不重叠型Schwarz交替法的加速收敛  

ACCELERATING THE CONVERGENCE OF THE ALTERNATING SUBDOMAIN SCHWARZ METHOD WITHOUT INTERSECTION

作　　者：王寿城[1] 

机构地区：[1]合肥工业大学理学院,合肥230009

出　　处：《应用数学学报》2004年第2期237-245,共9页Acta Mathematicae Applicatae Sinica

摘　　要：Matsokin 与 Nepomnyaschikh 所提出的不重叠型 Schwarz 交替法的算法中不含有松驰因子。我们知道它有与h 无关的几何收敛速度,但由于不含算法参数,该算法不能根据具体的情况加速收敛。本文提出加速收敛算法。我们在原算法的基础上引入两个松驰因子 θ_1,θ_2,并证明了除了例外均可实现加速收敛,θ_1=θ_1,θ_2=θ_2是满足均衡条件的最佳松驰因子。最后的算例表明该加速算法的有效性。There are no relaxation parameters in the algorithm of the alternating subdo- main Schwarz method without intersection given by Matsokin and Nepomnyaschilih. We know that the method converges geometrically, and the convergence is independent of h. Because of containing no relaxation parameters, the method cannot accelerate the conver- gence under any particular cases. In this paper, we give an algorithm which can accelerate the convergence. We add two relaxation parameters to the known algorithm. It has been proved that we can accelerate the convergence besides the exceptions, and θ_1, θ_2 are the optimum parameters under the balance condition. The last example shows the efficiency of our new algorithm.

关 键 词：几何收敛速度 第三边值问题 HELMHOLTZ方程 收敛性 

分 类 号：O175.8[理学—数学]