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

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 $O(N^{2})$ O ( N 2 ) to $O(N\log N)$ O ( N log N ) and the memory requirement for the coefficient matrix from $O(N^{2})$ O ( N 2 ) to $O(N)$ O ( N ) . Numerical experiments are carried out to show the utility of the fast collocation method.