Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
International Journal for Multiscale Computational Engineering
Fator do impacto: 1.016 FI de cinco anos: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Imprimir: 1543-1649
ISSN On-line: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i6.10
pages 549-559

Toward a Nonintrusive Stochastic Multiscale Design System for Composite Materials

Wei Wu
Rensselaer Polytechnic Institute
Jacob Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA

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.

Referências

  1. 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

  2. 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

  3. Eldred, M. and Burkardt, J., Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification.

  4. Fish, J. and Yuan, Z., N-scale model reduction theory. DOI: 10.1093/acprof:oso/9780199233854.003.0003

  5. Ganapathysubramanian, B. and Zabaras, N., Sparse grid collocation schemes for stochastic natural convection problems. DOI: 10.1016/j.jcp.2006.12.014

  6. Ganapathysubramanian, B. and Zabaras, N., Modeling multiscale diffusion processes in random heterogeneous media. DOI: 10.1016/j.cma.2008.03.020

  7. Gerstner, T. and Griebel, M., Numerical integration using sparse grids. DOI: 10.1023/A:1019129717644

  8. Ghanem, R. G. and Spanos, P. D., Stochastic Finite Elements—A Spectral Approach.

  9. Griebel, M., Adaptive sparse grid multilevel methods for elliptic PDEs based on finite differences. DOI: 10.1007/BF02684411

  10. 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

  11. Klimke, W. A., Uncertainty Modeling Using Fuzzy Arithmetic and Sparse Grids.

  12. Mathelin, L. and Hussaini, M. Y., A stochastic collocation algorithm for uncertainty analysis.

  13. Oskay, C. and Fish, J., Eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2006.08.015

  14. Shi, J. and Ghanem, R., A stochastic nonlocal model for materials with multiscale behavior. DOI: 10.1615/IntJMultCompEng.v4.i4.70

  15. Smolyak, S. A., Quadrature and integration formulas for tensor products of certain classes of functions.

  16. Walters, R. W., Towards stochastic fluid mechanics via polynomial chaos.

  17. Wu, W., Nonintrusive Stochastic Multsicale Design System.

  18. Xiu, D. and Karniadakis, G. E., The Wiener—Askey polynomial chaos for stochastic differential equations. DOI: 10.1137/S1064827501387826

  19. Xu, X. F., A multiscale stochastic finite element method on elliptic problems involving uncertainties. DOI: 10.1016/j.cma.2007.02.002

  20. Yuan, Z. and Fish, J., Multiple scale Eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2008.12.038


Articles with similar content:

COMPUTING GREEN'S FUNCTIONS FOR FLOW IN HETEROGENEOUS COMPOSITE MEDIA
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 1
David A. Barajas-Solano, Daniel Tartakovsky
A STOCHASTIC COLLOCATION METHOD FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS AND RANDOM INPUTS
International Journal for Uncertainty Quantification, Vol.10, 2020, issue 2
Lijun Yi, Ling Guo
EFFICIENT NUMERICAL METHODS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS THROUGH TRANSFORMATION TO EQUATIONS DRIVEN BY CORRELATED NOISE
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 4
Max Gunzburger, Ju Ming
UNCERTAINTY QUANTIFICATION IN LOW-FREQUENCY DYNAMICS OF COMPLEX BEAM-LIKE STRUCTURES HAVING A HIGH-MODAL DENSITY
International Journal for Uncertainty Quantification, Vol.3, 2013, issue 6
Anas Batou, Christian Soize
VARIABLE-SEPARATION BASED ITERATIVE ENSEMBLE SMOOTHER FOR BAYESIAN INVERSE PROBLEMS IN ANOMALOUS DIFFUSION REACTION MODELS
International Journal for Uncertainty Quantification, Vol.9, 2019, issue 3
Yuming Ba, Na Ou, Lijian Jiang