Artificial Boundary Conditions for Nonlocal Heat Equations on Unbounded Domain

作者：Zhang Wei^*; Yang Jiang; Zhang Jiwei; Du Qiang

来源：Communications in Computational Physics, 2017, 21(1): 16-39.

DOI：10.4208/cicp.OA-2016-0033

• Artificial boundary conditions
• nonlocal models
• Pade approximation
• nonlocal heat equations
• artificial boundary method

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 Pade 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.

• 出版日期2017-1
• 单位北京计算科学研究中心