A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition

doi:10.1016/j.jcp.2022.111213

CSpace

	A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition
	Zhao, Yue 1,2,3; Mao, Zhiping 4; Guo, Ling 5; Tang, Yifa 1,2; Karniadakis, George Em 3
	2022-07-15
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	461 页码:17
摘要	Modeling uncertainty propagation in anomalous transport applications leads to formulating stochastic fractional partial differential equations (SFPDEs), which require special algorithms for obtaining satisfactory accuracy at reasonable computational complexity. Here, we consider a stochastic fractional diffusion-reaction equation and combine a Galerkin spectral method based on poly-fractonomials with the modal decomposition of the stochastic fields to formulate effective numerical methods for SFPDEs. Specifically, we employ a generalized Karhunen-Loeve (KL) expansion and proper dynamically-orthogonal/bi-orthogonal (DO/BO) constraints to derive new Galerkin formulations for the mean solution, the time-dependent spatial basis, and the stochastic time-dependent coefficients. In addition, we employ a hybrid approach to tackle the singular limit of DO and BO equations for the case of deterministic initial conditions. The DO and BO formulations are mathematically equivalent but they exhibit computationally complementary properties. In demonstration examples, we investigate the interplay between randomness and non-locality and quantify this interaction for first time. In particular, we apply generalized polynomial chaos (gPC), DO, BO, and hybrid methods (i.e., combining gPC with DO or BO) to linear problems and (combining Quasi Monte Carlo (QMC) method with DO or BO) to nonlinear problems, and we compare our results to reference solutions obtained by well-resolved QMC simulations. We find that the DO and BO methods are both accurate approaches suitable for SFPDEs, with the BO method seemingly more accurate overall. The fractional order alpha affects strongly the accuracy of the solution and hence the required number of modes for multi-dimensional problems with parametric uncertainty. Both the DO and BO methods converge fast with respect to the number of modes, and they are especially effective for nonlinear problems and long-time integration for a modest number of stochastic dimensions. With regards to temporal discretization, the mean of the solution using the backward differentiation formula (BDF3) exhibits very high accuracy. (C)& nbsp;2022 Elsevier Inc. All rights reserved.
关键词	Uncertainty quantification Anomalous transport Quasi Monte Carlo simulation Generalized polynomial chaos Long-time integration Poly-fractonomials
DOI	10.1016/j.jcp.2022.111213
收录类别	SCI
语种	英语
资助项目	CSC
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000793700800001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61337
专题	中国科学院数学与系统科学研究院
通讯作者	Mao, Zhiping; Guo, Ling
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 2.Univ China Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Brown Univ, Div Appl Math, Providence, RI 02912 USA 4.Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China 5.Shanghai Normal Univ, Dept Math, Shanghai, Peoples R China
推荐引用方式 GB/T 7714	Zhao, Yue,Mao, Zhiping,Guo, Ling,et al. A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2022,461:17.
APA	Zhao, Yue,Mao, Zhiping,Guo, Ling,Tang, Yifa,&Karniadakis, George Em.(2022).A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition.JOURNAL OF COMPUTATIONAL PHYSICS,461,17.
MLA	Zhao, Yue,et al."A spectral method for stochastic fractional PDEs using dynamically-orthogonal/bi-orthogonal decomposition".JOURNAL OF COMPUTATIONAL PHYSICS 461(2022):17.