MODELING UNCERTAINTY OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS VIA GENERALIZED POLYNOMIAL CHAOS

Abstract eng:
We 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.

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