Fast collocation method for a two-dimensional variable-coefficient linear nonlocal diffusion model

Advances in Difference Equations

article

Zhang, Xuhao¹  Cheng, Aijie² 

[1] School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences);School of Mathematics, Shandong University

关键词: Nonlocal diffusion model;    Variable coefficient;    Fast collocation method;   

DOI  :  10.1186/s13662-020-02931-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, a fast collocation method is developed for a two-dimensional variable-coefficient linear nonlocal diffusion model. By carefully dealing with the variable coefficient in the integral operator and then analyzing the structure of the coefficient matrix, we can reduce the computational operations in each Krylov subspace iteration from$O(N^{2})$ to$O(N\log N)$ and the memory requirement for the coefficient matrix from$O(N^{2})$ to$O(N)$ . Numerical experiments are carried out to show the utility of the fast collocation method.

【 授权许可】

CC BY