三维有限元并行EBE方法

采用Jacobi预处理,推导了基于EBE方法的预处理共轭梯度算法,给出了有限元EBE方法在分布存储并行机上的计算过程,可以实现整个三维有限元计算过程的并行化。编制了三维有限元求解的PFEM(ParallelFiniteElementMethod)程序,并在网络机群系统上实现。采用矩形截面悬臂梁的算例,对PFEM程序进行了数值测试,对串行计算和并行计算的效率进行了分析,最后将PFEM程序应用于二滩拱坝-地基系统的三维有限元数值计算中。结果表明,三维有限元EBE算法在求解过程中不需要集成整体刚度矩阵,有效地减少了对内存的需求,具有很好的并行性,可以有效地进行三维复杂结构的大规模数值分析。

PARALLEL 3-D FINITE ELEMENT ANALYSIS BASED ON EBE METHOD

Jacobi preconditioned conjugate gradient (J-PCG) method based on element-by-element is derived and the calculation process of finite element method (FEM) is presented. The parallelization of the whole calculation process is implemented. A PFEM (Parallel Finite Element Method) program is developed and implemented on a cluster of workstation (COW) with this algorithm. The efficiency on both serial and parallel computer is tested with the case study of a cantilever beam, and it is also applied to FEM analysis of the Ertan arch-dam system. Numerical results show that 3-D finite element method based on element-by-element (EBE) policy utilizes element matrices, thereby avoiding the assembly of global stiffness matrix. Because it requires less memeory storage than conventional finite element solvers on a serial computer, it is very suitable for parallelization. For the parallel analysis of 3-D irregular and complicated structures like arch dams, the finite element EBE method is effective and reliable.