An adaptive wavelet optimized finite difference B-spline polynomial chaos method for random partial differential equations
作者：
Highlights：
• Wavelet optimized finite difference B-spline polynomial chaos method has been proposed for solving stochastic partial differential equations.
• An adaptive grid has been generated using the linear B-spline gPC for optimizing the numerical solution.
• The method has been tested on three stochastic partial differential equations with uncertain features.
• Mean and standard deviation have been plotted for each test problem along with their grid modifications.
• Also, CPU time taken by the proposed method is compared with the CPU time taken by the finite difference method on a uniform grid.
摘要
•Wavelet optimized finite difference B-spline polynomial chaos method has been proposed for solving stochastic partial differential equations.•An adaptive grid has been generated using the linear B-spline gPC for optimizing the numerical solution.•The method has been tested on three stochastic partial differential equations with uncertain features.•Mean and standard deviation have been plotted for each test problem along with their grid modifications.•Also, CPU time taken by the proposed method is compared with the CPU time taken by the finite difference method on a uniform grid.
论文关键词：Adaptivity,B-spline chaos,Partial differential equations,Uncertainty quantification,Wavelet optimized finite difference method
论文评审过程：Received 1 February 2021, Revised 5 October 2021, Accepted 8 October 2021, Available online 25 October 2021, Version of Record 25 October 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126738
