Research And Application Of Multi-layer Parallel Computing Approach For Finite Element Structural Analysis

Supercomputers of multi-core and multi-node architectures have become primary tools for high performance computing due to their great computing power and cost-to-performance effectiveness. However, the large-scale computing problems of finite element numerical simulations for complex structures cannot be substantially solved only by utilizing the high performance of supercomputers of multi-core and multi-node architectures. The only way to improve the quality and efficiency of engineering analysis is to research on the suitable parallel computing algorithms. Based on the high performance computing platform of "Dawning 5000A" supercomputer located at Shanghai supercomputer center, the multi-layer parallel computing approach for finite element structural analysis is studied and applied to projects. The main contents include:The efficient algorithms of parallel computing for finite element structural static and dynamic analysis are studied. According to the problem of low efficiency when conducting large-scale parallel computing with a large number of cores based on domain decomposition method, a multi-layer parallel computing approach is proposed. The proposed approach is constructed with the strategies of two-level partitioning and twice condensation based on the domain decomposition method. The data for parallel computing is first prepared through two-level partitioning to guarantee the load balancing within and across nodes of supercomputers of multi-core and multi-node architectures. Then during the parallel computing, on one hand, the size of problem to solve is considerably reduced through twice condensation and thus the convergence rate of interface problem is significantly improved. On the other hand, the intra-node and inter-node communications are separated through multi-layer parallel computing scheme and thus the communication efficiency is significantly improved. Numerical examples show that the proposed multi-layer parallel computing approach obtained higher speed-up and parallel efficiency compared with the conventional domain decomposition method. The more the number of cores was utilized, the more obvious effect could be observed.The efficient condensation algorithms to release the subdomain’s internal degrees of freedom are studied. In the procedure of condensation for subdomains in level 2, a compressed sparse row format condensation method is proposed based on the sparse storage techniques and sparse direct solvers. In the proposed method, the process of condensation is converted to the process of solving a series of linear equations and then the linear equations are solved with a sparse direct solver. It has the advantages of small memory requirement, high computational efficiency and ease of programming. This is contributed by two reasons. Firstly, only the non-zero elements of the stiffness matrix are stored with the sparse storage techniques. Secondly, the memory requirements and computational operations of solving linear equations with spares direct solvers are significantly reduced by fill-reducing ordering. In the procedure of condensation for subdomains in level 1, the conventional skyline storage format condensation algorithm is parallel modified in order to utilize all the processes in the same node and thus the multi-core computational resources in the node can be efficiently exploited.The development and integratation of high performance computing software for finite element analysis are carried out. In order to reduce the cost of system development and improve the quality and efficiency of software development, a secondary development scheme based on the serial finite element program generator is proposed. The overall design of software is carried out from the perspective of software engineering, including the determination of overall system implementation and the design of system function and structure. The detailed implementation of four main function modules, namely input/output module, forming system module, solving system module and calculating stresses and deformation module are presented based on the modular program design method. The system integration is realized according to the interface rules of different modules and call relations among them. The software development scheme proposed in this paper explores a new way for the development of application software for supercomputers.The application of large-scale engineering problems are carried out with the developed high performance computing software for finite element structural analysis. The Minpu II bridge in Shanghai was considered as the engineering application object of structural static analysis and the finite element simulation model of the whole bridge was established based on the full 3D virtual modeling method. A high-rise building was considered as the engineering application object of structural dynamic analysis and the finite element simulation model of the high-rise building under the effectiveness of explosive shock wave was established. The large-scale parallel computing of finite element numerical simulations for the two models was conducted on the high performance computing platform of "Dawning 5000A" supercomputer located at Shanghai supercomputer center with the developed software. Comparisons and analysis of the computing results and the performance of the parallel programs were done between the conventional domain decomposition method and the multi-layer parallel computing method. So validity, reliability and effectivity of the proposed multi-layer parallel computing approach were all validated.