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

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• 作者：Che Wang ; Hong Wang ; ^{hwang@math.sc.edu}
• 关键词：Fast collocation method ; Fractional diffusion equation ; Nonlocal diffusion model ; Nonlocal model
• 刊名：Journal of Computational Physics
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：330
• 期：Complete
• 页码：114-126
• 全文大小：348 K
• 卷排序：330

文摘

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(N3)O(N3) required by a commonly used direct solver to O(Nlog⁡N)O(Nlog⁡N) per iteration and the memory requirement from O(N2)O(N2) to O(N)O(N). Furthermore, the fast method reduces the computational work of assembling the stiffness matrix from O(N2)O(N2) to O(N)O(N). Numerical results are presented to show the utility of the fast method.