Efficient rare event simulation for failure problems in random media

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© 2015 Society for Industrial and Applied Mathematics.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.






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Liu, J, J Lu and X Zhou (2015). Efficient rare event simulation for failure problems in random media. SIAM Journal on Scientific Computing, 37(2). pp. A609–A624. 10.1137/140965569 Retrieved from https://hdl.handle.net/10161/14097.

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Jianfeng Lu

Professor of Mathematics

Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.

More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.

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