关键词: 有限元方法, 非结构网格, 弹性力学, 并行计算, 悬臂梁模型

Abstract: The numerical simulation of elasticity has been applied to many engineering fields such as architecture, machinery, chemical industry, material and spaceflight. With the increase in computation scale and precision of real-world applications, sequential algorithms are not able to satisfy applications' needs, especially for those with complicated CAD model and material. To alleviate this problem, we propose a parallel finite element algorithm based on hierarchical unstructured mesh, and apply it to elastic equations. Our algorithm consists of a novel unstructured mesh data structure obtained through hierarchical domain decomposition and a corresponding two-step algorithm for the stiff matrix of elasticity system. By comparing the results of a beam model with ANSYS, we validate the correctness of our algorithm. The results of steel tube model shows that our algorithm is able to solve problems with 1.5 billion cells and scale to 4080 processes.

Key words: finite element method (FEM), unstructured mesh, elastic mechanics, parallel computation, beam model