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Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos

机译:通过广义多项式混沌建模稳态扩散问题中的不确定性

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We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs. In particular, we focus on the solution of the Poisson equation with random diffusivity, forcing and boundary conditions. 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 [Amer. J. Math. 60 (1938) 897]. A Galerkin projection in random space is applied to derive the equation in the weak form.
机译:我们提出了一种基于不确定输入的随机椭圆型偏微分方程的广义多项式混沌算法。特别地,我们集中于泊松方程在随机扩散率,强迫和边界条件下的解。随机输入和解通过使用Askey方案中的正交多项式函数来频谱表示,作为对Wiener [Amer。最初的多项式混沌思想的概括。 J.数学60(1938)897]。应用随机空间中的Galerkin投影来推导弱形式的方程。

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