By combining the two-grid discretization with the partition of unity method, a parallel iterative finite element method for the linear elliptic equations is proposed and investigated. Since the construction of the partition of unity is based on the coarse mesh triangulation, the computational domain of each subproblem can be divided automatically and the number of subproblems can be arbitrarily huge as the coarse mesh parameter H tends to zero. That means our method can be easily implemented in high performance supercomputers or cluster of workstations. Theoretical results based on a priori error estimation of the scheme are obtained, which indicate that our method can reach the optimal convergence orders within a few two-grid iterations. Numerical results are reported to assess the theoretical results.

通过将两网格离散化与统一方法的划分相结合，提出并研究了线性椭圆方程的并行迭代有限元方法。由于统一分区的构造基于粗网格三角剖分，因此随着粗网格参数H趋于零，每个子问题的计算域都可以自动划分，并且子问题的数量可以任意大。这意味着我们的方法可以在高性能超级计算机或工作站集群中轻松实现。获得了基于该方案的先验误差估计的理论结果，这表明我们的方法可以在两次网格迭代中达到最佳收敛阶。报告数值结果以评估理论结果。