Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
Analytic regularity and collocation approximation for elliptic PDEs with random domain deformations
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DOI：
10.1016/j.camwa.2016.01.005
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发表时间：
2016-03-01
影响因子：
2.9
通讯作者：
Tempone, Raul F.
中科院分区：
文献类型：
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作者：
Castrillon-Candas, Julio E.;Nobile, Fabio;Tempone, Raul F.
在这项工作中，我们考虑近似给定兴趣量 (QoI) 的统计数据的问题，该问题取决于在由 N 个随机变量参数化的随机域上定义的线性椭圆偏微分方程的解。椭圆问题被重新映射到具有固定确定性域的相应偏微分方程上。我们证明了该解可以分析地扩展到 C-N 中关于随机变量的明确定义的区域。然后使用稀疏网格随机配置方法来计算 QoI 的均值和方差。最后，导出 QoI 均值和方差的收敛率，并将其与数值实验中获得的收敛率进行比较。 (C) 2016 Elsevier Ltd. 保留所有权利。
In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remapped onto a corresponding PDE with a fixed deterministic domain. We show that the solution can be analytically extended to a well defined region in C-N with respect to the random variables. A sparse grid stochastic collocation method is then used to compute the mean and variance of the QoI. Finally, convergence rates for the mean and variance of the QoI are derived and compared to those obtained in numerical experiments. (C) 2016 Elsevier Ltd. All rights reserved.