千万自由度以上的大规模有限元动力学分析在光机装置、武器系统等复杂装备研制过程中具有强烈的应用需求。随着大型装备复杂性的不断增加和精度、可靠性等要求的提高，对模态和振动分析求解规模和效率的要求也不断提高。国内现有商业软件在计算规模、效率及算法等方面受到了很大限制。本课题以大型装备的高效动力学分析为背景，基于Krylov-Schur、Jacobi-Davidson两种主流特征值算法和振型叠加法，在JAUMIN框架上研发模态和振动分析并行软件。通过研究和添加谱变换技术、大型线性方程组求解技术以及收缩和重启动技术等提升算法计算规模；通过研究系统矩阵剖分策略、软件体系架构以及软硬件匹配等提升算法的并行可扩展性。最终将研发的软件应用于光机装置等复杂装备，实现其千万自由度以上、数千CPU核的高效模态和振动分析并行计算，突破现有商业软件计算规模和效率等瓶颈问题。

In the development of large equipments such as the laser facility support structure and weapon systems, the demand for large-scale (over ten million degrees of freedom) parallel finite element dynamic analysis is very strong. The increasing complexity of large equipments, as well as their high requirements for precision and reliability, have made the solution scale of modal analysis become larger and larger, and a faster solving velocity is needed. The domestic commercial soft wares for modal analysis are limited due to their lower computing scale, poor efficiency and outdated algorithms. In this study, we take the dynamic analysis of large equipments as engineering backgrounds and develop the modal and vibration analysis software on the JAUMIN framework. Two predominant eigenvalue algorithms (i.e. Krylov-Schur and Jacobi-Davidson) and the mode superposition method are used for the corresponding algorithm designs. Some solving techniques such as spectral transformation, solution of large-scale linear systems, deflation and restarting techniques will be studied and added to heighten the computing scale. Also,we heighten the parallel scalability via the studies of matrix decomposition strategy, software framework design,as well as the matching between software and hardware. The finally formed software will be applied to the dynamic analysis of the laser facility support structures and other large equipments, where we'll realize the parallel mode and vibration solution with over ten million freedoms of degree and thousands of CPU processors. The bottleneck difficulties of solution scale and efficiency for domestic commercial soft wares will be prospectively broken by our endeavor.