Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs

doi:10.2172/1036255

GSTDTAP > 地球科学

DOI	10.2172/1036255
报告编号	Final Report
来源ID	OSTI ID: 1036255
	Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs
	X. Frank Xu
	2010-03-30
出版年	2010
页数	17
语种	英语
国家	美国
领域	地球科学
英文摘要	Multiscale modeling of stochastic systems, or uncertainty quantization of multiscale modeling is becoming an emerging research frontier, with rapidly growing engineering applications in nanotechnology, biotechnology, advanced materials, and geo-systems, etc. While tremendous efforts have been devoted to either stochastic methods or multiscale methods, little combined work had been done on integration of multiscale and stochastic methods, and there was no method formally available to tackle multiscale problems involving uncertainties. By developing an innovative Multiscale Stochastic Finite Element Method (MSFEM), this research has made a ground-breaking contribution to the emerging field of Multiscale Stochastic Modeling (MSM) (Fig 1). The theory of MSFEM basically decomposes a boundary value problem of random microstructure into a slow scale deterministic problem and a fast scale stochastic one. The slow scale problem corresponds to common engineering modeling practices where fine-scale microstructure is approximated by certain effective constitutive constants, which can be solved by using standard numerical solvers. The fast scale problem evaluates fluctuations of local quantities due to random microstructure, which is important for scale-coupling systems and particularly those involving failure mechanisms. The Green-function-based fast-scale solver developed in this research overcomes the curse-of-dimensionality commonly met in conventional approaches, by proposing a random field-based orthogonal expansion approach. The MSFEM formulated in this project paves the way to deliver the first computational tool/software on uncertainty quantification of multiscale systems. The applications of MSFEM on engineering problems will directly enhance our modeling capability on materials science (composite materials, nanostructures), geophysics (porous media, earthquake), biological systems (biological tissues, bones, protein folding). Continuous development of MSFEM will further contribute to the establishment of Multiscale Stochastic Modeling strategy, and thereby potentially to bring paradigm-shifting changes to simulation and modeling of complex systems cutting across multidisciplinary fields.
英文关键词	Multiscale Stochastic Modeling (MSM) Multiscale Stochastic Finite Element Method (MSFEM)
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来源平台	US Department of Energy (DOE)
引用统计
文献类型	科技报告
条目标识符	http://119.78.100.173/C666/handle/2XK7JSWQ/5010
专题	地球科学
推荐引用方式 GB/T 7714	X. Frank Xu. Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs,2010.