基于自然边界归化的非重叠型区域分解算法  

Non-overlapping Domain Decomposition Method Based on the Natural Boundary Reduction

作　　者：刘敬刚[1] 

机构地区：[1]华北电力大学(保定)数理系,保定071003

出　　处：《工程数学学报》2009年第3期542-546,共5页Chinese Journal of Engineering Mathematics

基　　金：华北电力大学青年教师科研基金(200511015)

摘　　要：基于半平面上的自然边界归化理论,给出了一类带凹槽的半无界区域上椭圆型方程边值问题的非重叠型区域分解算法。证明了算法具有与有限元剖分网格参数无关的收敛性,适当选取松弛因子,算法是几何收敛的,并给出了松弛因子的一般取值,数值例子表明了算法的有效性。Based on the theory of natural boundary reduction, a non-overlapping domain decompo- sition method is applied to elliptic boundary value problems on a kind of unbounded half plane with a cave. It is proved that the convergence rate of the algorithm is independent of the finite element mesh size. With proper selection of the relaxation factor, it is shown that the convergence rate of the algorithm is geometrical. Furthermore, the general values of the relaxation factor are given. The numerical example shows that the algorithm is effective.

关 键 词：自然边界归化 椭圆型边值问题 非重叠型区域分解算法 

分 类 号：O241.82[理学—计算数学]