Volume 21, Issue 1
Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

Wei Zhang ,  Jiang Yang ,  Jiwei Zhang and Qiang Du

10.4208/cicp.OA-2016-0033

Commun. Comput. Phys., 21 (2017), pp. 16-39.

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  • 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 Pad´e 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.

  • History

Published online: 2018-04

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