Asymptotic Results of Schwarz Waveform Relaxation Algorithm for Time Fractional Cable Equations (Communications in Computational Physics, 2018)
The equioscillation principle is an important rule to fix the parameter for theSchwarz waveform relaxation (SWR) algorithm with Robin transmission conditions.For parabolic PDEs with integer order temporal derivative, such a principle yieldsoptimal Robin parameter, while in our previous study we found numerically that itis not always the case for time fractional PDEs: the Robin parameter determined bythe equioscillation principle is sometimes far away from optimal. In this paper, byusing the time fractional Cable equations as the model, we show that our previousfinding does not happen occasionally but an inherent property of the SWR algorithm.Our analysis also reveals an essential difference between the asymptotic convergencerates in the overlapping and non-overlapping cases. Numerical results are providedto validate our theoretical analysis.