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Multiscale Stochastic Finite Element Method on Random Boundary Value Problems

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High Performance Computing and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5938))

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Abstract

In this paper, we present a novel Multiscale Stochastic Finite Element Method (MSFEM) to solve boundary value problems involving random heterogeneous materials. The Green-function-based MSFEM decomposes a boundary value problem into three subproblems at three length scales with each being solved with reduced computational cost. A numerical example is provided to illustrate the MSFEM.

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References

  1. Adams, R.A.: Sobolev spaces. Academic Press, New York (1975)

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  2. Xu, X.F., Chen, X., Shen, L.: A Green-function-based multiscale method for uncertainty quantification of finite body heterogeneous materials. Comput. Struct. (2009) (in press), doi:10.1016/j.compstruc.2009.05.009

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  3. Xu, X.F.: A multiscale stochastic finite element method on elliptic problems involving uncertainties. Comput. Methods Appl. Mech. Engrg. 196, 2723–2736 (2007)

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Interdisciplinary Science, College of Mathematical Science, Capital Normal University, Beijing, 100048, China

    Lihua Shen

  2. Department of Civil, Environmental, and Ocean Engineering, Stevens Institute of Technology, Hoboken, NJ, 07037, USA

    X. Frank Xu

Authors
  1. Lihua Shen
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  2. X. Frank Xu
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Editor information

Editors and Affiliations

  1. School of Computer Engineering and Science, Shanghai University, 200072, Shanghai, P.R. China

    Wu Zhang  & Weiqin Tong  & 

  2. Schulich School of Engineering, University of Calgary, T2N 1N4, Calgary, AB, Canada

    Zhangxin Chen

  3. Department of Mathematics, University of Wyoming, 1000 University Avenue, 82071-3036, Laramie, WY, USA

    Craig C. Douglas

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© 2010 Springer-Verlag Berlin Heidelberg

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Shen, L., Xu, X.F. (2010). Multiscale Stochastic Finite Element Method on Random Boundary Value Problems. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (eds) High Performance Computing and Applications. Lecture Notes in Computer Science, vol 5938. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11842-5_49

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  • DOI: https://doi.org/10.1007/978-3-642-11842-5_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11841-8

  • Online ISBN: 978-3-642-11842-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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