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.

中文翻译：

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二维变系数线性非局部扩散模型的快速配置方法

本文针对二维变系数线性非局部扩散模型，提出了一种快速配置方法。通过在积分算子中仔细处理可变系数，然后分析系数矩阵的结构，我们可以将每次Krylov子空间迭代中的计算运算从\（O（N ^ {2}）\）减少到\（O（ N \ log N）\）和系数矩阵从\（O（N ^ {2}）\）到\（O（N）\）的存储要求。数值实验表明了快速配置方法的实用性。