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

Wei Zhang, Jiang Yang, Jiwei Zhang & Qiang Du

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

Published online: 2018-04

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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.

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@Article{CiCP-21-16, author = {Wei Zhang, Jiang Yang, Jiwei Zhang and Qiang Du}, title = {Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {1}, pages = {16--39}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0033}, url = {http://global-sci.org/intro/article_detail/cicp/11230.html} }
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