OPTIMIZED SCHWARZ METHODS WITH ROBIN TRANSMISSION CONDITIONS FOR PARABOLIC PROBLEMS

In this paper, optimized Schwarz methods with Robin transmission conditions are considered for solving the time-dependent linear algebraic systems resulting from finite element approximations for parabolic problems. We use both analysis and numerical experiments to investigate the convergence behavior. Particularly, we check the influence of the time step size on the convergence rate. We get the estimate of the upper bound of convergence rate 1 - O(min{h(1/2) H-1/2, h(1/2) H-3/2 tau(-1)}), where h is the mesh size, H is the size of subdomains, and tau is the time step size. Our numerical results show that the convergence rate of this method is fast. We also search for the optimal parameter lambda by experiments and find the rule of its distribution.