Solution of a stochastic Darcy equation by polynomial chaos expansion

被引：2

作者：

Shalimova I.A. ^{[1
]}

Sabelfeld K.K. ^{[1
]}

机构：

[1] Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk

来源：

Numerical Analysis and Applications | 2017年 / 10卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

Darcy equation; Karhunen–Loève expansion; Monte Carlo method; polynomial chaos; probabilistic collocation method;

D O I：

10.1134/S1995423917030077

中图分类号：

学科分类号：

摘要：

This paper deals with solving a boundary value problem for the Darcy equation with a random hydraulic conductivity field.We use an approach based on polynomial chaos expansion in a probability space of input data.We use a probabilistic collocation method to calculate the coefficients of the polynomial chaos expansion. The computational complexity of this algorithm is determined by the order of the polynomial chaos expansion and the number of terms in the Karhunen–Loève expansion. We calculate various Eulerian and Lagrangian statistical characteristics of the flow by the conventional Monte Carlo and probabilistic collocation methods. Our calculations show a significant advantage of the probabilistic collocation method over the directMonte Carlo algorithm. © 2017, Pleiades Publishing, Ltd.

引用

页码：259 / 271

页数：12

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