Special quasirandom structures: A selection approach for stochastic homogenization

被引：15
|
作者：
Le Bris, Claude [1 ,2 ]
Legoll, Frederic [1 ,2 ]
Minvielle, William [1 ,2 ]
机构：
[1] Ecole Ponts, 6 & 8 Ave Blaise Pascal, F-77455 Marne La Vallee 2, France
[2] INRIA, 6 & 8 Ave Blaise Pascal, F-77455 Marne La Vallee 2, France
来源：
MONTE CARLO METHODS AND APPLICATIONS | 2016年 / 22卷 / 01期
关键词：
Stochastic homogenization; elliptic partial differential equations; variance reduction; selection approach;
D O I：
10.1515/mcma-2016-0101
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [23-25], consists in selecting random realizations that best satisfy some statistical properties (such as the volume fraction of each phase in a composite material) usually only obtained asymptotically. We study the approach theoretically in some simplified settings (one-dimensional setting, perturbative setting in higher dimensions), and numerically demonstrate its efficiency in more general cases.
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页码：25 / 54
页数：30
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