关键词: 并行有限元, 可扩展并行计算, 岩土工程, 对偶原始有限元撕裂内联法（FETI-DP）

Abstract: The scalable parallel computation of finite element models with hundreds of millions of elements is discussed. The software and hardware solutions for the preprocessing, parallel computing method, software algorithms, and postprocessing are proposed. A finite element model of one hundred million elements is generated by grid encryption method. And the dual-primal finite element tearing and interconnecting method (FETI-DP) is utilized to solve the finite element system of equations. The topological connections among sub-domains are set up based on graph theories. Point to point communications are built to accelerate data exchange among sub-domains and to avoid the time-consuming global communications. Some modules are written based on an in-house code using object-oriented programming technique and message passing interface (MPI). A numerical example with more than one hundred million number of elements is carried out using 5000 cores at the same time; and super-linear speedup is obtained. The postprocessing is performed on a graphical workstation; and the interactive operations respond quickly. The study shows two big improvements: one is that the numerical model has more than one hundred million numbers of elements; the second is that 5 000 cores are used at the same time and high efficiency is obtained. The research results show that the high resolution numerical simulations provide an efficient tool for large size and complex geological conditions simulations in geotechnical engineering.

Key words: parallel finite elements, scalable parallel computation, geotechnical engineering, dual-primal finite element tearing and interconnecting method (FETI-DP)