Publicou 6 edições por ano
ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352
Indexed in
Toward a Nonintrusive Stochastic Multiscale Design System for Composite Materials
RESUMO
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.
-
Cao, Y., Gillespie, D., and Petzold, L., Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems. DOI: 10.1016/j.jcp.2004.12.014
-
DeVolder, B., Glimm, J., Grove, J. W., Kang, Y., Lee, Y., Pao, K., Sharp, D. H., and Ye, K., Uncertainty quantification for multiscale simulations. DOI: 10.1115/1.1445139
-
Eldred, M. and Burkardt, J., Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification.
-
Fish, J. and Yuan, Z., N-scale model reduction theory. DOI: 10.1093/acprof:oso/9780199233854.003.0003
-
Ganapathysubramanian, B. and Zabaras, N., Sparse grid collocation schemes for stochastic natural convection problems. DOI: 10.1016/j.jcp.2006.12.014
-
Ganapathysubramanian, B. and Zabaras, N., Modeling multiscale diffusion processes in random heterogeneous media. DOI: 10.1016/j.cma.2008.03.020
-
Gerstner, T. and Griebel, M., Numerical integration using sparse grids. DOI: 10.1023/A:1019129717644
-
Ghanem, R. G. and Spanos, P. D., Stochastic Finite Elements—A Spectral Approach.
-
Griebel, M., Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. DOI: 10.1007/BF02684411
-
Iman, R. L. and Conover, W. J., Small sample sensitivity analysis techniques for computer models with an application to risk assessment. DOI: 10.1080/03610928008827996
-
Klimke, W. A., Uncertainty Modeling Using Fuzzy Arithmetic and Sparse Grids.
-
Mathelin, L. and Hussaini, M. Y., A stochastic collocation algorithm for uncertainty analysis.
-
Oskay, C. and Fish, J., Eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2006.08.015
-
Shi, J. and Ghanem, R., A stochastic nonlocal model for materials with multiscale behavior. DOI: 10.1615/IntJMultCompEng.v4.i4.70
-
Smolyak, S. A., Quadrature and integration formulas for tensor products of certain classes of functions.
-
Walters, R. W., Towards stochastic fluid mechanics via polynomial chaos.
-
Wu, W., Nonintrusive Stochastic Multsicale Design System.
-
Xiu, D. and Karniadakis, G. E., The Wiener—Askey polynomial chaos for stochastic differential equations. DOI: 10.1137/S1064827501387826
-
Xu, X. F., A multiscale stochastic finite element method on elliptic problems involving uncertainties. DOI: 10.1016/j.cma.2007.02.002
-
Yuan, Z. and Fish, J., Multiple scale Eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2008.12.038
-
Fish Jacob, Towards a General Purpose Design System for Composites, in Multiscale Simulations and Mechanics of Biological Materials, 2013. Crossref
-
Fish Jacob, Wu Wei, A nonintrusive stochastic multiscale solver, International Journal for Numerical Methods in Engineering, 88, 9, 2011. Crossref
-
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
-
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