000004879 001__ 4879
000004879 005__ 20141119144601.0
000004879 04107 $$aeng
000004879 046__ $$k2002-06-02
000004879 100__ $$aXiu, Dongbin
000004879 24500 $$aMODELING UNCERTAINTY OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS VIA GENERALIZED POLYNOMIAL CHAOS

000004879 24630 $$n15.$$pProceedings of the 15th ASCE Engineering Mechanics Division Conference
000004879 260__ $$bColumbia University in the City of New York
000004879 506__ $$arestricted
000004879 520__ $$2eng$$aWe present a generalized polynomial chaos algorithm to solve the elliptic boundary value problems suject to stochastic uncertain inputs. In particular we focus on the solution of the Poisson equation with random diffusivity and forcing. The stochastic input and solution are represented spectrally by employing the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener (1938). A Galerkin projection in random space is applied to satisfy the equations in weak form. The resulting set of deterministic equations is solved iteratively by a block Gauss-Seidel technique. Both discrete and continuous stochastic distributions are considered and convergence is demonstrated for model problems. 

000004879 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000004879 653__ $$auncertainty, random diffusion, polynomial chaos

000004879 7112_ $$a15th ASCE Engineering Mechanics Division Conference$$cNew York (US)$$d2002-06-02 / 2002-06-05$$gEM2002
000004879 720__ $$aXiu, Dongbin$$iKarniadakis, George Em
000004879 8560_ $$ffischerc@itam.cas.cz
000004879 8564_ $$s163276$$uhttps://invenio.itam.cas.cz/record/4879/files/479.pdf$$yOriginal version of the author's contribution as presented on CD, .
000004879 962__ $$r4594
000004879 980__ $$aPAPER