摘要针对水利工程中的大型复杂三维结构对大规模数值计算的需求，基于J-PCG方法(Jacobi预处理共轭梯度法)，建立了有限元EBE(element-by-element)方法在分布存储并行机上的计算算法。该算法不用考虑网格拓扑结构和单元的排序，同时不形成整体刚度矩阵，而且避免了对复杂的三维结构进行区域分解。采用上述算法编制了三维有限元并行求解的PFEM(parallel finite element method)程序，并在网络机群系统上实现，然后将其应用到二滩拱坝–地基系统和水布娅地下洞室的三维有限元数值计算中。数值计算结果表明，三维有限元并行EBE方法非常适合于水利工程中三维复杂结构的大规模数值计算。
Abstract：The large-scale numerical analysis in hydraulic engineering gives rise to the need for high-performance computation. To meet it，the algorithm of parallel finite element based on EBE (element-by-element) method is put forward by using J-PCG (Jacobi preconditioned conjugate gradient) method. The algorithm does not invoke any special partitioning of the domain，topology of mesh or element ordering. Global stiffness matrix does not need to be formed and the decomposition of 3D complicate domain can be avoided with this algorithm. A PFEM (parallel finite element method) program is developed and implemented on cluster of workstation (COW). Then it is applied to finite element analysis of arch dam system of the Ertan Project and caverns of the Shuibuya Project. The calculated numerical results show that parallel finite element based on EBE method is applicable for large-scale numerical analysis of 3D structures in hydraulic engineering.
