Skip to main content
Log in

A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

In this paper, an adaptive boundary element method (BEM) is presented for solving 3-D elasticity problems. The numerical scheme is accelerated by the new version of fast multipole method (FMM) and parallelized on distributed memory architectures. The resulting solver is applied to the study of representative volume element (RVE) for short fiber-reinforced composites with complex inclusion geometry. Numerical examples performed on a 32-processor cluster show that the proposed method is both accurate and efficient, and can solve problems of large size that are challenging to existing state-of-the-art domain methods.

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

Access this article

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

  1. Barnes J., Hut P.: A hierarchical O(N log N)) force calculation algorithm. Nature, 324: 446–449 (1986)

    Google Scholar 

  2. Greengard L., Rokhlin V.: A fast algorithm for particle simulations. J. Comput. Phys., 73: 325–348 (1987)

    Google Scholar 

  3. Carrier J., Greengard L., Rokhlin V.: A fast adaptive multipole algorithm for particle simulations. SIAM J. Sci. Stat. Comput., 9: 669–686 (1988)

    Google Scholar 

  4. Cheng H., Greengard L., Rokhlin V.: A fast adaptive multipole algorithm in three dimensions. J. Comput. Phys., 155: 468–498 (1999)

    Google Scholar 

  5. Nishimura N.: Fast multipole accelerated boundary integral equation methods. Appl. Mech. Rev., 55(4): 299–324 (2002)

    Google Scholar 

  6. Warren M.S., Salmon J.K.: A parallel hashed oct-tree N-body algorithm. In: Proceedings of the 1993 ACM/IEEE Conference on Supercomputing, Portland, Oregon, US, ACM Press, New York, 12–21 (1993)

  7. Leathrum J.F., Board J.A.: The parallel fast multipole algorithm in three dimensions. Technical Report TR92-001, Duke University, Department of Electrical Engineering, 1992

  8. Rankin W.T.: Efficient Parallel Implementations of Multipole Based N-Body Algorithms, [PhD thesis], Duke University, 1999

  9. Grama A., Kumar V., Same A.: Parallel hierarchical solvers and preconditioners for boundary element methods. SIAM J. Sci. Comput., 20: 337–358 (1998)

    Google Scholar 

  10. Mammoli A.A., Ingber M.S.: Parallel multipole BEM simulation of two-dimensional suspension flows. Engineering Analysis with Boundary Elements, 24: 65–73 (2000)

    Google Scholar 

  11. Yuan Y., Banerjee P.: A parallel implementation of a fast multipole-based 3-D capacitance extraction program on distributed memory multicomputers. J. Parallel. Distrib. Comput., 61(12): 1751–1774 (2001)

    Google Scholar 

  12. Nabors K., White J: FASTCAP: A multipole-accelerated 3-D capacitance extraction program. IEEE Trans. Computer Aided Design, 10(11): 1447–1459 (1991)

    Google Scholar 

  13. Fu Y.H., Klimkowski K.J., Rodin G.J., et al: A fast solution method for three-dimensional many-particle problems of linear elasticity. Int. J. Numer. Methods Engng., 42: 1215–1229 (1998)

    Google Scholar 

  14. Liu Y.J., Nishimura N., Otani Y.: A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model. ASME Journal of Applied Mechanics, 72(1): 115–128 (2005)

    Google Scholar 

  15. Snir M., Otto S.W., Huss-Lederman S., Walker D.W., Dongarra J.J., MPI: The Complete Reference, The MIT Press, 1996

  16. Zhu Y.T., Beyerlein I.J.: Bone-shaped short fiber composites – an overview. Materials Science and Engineering, A326: 208–227 (2002)

    Google Scholar 

  17. Wang H.T., Yao Z.H.: Application of a new fast multipole BEM for simulation of 2D elastic solid with large number of inclusions. Acta Mechanica Sinica, 20(6): 613–622 (2004)

    Google Scholar 

  18. Wang H.T., Yao Z.H.: A new fast multipole boundary element method for large scale analysis of mechanical properties in 3D particle-reinforced composites. Computer Modeling in Engineering & Sciences, 7(1): 85–95 (2005)

    Google Scholar 

  19. Sagan H.: Space-Filling Curves. Springer-Verlag, New York, 1994

  20. Ingber M.S., Papathanasiou T.D.: A parallel-supercomputing investigation of the stiffness of aligned, short-fiber-reinforced composites using the boundary element method. International Journal for Numerical Methods in Engineering, 40: 2477–3491 (1997)

    Google Scholar 

  21. Zheng Q.S., Du D.X.: Closed-form interacting solutions for overall elastic moduli of composite materials with multi-phase inclusions. Key Engineering Materials, 145-149: 479–488 (1998)

    Google Scholar 

  22. Chen X., Papathanasiou T.D.: Interface stress distributions in transversely loaded continuous fiber composites: parallel computation in multi-fiber RVEs using the boundary element method. Composites Science and Technology, 64: 1101–1114 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhenhan Yao.

Additional information

The project supported by the National Natural Science Foundation of China (10472051).

The English text was polished by Yunming Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lei, T., Yao, Z., Wang, H. et al. A parallel fast multipole BEM and its applications to large-scale analysis of 3-D fiber-reinforced composites. Acta Mech Mech Sinica 22, 225–232 (2006). https://doi.org/10.1007/s10409-006-0099-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-006-0099-1

Keywords

Navigation