非结构网格上弹性力学数值模拟的并行实现

Parallel Computation for Elastic Mechanical Numerical Simulation on Unstructured Mesh

弹性力学数值模拟被广泛应用到建筑、机械、化工、材料、航天等工程领域.随着计算规模和精度的不断提高,普通串行程序已经不能满足应用的需求,需要研制并行应用程序.面向非结构网格,提出了一种基于层次化网格数据结构的并行有限元算法,并用来求解弹性力学方程组.最后,用数值结果验证了网格数据结构和并行算法的正确性和扩展性.数值结果显示弹性力学并行程序可成功扩展到4 080进程,网格规模达到15亿单元.

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.