کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
559125 | 1451861 | 2016 | 22 صفحه PDF | دانلود رایگان |
• An extension to the multi-element polynomial chaos methodology is offered.
• Two different error criteria for partitioning are proposed.
• These criteria are applied to differential equations and mechanical oscillators.
• Results are compared with original partitioning methodology.
• The proposed criteria are more robust and faster to converge.
This paper presents and compares different methodologies to create an adaptive stochastic space partitioning in polynomial chaos applications which use a multi-element approach. To implement adaptive partitioning, Wan and Karniadakis first developed a criterion based on the relative error in local variance. We propose here two different error criteria: one based on the residual error and the other on the local variance discontinuity created by partitioning. The methods are applied to classical differential equations with long-term integration difficulties, including the Kraichnan–Orszag three-mode problem, and to simple linear and nonlinear mechanical systems whose stochastic dynamic responses are investigated. The efficiency and robustness of the approaches are investigated by comparison with Monte-Carlo simulations. For the different examples considered, they show significantly better convergence characteristics than the original error criterion used.
Journal: Mechanical Systems and Signal Processing - Volumes 66–67, January 2016, Pages 201–222