Nonoverlapping Schwarz Waveform Relaxation Algorithm for a Class of Time-Fractional Heat Equations

In this paper, we analyze the convergence properties of the Schwarz waveform relaxation (SWR) algorithm with Robin transmission conditions (TCs) for a class of heat equations with Riemann-Liouville fractional derivative. The Robin TCs contain a free parameter, which has a significant effect on the convergence rate of the SWR algorithm, and optimizing this parameter is an important step for the convergence analysis of the SWR algorithm. By studying the monotonic properties of the convergence factor obtained by applying the Fourier transform to the error functions, we provide a realiable choice of the Robin parameter in the nonoverlapping case. Numerical results are provided, which show that the analyzed Robin parameter results in satisfactory convergence rate.