A fast collocation method for a variable-coefficient nonlocal diffusion model

JOURNAL OF COMPUTATIONAL PHYSICS

卷:330

Article

Wang, Che¹  Wang, Hong¹ 

[1] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

关键词: Fast collocation method;    Fractional diffusion equation;    Nonlocal diffusion model;    Nonlocal model;   

DOI  :  10.1016/j.jcp.2016.11.003

来源: Elsevier

【 摘 要 】

We develop a fast collocation scheme for a variable-coefficient nonlocal diffusion model, for which a numerical discretization would yield a dense stiffness matrix. The development of the fast method is achieved by carefully handling the variable coefficients appearing inside the singular integral operator and exploiting the structure of the dense stiffness matrix. The resulting fast method reduces the computational work from O (N-3) required by a commonly used direct solver to O (N log N) per iteration and the memory requirement from O (N-2) to O (N). Furthermore, the fast method reduces the computational work of assembling the stiffness matrix from O (N-2) to O (N). Numerical results are presented to show the utility of the fast method. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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