基于CUDA的有限元矩阵并行装配算法研究

构建航天飞行器的结构有限元模型是准确模拟飞行仿真、完成飞行器在轨飞行阶段结构故障监测和诊断的基础。采用细长体飞行器简化梁模型,提出新的基于CUDA(Compute Unified Device Architecture)的有限元单元刚度矩阵生成和总刚度矩阵组装算法。依据梁单元矩阵的对称性,结合GPU硬件架构提出并行生成算法并进行改进。为有效减少装配时间,在装配过程中采用着色算法,提出了基于GPU(Graphics Processing Unit)共享内存的非零项组装策略,通过在不同计算平台下算例对比,验证了新算法的快速性。数值算例表明,本文算法的求解效率较高,针对一定计算规模内的模型可满足快速计算与诊断的实时性要求。

Research on parallel assembly algorithms of finite element matrices based on CUDA

Constructing the finite element model of a spacecraft structure is the basis of flight simulation,structural fault monitoring and diagnosis during the on-orbit flight phase.A new stiffness matrix generation and assembly algorithm in the finite element method based on CUDA is proposed based on the simplified beam model of slender body aircraft.According to the symmetry of the beam element stiffness,a parallel algorithm is proposed and improved by combining with GPU hardware architecture.In order to reduce the stiffness matrix assembly time effectively,the famous coloring algorithm was used in the assembly process,and a non-zero assembly strategy based on GPU Shared memory was proposed.Numerical examples show that the algorithm presented in this paper is efficient.The algorithm satisfies the real-time requirement of fast calculation and diagnosis for the model in a certain calculation scale.