Paper Info
Title
Ensemble Time-Stepping Algorithm for the Convection-Diffusion Equation with Random Diffusivity.
Abstract
In this paper, we develop two ensemble time-stepping algorithms to solve the convection-diffusion equation with random diffusion coefficients, forcing terms and initial conditions based on the pseudo-spectral stochastic collocation method. The key step of the pseudo-spectral stochastic collocation method is to solve a number of deterministic problems derived from the original stochastic convection-diffusion equation. In general, a common way to solve the set of deterministic problems is by using the backward differentiation formula, which requires us to store the coefficient matrix and right-hand-side vector multiple times, and solve them one by one. However, the proposed algorithm only need to solve a single linear system with one shared coefficient matrix and multiple right-hand-side vectors, reducing both storage required and computational cost of the solution process. The stability and error analysis of the first- and second-order ensemble time-stepping algorithms are provided. Several numerical experiments are presented to confirm the theoretical analyses and verify the feasibility and effectiveness of the proposed method.
Year
DOI
Venue
2019
10.1007/s10915-018-0890-8
J. Sci. Comput.
Keywords
Field
DocType
Ensemble time-stepping algorithm, Convection-diffusion equation, Random diffusivity, Stochastic collocation method, Backward differentiation formula, 60H15, 35R60, 65M12, 65M60
Convection–diffusion equation,Coefficient matrix,Linear system,Mathematical analysis,Algorithm,Forcing (mathematics),Backward differentiation formula,Collocation method,Thermal diffusivity,Mathematics
Journal
Volume
Issue
ISSN
79
2
1573-7691
Citations 
PageRank 
References 
1
0.36
14
Authors
3
Name
Order
Citations
PageRank
Ning Li114548.40
J. Fiordilino251.53
Xinlong Feng313522.33