A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data
A Weighted Reduced Basis Method for Elliptic Partial Differential Equations with Random Input Data
复制标题
具有随机输入数据的椭圆偏微分方程的加权减基法
DOI：
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发表时间：
2013
影响因子：
2.9
通讯作者：
G. Rozza
中科院分区：
文献类型：
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作者：
Peng Chen;A. Quarteroni;G. Rozza
在这项工作中，我们提出并分析了一个加权缩减基方法来解决椭圆型偏微分方程（PDE）与随机输入数据。首先将偏微分方程转化为一个依赖于有限个参数的加权参数椭圆问题。在贪婪抽样过程中，通过给样本分配不同的权重，考虑了不同参数值下解的独特重要性。先验收敛性分析进行了建设性逼近的精确解的加权参数。数值算例表明，在单变量和多变量随机问题中，该方法优于缩减基方法和随机配点方法.
In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of parameters. Distinctive importance of the solution at different values of the parameters is taken into account by assigning different weights to the samples in the greedy sampling procedure. A priori convergence analysis is carried out by constructive approximation of the exact solution with respect to the weighted parameters. Numerical examples are provided for the assessment of the advantages of the proposed method over the reduced basis method and the stochastic collocation method in both univariate and multivariate stochastic problems.