000004820 001__ 4820
000004820 005__ 20141119144556.0
000004820 04107 $$aeng
000004820 046__ $$k2002-06-02
000004820 100__ $$aJardak, M.
000004820 24500 $$aSPECTRAL STOCHASTIC HOMOGENIZATION

000004820 24630 $$n15.$$pProceedings of the 15th ASCE Engineering Mechanics Division Conference
000004820 260__ $$bColumbia University in the City of New York
000004820 506__ $$arestricted
000004820 520__ $$2eng$$aAn original method of stochastic homogenization is developed and applied to a class of PDEs that is representative of a large number of problems in science and engineering. The starting point is a governing differential equation whose coefficients are modeled as stochastic processes with multi-scale oscillatory components. Even the deterministic versions of these equations present great chal lenges to numerical analysis methodologies, justifying various approaches to homogenization. The difficulty in the present situation is compounded by the explicit stochastic modeling of the variability in the heterogeneous coefficients. The present situation, therefore, corresponds to a situation involving highly heterogeneous materials with stochastic variability. A new system of stochastic differential equations is then obtained with random variables as effective coefficients. These coefficients are obtained through an asymptotic analysis that effectively identifies a macro-scale system as the limit of a micro-scale representative volume (REV) as this volume goes to zero. This resulting system of equations can then be resolved by relying on standard numerical integration schemes. The above methodology is integrated with the polynomial chaos representation of stochastic processes resulting in computationally tractable algorithms for evaluating the homogenized coefficients. These algorithms involve simple quadratures over the REV. An application to a multi-scale stochastic diffusion equation is used to highlight the theory, implementation and features of the proposed methodology. 

000004820 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000004820 653__ $$aRandom media,Stochastic homogenization, Elliptic equation, Polynomial Chaos, Spectral methods

000004820 7112_ $$a15th ASCE Engineering Mechanics Division Conference$$cNew York (US)$$d2002-06-02 / 2002-06-05$$gEM2002
000004820 720__ $$aJardak, M.$$iGhanem, R.G.
000004820 8560_ $$ffischerc@itam.cas.cz
000004820 8564_ $$s647737$$uhttps://invenio.itam.cas.cz/record/4820/files/384.pdf$$yOriginal version of the author's contribution as presented on CD, .
000004820 962__ $$r4594
000004820 980__ $$aPAPER