A Parallel Solution Method for Structural Dynamic Response Analysis

Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


With the continuous improvements of technology in and around multi-core CPU:s and GPU:s there is a strong desire to exploit this technology in its full potential. For structural dynamics problems, the domain decomposition is a very mature technique that is well adapted to parallel computations in multi-core machines as it is almost trivially parallelizable. However, competing alternatives with model reduction without parallel computation has also reached an extremely high level of maturity and are thus highly competitive. In this paper, a domain decomposition method, in a procedure named the split-stitch-spread (S3) procedure, is proposed to do transient analysis of large finite element models in parallel. In the method, the structure splits into model substructures with elastic interfacial substructures coupling them together. Each of them can be sent to different computer cores to do time discretization. The model substructures stitch to each other by using interfacial forces and as a result, the systems’ state sequence will be obtained. The solution can then be spread into the substructures and response quantities can be evaluated in parallel processing. The method is applied to a multi-story building subjected to earthquake loading and the results are compared with mode displacement method as a model reduction method with focus on computational efficiency.


Domain decomposition Parallel substructure Transient analysis Interfacial coupling Elastic interface 


  1. 1.
    Dickens JM, Nakagawa JM, Wittbrodt MJ (1997) A critique of mode acceleration and modal truncation augmentation methods for modal response analysis. Comput Struct 62(6):985–998CrossRefzbMATHGoogle Scholar
  2. 2.
    Rahrovani S, Khorsand Vakilzadeh M, Abrahamsson T (2014) Modal dominancy analysis based on modal contribution to frequency response function -norm. Mech Syst and Signal Processing 48(1–2): 218–231Google Scholar
  3. 3.
    Davis TA (2004) Algorithm 832: UMFPACK V4.3 – an unsymmetric-pattern multifrontal method. ACM Trans Math Softw 30(2):96–199Google Scholar
  4. 4.
    Hochbruck M, Ostermann A (2010) Exponential integrators. Acta Numer 19:209–286CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Yaghoubi V, Abrahamsson T (2014) An efficient simulation method for structures with local nonlinearity. In: Kerschen G (ed) Nonlinear dynamics. Conference proceedings of the society for experimental mechanics series. vol 2. Springer International Publishing, pp 141–149. doi: 10.1007/978-3-319-04522-1_13
  6. 6.
    Yang Y-S, Hsieh S-K, Hsieh T-J (2012) Improving parallel substructuring efficiency by using a multilevel approach. J Comput Civ Eng 26(4):457–464CrossRefzbMATHGoogle Scholar
  7. 7.
    Farhat C, Crivelli L, Roux F-X (1994) A transient FETI methodology for large-scale parallel implicit computations in structural mechanics. Int J Numer Methods Eng 37(11):1945–1975CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Farhat C, Roux F-X (1991) A method of finite element tearing and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng 32(6):1205–1227CrossRefzbMATHGoogle Scholar
  9. 9.
    Gonzales J, Park KC (2012) A simple explicit–implicit finite element tearing and interconnecting transient analysis algorithm. Int J Numer Methods Eng 89(10): 1203–1226Google Scholar
  10. 10.
    Tak M, Park T (2013) High scalable non-overlapping domain decomposition method using a direct method for finite element analysis. Comput Methods Appl Mech Eng 264:108–128CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Tianyun L, Chongbin Z, Qingbin L, Lihong Z (2012) An efficient backward Euler time-integration method for nonlinear dynamic analysis of structures. Comput Struct 1 volumes 06–107: 20–28Google Scholar
  12. 12.
    Felippa CA, Park KC (1979) Direct time integration methods in nonlinear structural dynamics. Comput Methods Appl Mech Eng 17(18): 277–313CrossRefGoogle Scholar
  13. 13.
    Gaurav, Wojtkiewicz SF, Johnson EA (2011) Efficient uncertainty quantification of dynamical systems with local nonlinearities and uncertainties. Probab Eng Mech 26:561–569CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2015

Authors and Affiliations

  1. 1.Department of Applied MechanicsChalmers University of TechnologyGothenburgSweden

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