کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
522576 867836 2010 22 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Multi-element probabilistic collocation method in high dimensions
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Multi-element probabilistic collocation method in high dimensions
چکیده انگلیسی

We combine multi-element polynomial chaos with analysis of variance (ANOVA) functional decomposition to enhance the convergence rate of polynomial chaos in high dimensions and in problems with low stochastic regularity. Specifically, we employ the multi-element probabilistic collocation method MEPCM [1] and so we refer to the new method as MEPCM-A. We investigate the dependence of the convergence of MEPCM-A on two decomposition parameters, the polynomial order μ and the effective dimension ν  , with ν≪Nν≪N, and N   the nominal dimension. Numerical tests for multi-dimensional integration and for stochastic elliptic problems suggest that ν⩾μν⩾μ for monotonic convergence of the method. We also employ MEPCM-A to obtain error bars for the piezometric head at the Hanford nuclear waste site under stochastic hydraulic conductivity conditions. Finally, we compare the cost of MEPCM-A against Monte Carlo in several hundred dimensions, and we find MEPCM-A to be more efficient for up to 600 dimensions for a specific multi-dimensional integration problem involving a discontinuous function.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 229, Issue 5, 1 March 2010, Pages 1536–1557
نویسندگان
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