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Paper Code  
Title   Optimized Schwarz methods with Robin transmission conditions for parabolic problems
Authors   Xu Xuejun
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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.

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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.

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