Fast Multipole BEM for Simulation of 2-D Solids Containing Large Numbers of Cracks

• 作 者: 王朋波 姚振汉 王海涛
• 机 构: Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China,Department of Engine
• 出 处: Tsinghua Science and Technology
• 发表日期: 2005年01期
• 关键词: Numbers dimensionality kernel infinity overcome powerful traction infinite singu

The fast multipole method was used to solve the traction boundary integral equation for 2-D crack analysis. The use of both multipole and local expansions reduces both the computational complexity and the memory requirement to O(N). The multipole expansion uses a complex Taylor series expansion to reduce the number of multipole moments. The generalized minimum residual method solver (GMRES) was selected as the iterative solver. An improved preconditioner for GMRES was developed which uses less CPU time and less memory. A new initial candidate vector for the iterative solver was developed to further improve the efficiency. The numerical examples apply the method to the analysis of cracks in infinite 2-D space with the largest model having 900 000 degrees of freedom.

The use of both multipole and local expansions reduces both the computational complexity and the memory requirement to O (N). The multipole expansion uses a complex Taylor series expansion to reduce the number of multipole moments. The generalized minimum residual method solver (GMRES) was selected as the iterative solver. An improved preconditioner for GMRES was developed which uses less CPU time and less memory. A new initial candidate vector for the iterative solver was developed to further improve the efficiency. The numerical examples apply the method to the analysis of cracks in infinite 2-D space with the largest model having 900 000 degrees of freedom.