scholarly journals A Preconditioned Fast Collocation Method for a Linear Nonlocal Diffusion Model in Convex Domains

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 182366-182375
Author(s):  
Xuhao Zhang ◽  
Aijie Cheng ◽  
Hong Wang
Keyword(s):  
Collocation Method ◽  
Diffusion Model ◽  
Nonlocal Diffusion ◽  
Convex Domains

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

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xuhao Zhang ◽  
Aijie Cheng
Keyword(s):  
Collocation Method ◽  
Diffusion Model ◽  
Variable Coefficient ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Coefficient Matrix ◽  
Nonlocal Diffusion ◽  
Two Dimensional ◽  
Subspace Iteration ◽  
Dimensional Variable

Abstract 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.

scholarly journals Numerical solution of a coupled reaction-diffusion model using barycentric interpolation collocation method

2020 ◽  
Vol 24 (4) ◽  
pp. 2561-2567
Author(s):  
Yu Zhang ◽  
Wei Zhang ◽  
Chenhui Zhao ◽  
Yulan Wang
Keyword(s):  
Approximate Solution ◽  
Numerical Solution ◽  
Collocation Method ◽  
Diffusion Model ◽  
Numerical Experiments ◽  
Reaction Diffusion ◽  
Barycentric Interpolation ◽  
Reaction Diffusion Model ◽  
Linear Reaction ◽  
Coupled Reaction

In thermal science, chemical and mechanics, the non-linear reaction-diffusion model is very important, and an approximate solution with high precision is always needed. In this article, the barycentric interpolation collocation method is proposed for this purpose. Numerical experiments show that the proposed approach is highly reliable.

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