Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain. (5th December 2016)

• Record Type: Journal Article
• Authors: Zhang, Wei; Yang, Jiang; Zhang, Jiwei; Du, Qiang
• Is Part Of: Communications in computational physics. Volume 21:Number 1(2017:Jan.)
• Page Start: 16
• Page End: 39
• Publication Date: 2016-12-05
• Subjects: 45A05, -- 65D99, -- 65R20; Artificial boundary conditions, -- nonlocal models, -- Padé approximation, -- nonlocal heat equations, -- artificial boundary method; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.OA-2016-0033
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: This paper is concerned with numerical approximations of a nonlocal heat equation define on an infinite domain. Two classes of artificial boundary conditions (ABCs) are designed, namely, nonlocal analog Dirichlet-to-Neumann-type ABCs (global in time) and high-order Padé approximate ABCs (local in time). These ABCs reformulate the original problem into an initial-boundary-value (IBV) problem on a bounded domain. For the global ABCs, we adopt a fast evolution to enhance computational efficiency and reduce memory storage. High order fully discrete schemes, both second-order in time and space, are given to discretize two reduced problems. Extensive numerical experiments are carried out to show the accuracy and efficiency of the proposed methods.