A Multilevel Hierarchical Parallel Algorithm for Large-Scale Finite Element Modal Analysis

The strict and high-standard requirements for the safety and stability of major engineering systems make it a tough challenge for large-scale finite element modal analysis. At the same time, realizing the systematic analysis of the entire large structure of these engineering systems is extremely meaningful in practice. This article proposes a multilevel hierarchical parallel algorithm for large-scale finite element modal analysis to reduce the parallel computational efficiency loss when using heterogeneous multicore distributed storage computers in solving large-scale finite element modal analysis. Based on two-level partitioning and four-transformation strategies, the proposed algorithm not only improves the memory access rate through the sparsely distributed storage of a large amount of data but also reduces the solution time by reducing the scale of the generalized characteristic equation (GCEs). Moreover, a multilevel hierarchical parallelization approach is introduced during the computational procedure to enable the separation of the communication of inter-nodes, intra-nodes, heterogeneous core groups (HCGs), and inside HCGs through mapping computing tasks to various hardware layers. This method can efficiently achieve load balancing at different layers and significantly improve the communication rate through hierarchical communication. Therefore, it can enhance the efficiency of parallel computing of large-scale finite element modal analysis by fully exploiting the architecture characteristics of heterogeneous multicore clusters. Finally, typical numerical experiments were used to validate the correctness and efficiency of the proposed method. Then a parallel modal analysis example of the cross-river tunnel with over ten million degrees of freedom (DOFs) was performed, and ten-thousand core processors were applied to verify the feasibility of the algorithm.