关于Schwarz交替法的收敛因子

§1.Schwarz交替法的收敛因子 我们就二阶自共轭椭圆型方程的Dirichlet问题来讨论.设Ω?R~2为一多边形区域, a(u,v)=(f,v),v∈H_0~1(Ω),f∈H~(-1)(Ω), u∈H_0~1(Ω)是定义在其上的边值问题的变分形式,双线性型时a(·,·)满足

On the Convergence Factor of the Schwarz Alternating Method

Theoretical analysis for model problems and numerical experiments show that when sub-domains are fixed, the convergence factor of the Schwarz alternating method for discretized pro-blems is independent of the discretization step, and we prove this property under some assump-tions. We also give expression of the convergence factor of the Schwarz alternating method inwhich the subdomain problems are solved approximatively by iterative methods and use it to dis-cuss the optimal number of iterations on the subdomain problems.