Paper Info
Title
Fast Evaluation Of Artificial Boundary Conditions For Advection Diffusion Equations
Abstract
An artificial boundary method is developed for solving the one-dimensional advection diffusion equation in the real line. In order to construct a fully discrete fast numerical algorithm with rigorous error analysis, we start with the two-step backward difference formula for time discretization of the advection diffusion equation in the whole real line. Then, we use the discrete analogue of the Laplace transform to derive a second-order time-stepping scheme in a bounded domain equipped with a discrete artificial boundary condition (ABC). The Galerkin finite element method is used for spatial discretization. To expedite the evaluation of time convolution involved in the discrete ABC, we propose a fast algorithm based on the best rational approximation of square root function in subdomains of the complex plane. An estimate for this best rational approximation enables us to prove optimal-order convergence of the fully discrete numerical scheme (integrating the fast approximation algorithm). Several numerical examples are provided to illustrate the convergence of numerical solutions and the effectiveness of the proposed fast approximation algorithm.
Year
DOI
Venue
2020
10.1137/19M130145X
SIAM JOURNAL ON NUMERICAL ANALYSIS
Keywords
DocType
Volume
artificial boundary method, fast algorithm, advection diffusion equation, rational approximation, error estimates
Journal
58
Issue
ISSN
Citations 
6
0036-1429
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Ting Sun13912.08
Jilu Wang201.35
Chunxiong Zheng300.34