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Efficient rare event simulation for failure problems in random media

Publication ,  Journal Article
Liu, J; Lu, J; Zhou, X
Published in: SIAM Journal on Scientific Computing
January 1, 2015

In this paper we study rare events associated to the solutions of an elliptic partial differential equation with a spatially varying random coefficient. The random coefficient follows the lognormal distribution, which is determined by a Gaussian process. This model is employed to study the failure problem of elastic materials in random media in which the failure is characterized by the criterion that the strain field exceeds a high threshold. We propose an efficient importance sampling scheme to compute the small failure probability in the high threshold limit. The change of measure in our scheme is parametrized by two density functions. The efficiency of the importance sampling scheme is validated by numerical examples.

Duke Scholars

Published In

SIAM Journal on Scientific Computing

DOI

EISSN

1095-7197

ISSN

1064-8275

Publication Date

January 1, 2015

Volume

37

Issue

2

Start / End Page

A609 / A624

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Liu, J., Lu, J., & Zhou, X. (2015). Efficient rare event simulation for failure problems in random media. SIAM Journal on Scientific Computing, 37(2), A609–A624. https://doi.org/10.1137/140965569
Liu, J., J. Lu, and X. Zhou. “Efficient rare event simulation for failure problems in random media.” SIAM Journal on Scientific Computing 37, no. 2 (January 1, 2015): A609–24. https://doi.org/10.1137/140965569.
Liu J, Lu J, Zhou X. Efficient rare event simulation for failure problems in random media. SIAM Journal on Scientific Computing. 2015 Jan 1;37(2):A609–24.
Liu, J., et al. “Efficient rare event simulation for failure problems in random media.” SIAM Journal on Scientific Computing, vol. 37, no. 2, Jan. 2015, pp. A609–24. Scopus, doi:10.1137/140965569.
Liu J, Lu J, Zhou X. Efficient rare event simulation for failure problems in random media. SIAM Journal on Scientific Computing. 2015 Jan 1;37(2):A609–A624.

Published In

SIAM Journal on Scientific Computing

DOI

EISSN

1095-7197

ISSN

1064-8275

Publication Date

January 1, 2015

Volume

37

Issue

2

Start / End Page

A609 / A624

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics