Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 815–825
Abstract
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(N3) of operations and O(N2) 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(N3) to O(Nlog2N) and memory requirement from O(N2) 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-597
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 815–825
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: collocation method dense matrices fast methods non-local diffusion peridynamics.