球面上Poisson方程的两子域加性Schwarz算法

The Optimal Additive Schwarz Algorithm with Two Sub-domains for Solving Poisson Equation on the Sphere

研究求解球面上的Poisson方程的加性Schwarz算法。对于两子域加性Schwarz算法,通过选取最优参数得到子域内边界上的优化传输条件,由此得到的最优加性算法可大大加快收敛的速度;而且,算法具有有限步收敛性。

The optimal additive Schwarz algorithm for solving Poisson equation on the sphere is considered. For additive Schwarz algorithm with two subdomains, the optimal parameter can use to obtain the optimal transfer conditions on the inner boundaries of the subdomains. The corresponding optimal additive algorithm can accelerate the rate of the convergence. Moreover, the algorithm can terminate in steps.