Concerning the time-consuming problem of finite element analysis for solving the nonlinear dynamic problems of large-scale structure, some parallel computational strategies for implementing explicit nonlinear finite element analysis were proposed under the environment of Message Passing Interface (MPI) cluster. Based on the technique of domain decomposition with explicit message passing, using overlapped, non-overlapped domain decomposition techniques and Dynamic Task Allocation (DTA) algorithm, domain decomposition parallel algorithms for overlapped domain, non-overlapped domain, clustering for DTA, DTA and Dynamic Load Balancing (DLB) were researched by overlapping calculations and communications to improve the performance of communication between processors. A parallel finite element analysis program was developed with message passing interface as software development environment. Some numerical examples were implemented on workstation cluster to evaluate the performance of the parallel algorithm, the computation performance was also compared with the conventional Newmark algorithm. The experimental results show that the performance of the algorithm for dynamic task allocation with clustering technique is better than that of the dynamic task allocation, which is lower than that of the domain decomposition algorithm, and the dynamic load balancing algorithm is the best. For the problem with the same size, the proposed algorithms are faster and better than conventional Newmark algorithm. The proposed algorithms are efficient for parallel computing of nonlinear dynamic problems of structure.

Finite element analysis for elastic-plastic problem is very time-consuming. A parallel substructure Preconditioned Conjugate Gradient (PCG) algorithm combined with Minimal Residual (MR) smoothing was proposed under the environment of Message Passing Interface (MPI) cluster. The proposed method was based on domain decomposition, and substructure was treated as isolated finite element model via the interface conditions. Throughout the analysis, each processor stored only the information relevant to its substructure and generated the local stiffness matrix. A parallel substructure oriented preconditioned conjugate gradient method was developed, which combined with MR smoothing and diagonal storage scheme. Load balance was discussed and interprocessor communication was optimized in the parallel algorithm. A substepping scheme to integrate elastic-plastic stress-strain relations was used. The errors in the integration process were controlled by adjusting the substep size automatically according to a prescribed tolerance. Numerical example was implemented to validate the performance of the proposed PCG algorithm on workstation cluster. The performance of the proposed PCG algorithm was analyzed and the performance was compared with conventional PCG algorithm. The example results indicate that the proposed algorithm has good speedup and efficiency and is superior in performance to the conventional PCG algorithm. The proposed algorithm is efficient for parallel computing of 3D elastic-plastic problems.