Year: 2019
Communications in Computational Physics, Vol. 25 (2019), Iss. 2 : pp. 390–415
Abstract
The equioscillation principle is an important rule to fix the parameter for the Schwarz waveform relaxation (SWR) algorithm with Robin transmission conditions. For parabolic PDEs with integer order temporal derivative, such a principle yields optimal Robin parameter, while in our previous study we found numerically that it is not always the case for time fractional PDEs: the Robin parameter determined by the equioscillation principle is sometimes far away from optimal. In this paper, by using the time fractional Cable equations as the model, we show that our previous finding does not happen occasionally but an inherent property of the SWR algorithm. Our analysis also reveals an essential difference between the asymptotic convergence rates in the overlapping and non-overlapping cases. Numerical results are provided to validate our theoretical analysis.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0177
Communications in Computational Physics, Vol. 25 (2019), Iss. 2 : pp. 390–415
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Schwarz waveform relaxation fractional Cable equation parameter optimization asymptotic analysis.