Parallel computing of large-scale modal ananlysis based on Jacobi-Davidson algorithm

Some improvements and parallel computing studies were carried out about the Jacobi-Davidson(J-D) method. Some strategies, such as the spectral transformation technique, restart and deflation techniques, were integrated with the J-D method to make it suitable for large-scale modal analysis. A parallel modal analysis system based on PANDA framework was created using the improved J-D algorithm and various numerical software packages. Utilizing the analysis system and parallel computers, the parallel scalability of the J-D algorithm was studied via numbers of tests on an engineering structure. The maximum computing scale is over 10 million degrees of freedom, and the maximum number of parallel CPU processors attains 128. The influences of inner iteration steps and number of restarted vectors on the convergence velocity of outer iterations were studied, and the speedup curves for different scales were obtained. The results show that the improved J-D method is competent for the large-scale modal analysis, the memory cost increases linearly with the computing scale and only 39.4 GB of memory is needed for the modal analysis of 10.25 million scale. Also, the improved J-D method takes on an excellent parallel scalability that the speedup curves are almost linear within 128 testing processors and the curve is gradually close to the ideal speedup one as the computing scale is accreting. The parallel efficiency of 10.25 million scale with 128 processors attains 88.1%.