Multi-Element Stochastic Galerkin Method Based on Edge Detection for Uncertainty Quantification of Discontinuous Responses
Multi-Element Stochastic Galerkin Method Based on Edge Detection for Uncertainty Quantification of Discontinuous Responses
复制标题
基于边缘检测的多元素随机伽辽金方法用于间断响应的不确定性量化
DOI：
10.1115/1.4049200
复制
发表时间：
2020
影响因子：
0.6
通讯作者：
Oyama Akira
中科院分区：
文献类型：
--
作者：
Kawai Shigetaka;Oyama Akira
我们提出了一种新的多元广义多项式混沌（MEgPC）方法，以最大限度地减少现有的MEgPC所需的计算成本，以规避吉布斯现象中存在的随机空间中的不连续性。所提出的方法使用边缘检测来捕获具有最小分解的解的不连续行为。相比之下，现有的MEgPC迭代将随机空间分成两个相等的部分，直到达到足够的分辨率水平。我们利用的事实，即随机Galerkin（SG）方法便于自适应细化的分解在每个时间步的计算过程中所提出的方法。两个测试问题的数值实验证明了所提出的方法的性能。结果表明，所提出的方法是一致的更准确的比传统的方法足够高的多项式阶数与最小的额外计算成本，以捕捉不连续性。
We propose a new multi-element generalized polynomial chaos (MEgPC) method to minimize the computational costs required for the existing MEgPC to circumvent the Gibbs phenomenon in the presence of discontinuities in a random space. The proposed method uses edge detection to capture the discontinuous behavior of a solution with minimal decomposition. In contrast, the existing MEgPC iterates splitting the random space into two equal parts until achieving a sufficient resolution level. We take advantage of the fact that the stochastic Galerkin (SG) methods facilitate adaptive refinement of the decomposition at every time-step during a computation for the proposed method. The numerical experiments for two-test problems demonstrate the performance of the proposed method. The results show that the proposed method is consistently more accurate than conventional methods for sufficiently high polynomial orders with minimal additional computational costs to capture discontinuities.