AN EFFICIENT COLLOCATION METHOD FOR A NON-LOCAL DIFFUSION MODEL

作者：Tian Hao^*; Wang Hong; Wang Wenqia

来源：International Journal of Numerical Analysis and Modeling, 2013, 10(4): 815-825.

• collocation method
• dense matrices
• fast methods
• non-local diffusion
• peridynamics

The non-local diffusion model provides an appropriate description of the deformation of a continuous body involving discontinuities or other singularities, which cannot be described properly by classical theory of solid mechanics. However, because the non-local nature of the non-local diffusion operator, the numerical methods for non-local diffusion model generate dense or even full stiffness matrices. A direct solver typically requires O(N-3) of operations and O(N-2) of memory where N is the number of unknowns. We develop a fast collocation method for the non-local diffusion model which has the following features: (i) It reduces the computational cost from O(N-3) to O(N log(2) N) and memory requirement from O(N-2) to O(N). (ii) It requires only one-fold integration in the evaluation of the stiffness matrix. Numerical experiments show the utility of the method.

• 出版日期2013
• 单位山东大学