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International Journal for Multiscale Computational Engineering

年間 6 号発行

ISSN 印刷: 1543-1649

ISSN オンライン: 1940-4352

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Indexed in

Toward a Nonintrusive Stochastic Multiscale Design System for Composite Materials

巻 8, 発行 6, 2010, pp. 549-559
DOI: 10.1615/IntJMultCompEng.v8.i6.10
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要約

In this paper we study a nonintrusive stochastic collocation method in combination with a reduced-order homogenization method for solving partial differential equations with oscillatory random coefficients. The method consists of the two-scale homogenization in space, eigendeformation-based model reduction, Galerkin approximation of the reduced-order problem in space, and collocation approximation based on a sparse grid in the probability space that naturally leads to a nonintrusive approach. By this approach the solution of the original stochastic partial differential equations is constructed from a set of decoupled deterministic solutions from which statistical information is obtained. Preliminary numerical experiments are conducted to determine the feasibility of the method for solving two-scale problems in heterogeneous media.

参考
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によって引用された
  1. Fish Jacob, Towards a General Purpose Design System for Composites, in Multiscale Simulations and Mechanics of Biological Materials, 2013. Crossref

  2. Fish Jacob, Wu Wei, A nonintrusive stochastic multiscale solver, International Journal for Numerical Methods in Engineering, 88, 9, 2011. Crossref

  3. Wu Yuching, Xiao Jianzhuang, Implementation of the Multiscale Stochastic Finite Element Method on Elliptic PDE Problems, International Journal of Computational Methods, 14, 01, 2017. Crossref

  4. Mehrez Loujaine, Fish Jacob, Aitharaju Venkat, Rodgers Will R., Ghanem Roger, A PCE-based multiscale framework for the characterization of uncertainties in complex systems, Computational Mechanics, 61, 1-2, 2018. Crossref

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