无单元伽辽金法的并行计算

对无单元伽辽金法的并行计算进行了详细研究,并将其应用于弹性动力学问题。使用并行桶搜索算法进行节点搜索,使用并行几何搜索算法进行样点搜索,讨论了移动最小二乘MLS(Moving Least Squares)形函数及其导数的并行计算和方程组的并行求解,并利用多层图形划分实现负载平衡。最后给出了并行无单元伽辽金法应用于弹性动力学的计算流程和实例。计算结果表明无单元伽辽金法具有很高的并行性和很好的并行效率,对其进行并行计算具有非常重要的意义。

Parallel computing of element-free galerkin method for elasto-dynamics

Parallel algorithms of Element-free Galerkin (EFG) Method were studied for elasto-dynamics.Parallel bucket search was used to perform nodal search,and parallel geometry search was used for sample-point search.We discussed the parallel computing the shape functions and their derivatives of moving least squares method(MLS),and employed SSOR-PPCG to solve the system of linear equations.A very important part of parallel computing of EFG, load balance,was solved with the aid of multilevel graph partitioning algorithm.Finally,we described the computing flowchart of parallel EFG for elastodynamics,and analyzed a numerical example.The numerical results are in good agreement with exact solution and show that parallel EFG possesses large parallel potential and high parallel efficiency.Parallel computing is very significant to EFG for dynamical problems.