无界区域上平面弹性方程的D-N交替算法及其收敛性

D-N Alternating Algorithm and Its Convergence for The Problem of Plane Elasticity Equation on Unbounded Domains

本文利用有限元法和自然边界归化的非重叠型区域分解算法研究无界区域上平面弹性方程,该算法对求解无界区域平面弹性方程问题非常有效.给出连续和离散情形的D-N算法及其算法的收敛性分析,适当选取松弛因子,证明算法是几何收敛的.

In this paper, a non-overlapping domain decomposition method by using of the finite element method and the natural boundary reduction is investigated for solving problems of the plane elasticity equation. This method is very effective for solving the plane elasticity equation over unbounded domains especially. The D - N alternating algorithm （including continuous and discrete form） and its convergence analysis are presented, with proper selection of the relaxation factor it is proved that the convergence rate of the algorithm is geometrical.