Computing quantities of interest for random domains with second order shape sensitivity analysis
Computing quantities of interest for random domains with second order shape sensitivity analysis
复制标题
使用二阶形状敏感性分析计算随机域的感兴趣量
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
B. Puig
中科院分区：
文献类型：
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作者：
M. Dambrine;H. Harbrecht;B. Puig
我们考虑给定区域的随机扰动。假设这些扰动的特征振幅很小。我们感兴趣的数量的兴趣，这取决于随机域通过边值问题。我们推导出该输出函数分布的一阶矩的渐近展开式。本文提出了一种简单而有效的方法来计算这些展开式的系数，只要随机扰动允许低秩谱表示。通过数值实验，我们将我们的展开式与蒙特-卡罗模拟进行了比较。数学学科分类。60 G35、65 N75、65 N99。
We consider random perturbations of a given domain. The characteristic amplitude of these perturbations is assumed to be small. We are interested in quantities of interest which depend on the random domain through a boundary value problem. We derive asymptotic expansions of the first moments of the distribution of this output function. A simple and efficient method is proposed to compute the coefficients of these expansions provided that the random perturbation admits a low- rank spectral representation. By numerical experiments, we compare our expansions with Monte-Carlo simulations. Mathematics Subject Classification. 60G35, 65N75, 65N99.