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

Wei Zhang, Jiang Yang, Jiwei Zhang & Qiang Du

DOI: 10.4208/cicp.OA-2016-0033

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

Published online: 2018-04

[An open-access article; the PDF is free to any online user.]

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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 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.

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COPYRIGHT: © Global Science Press

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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 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0033}, url = {http://global-sci.org/intro/article_detail/cicp/11230.html} }
TY - JOUR T1 - Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain AU - Wei Zhang, Jiang Yang, Jiwei Zhang & Qiang Du JO - Communications in Computational Physics VL - 1 SP - 16 EP - 39 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.OA-2016-0033 UR - https://global-sci.org/intro/article_detail/cicp/11230.html KW - AB -

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.

Wei Zhang, Jiang Yang, Jiwei Zhang and Qiang Du. (2018). Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain. Communications in Computational Physics. 21 (1). 16-39. doi:10.4208/cicp.OA-2016-0033
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