随机有限元分析的二级区域分解并行求解算法

采用蒙特卡罗模拟(MCS)和加权积分法对二维问题进行随机有限元分析。尽管MCS方法对任何有确定解的问题都具有求解精度高的优点,但由于求解所需的计算量巨大使其应用受到限制。利用并行求解技术可有效地处理这种密集型计算问题。基于有限元分裂对接法(FETI)的并行特性并利用预处理共轭梯度法(PCG)的求解高效性,结合整体子区域实现(GSI-PCG)和FETI法,提出二级求解算法,并在工作站机群上实现了数值算例。算例计算结果表明本文GSI(PCG)-FETI算法具有较高的并行加速比和并行效率,具有良好的性能,可有效地进行二维问题的随机有限元分析。

A two-level domain decomposition parallel algorithm for stochastic finite element analysis

The Monte Carlo simulation(MCS) and the weighted integral method are used to implement efficient numerical computing of stochastic finite element analysis for 2D problem.Although MCS approache has the advantage that accurate solution can be obtained for any type of problem whose deterministic solution is known,its applicability is restricted by the high computational effort.The parallel solution technique can treat the highly computationally demanding problem.In order to exploit the parallelizable feature of the finite element tearing and interconnecting method(FETI) and to take advantage of the efficiency of the preconditioned conjugate gradient method,a two-level algorithm is proposed based on the combination of the GSI-PCG method and the FETI method.Numerical example is implemented to evaluate the performance of the proposed parallel algorithm on the workstation cluster.The results of examples show that the proposed GSI(PCG)-FETI algorithm has higher parallel speed-up ratio and parallel efficiency.So it is suitable for treatment of stochastic finite element analysis for 2D problem.