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 Paper Code Title Optimized Schwarz methods with Robin transmission conditions for parabolic problems Authors Xu Xuejun Corresponding Author Year 2008 Title of Journal Volume 31 Number 3 Page 608-623 Abstract Abstract 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. Full Text Full Text Link Others: Abstract 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. Classification: Source: