Speaker: Dr. Hao Tian, Beijing Computational Science Research Center

Abstract: Peridynamic theory provides an appropriate description of the deformation of a continuous body involving discontinuities or other singularities. However, the operators in the peridynamic models are non-local, so the resulting numerical methods generate dense stiffness matrices. Gaussian types of direct solvers were traditionally used solve these problems, which requires O(delta^2 N^3) of operations and O(delta^2 N^2) of memory where N is the number of spatial nodes and delta is length of the horizon. This imposes significant computational and memory challenge for a non-local model, especially for problems in multiple space dimensions. A simplified model, which assumes that the horizon of the material delta = O(1/N), was proposed to reduce the computational cost and memory requirement to O(N). However, the drawback is that the corresponding error estimate becomes one-order suboptimal. We develop a fast collocation method for the linear full non-local model by exploiting the structure of the stiffness matrix. The new method reduces the computational work from O(N^3) required by the traditional methods to O(N logN logN) and the memory requirement from O(N^2) to O(N) without using any lossy compression.  

Date&Time: December 13, 2013 (Friday), 14:30–15:30
Location: 606 Conference Room