Reducing Computational and Memory Cost of Substructuring Technique in Finite Element Models

Document Type : Research

Authors

1 MSc, Department of Civil Engineering, Shahed University, Tehran, Iran

2 Assistant Professor, Civil Engineering Department, Faculty of Engineering, Shahed University, Tehran, Iran.

Abstract

Substructuring in the finite element method is a technique that reduces computational cost and memory usage for analysis of complex structures. The efficiency of this technique depends on the number of substructures in different problems. Some subdivisions increase computational cost, but require little memory usage and vice versa. In the present study, the cost functions of computations and memory usage are extracted in terms of number of subdivisions and optimized mathematically. The results are presented in the form of tables which recommend the proper substructuring for different number of elements. A combined case is also considered which investigates balanced reduction of computational and memory cost for 2D problems. Several numerical examples are analyzed numerically to demonstrate the abilities and efficiency of the proposed computational algorithm for structured and unstructured mesh.
 

Keywords

References

1. Badia, S., Verdugo, F., "Robust and scalable domain decomposition solvers for unfitted finite element methods", Journal of Computational and Applied Mathematics, vol 344, 2018, p. 740-759. [DOI:10.1016/j.cam.2017.09.034]
2. Boo, S.H., Oh M.H., "Automated static condensation method for local analysis of large finite element models", Structural Engineering and Mechanics, vol 61, 2017, p. 481-495. [DOI:10.12989/sem.2017.61.6.807]
3. Farhat, C., "A simple and efficient automatic FEM domain decomposer", Comp. and Struc, vol 28, 1988, p. 579-602. [DOI:10.1016/0045-7949(88)90004-1]
4. Farhat, C., Maman, N., Brown, G.W., "Mesh partitioning for implicit computations via iterative domain decomposition: impact and optimization of the subdomain aspect ratio", Int. J. Num. Meth. Eng., vol 38, 1995, p. 989-1000. [DOI:10.1002/nme.1620380608]
5. Farhat, C., Roux, F.X., "A method of finite element tearing and interconnecting and its parallel solution algorithm", Int. J. Num. Meth. Eng., vol 32, 1991, p. 1205-1227. [DOI:10.1002/nme.1620320604]
6. Fonseka, M.C.M., "A sub-structure condensation technique in finite element analysis for the optimal use of computer memory", Comp. and Struc., vol 49, 1993, p. 537-543. [DOI:10.1016/0045-7949(93)90055-I]
7. Gurujee, C.S., Deshpande, V.L., "An improved method of substructure analysis", Comp. and Struc., vol 8, 1978, p. 147-152. [DOI:10.1016/0045-7949(78)90171-2]
8. Kaveh, A., "Decomposition for Parallel Computing: Graph Theory Methods", Computational Structural Analysis and Finite Element Methods, Springer Int. Pub, 2014. [DOI:10.1007/978-3-319-02964-1_8]
9. Kaveh, A., Roosta, G.R., "Graph-theoretical methods for substructuring, subdomaining and ordering", Int. J. Space Struc., vol 10, 1995, p. 121-132. [DOI:10.1177/026635119501000205]
10. Li, J., Hao, H., "Numerical study of structural progressive collapse using substructure technique", Eng. Struc., vol 52, 2013, p. 101-113. [DOI:10.1016/j.engstruct.2013.02.016]
11.Mehrdoost, Z., Bahrainian, S.S., "A multilevel tabu search algorithm for balanced partitioning of unstructured grids", International Journal for Numerical Methods in Engineering, vol 105, 2016, p. 678-692. [DOI:10.1002/nme.5003]
12. Minka, T. The Lightspeed MATLAB Toolbox, [online] Available: https://github.com/tminka/lightspeed.
13. Njomo, W., Ozay, G., "Sequential analysis coupled with optimized substructure technique modeled on 3D-frame construction process", Eng. Struc., vol 80, 2014, p. 200-210. [DOI:10.1016/j.engstruct.2014.08.049]
14. Noor, A.K., Kamel, H.A., Fulton, R.E., "Substructuring techniques: status and projections", Comp. and Struc., vol 8, 1978, p. 621-632. [DOI:10.1016/0045-7949(78)90100-1]
15. Novikov, A., Piminova, N., Kopysov, S., Sagdeeva, Y., "Layer-by-layer partitioning of finite element meshes for multicore architectures", Communications in Computer and Information Science, vol 687, 2016, p. 106-117. [DOI:10.1007/978-3-319-55669-7_9]
16. Predari, M., Esnard, A., Roman, J., "Comparison of initial partitioning methods for multilevel direct k-way graph partitioning with fixed vertices", Parallel Computing, vol 66, 2017, p. 22-39. [DOI:10.1016/j.parco.2017.05.002]
17. Przemieniecki, J.S., "Matrix Structural Analysis of Substructures", AIAA Journal, vol 1, 1963, p. 138-147. [DOI:10.2514/3.1483]
18. Shen, Y., Yin, X.C., "Dynamic substructure analysis of stress waves generated by impacts on non-uniform rod structures", Mechanism and Machine Theory, vol 74, 2014, p. 154-172. [DOI:10.1016/j.mechmachtheory.2013.12.004]
19. Vanderstraeten, D., Keunings, R., "Optimized partitioning of unstructured finite element meshes", Int. J. Num. Meth. Eng., vol 38, 1995, p. 433-450. [DOI:10.1002/nme.1620380306]
20. Wang, J., Li Q., Zhu, Z., "Mixed substructure synthesis method with physics-impedance-modal parameter", Structural Engineering and Mechanics, vol 8, 1999, p. 505-512. [DOI:10.12989/sem.1999.8.5.505]
21. Yang, Y.S., Hsieh, S.H., Hsieh, T.J., "Improving parallel substructuring efficiency by using a multilevel approach", J. Comp. Civil Eng., vol 26, 2011, p. 457-464. [DOI:10.1061/(ASCE)CP.1943-5487.0000142]
Numerical Methods in Civil Engineering
Volume 2, Issue 3
March 2018
Pages 45-57

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History

  • Receive Date: 06 September 2017
  • Revise Date: 06 January 2018
  • Accept Date: 06 February 2018

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