. (2004), "Generating optimised partitions for parallel finite element computations employing float-encoded genetic algorithms", Comput. Model. Eng. Sci., 5, 213-234. https://doi.org/10.1007/978-3-319-55669-7_9.
  23. Novikov, A., Piminova, N., Kopysov, S. and Sagdeeva, Y. (2016), "Layer-by-layer partitioning of finite element meshes for multicore architectures", Commun. Comput. Inform. Sci., 687, 106-117. https://doi.org/10.1007/978-3-319-55669-7_9.
  24. Pan, Q. and Zhou, C. (2013), "A finite element sub- partition method for simulating crack extension independent to global mesh", Acta Mechanica Solida Sinica, 34, 13-19.
  25. Pothen, A., Simon, H.D. and Liou, K.P. (1990), "Partitioning sparse matrices with eigenvectors of graphs", SIAM J. Matrix Anal. Appl., 11, 430-452. https://doi.org/10.1137/0611030.
  26. Predari, M., Esnard, A. and Roman, J. (2017), "Comparison of initial partitioning methods for multilevel direct k-way graph partitioning with fixed vertices", Parallel Comput., 66, 22-39. https://doi.org/10.1016/j.parco.2017.05.002.
  27. Przemieniecki, J.S. (1963), "Matrix structural analysis of substructures", AIAA J., 1, 138-147. https://doi.org/10.2514/3.1483.
  28. Simon, H.D. (1991), "Partitioning of unstructured problems for parallel processing", Comput. Syst. Eng., 2, 135-148. https://doi.org/10.1016/0956-0521(91)90014-V.
  29. Stavroulakis, G., Giovanis, D.G., Papadopoulos, V. and Papadrakakis, M. (2017), "A GPU domain decomposition solution for spectral stochastic finite element method", Comput. Meth. Appl. Mech. Eng., 327, 392-410. https://doi.org/10.1016/j.cma.2017.08.042.
  30. Yang, Y.S. and Hsieh, S.H. (2002), "Iterative mesh partitioning optimization for parallel nonlinear dynamic finite element analysis with direct substructuring", Comput. Mech., 28, 456-468. https://doi.org/10.1007/s00466-002-0310-6.
  31. Yui, H. and Nishimura, S. (2018), "A cost effective graph-based partitioning algorithm for a system of linear equations", Int. J. Comput. Sci. Eng., 16, 181-190. https://doi.org/10.1504/IJCSE.2018.090440.