TY - JOUR
T1 - Asymptotic Results of Schwarz Waveform Relaxation Algorithm for Time Fractional Cable Equations
AU - Shu-Lin Wu & Chengming Huang
JO - Communications in Computational Physics
VL - 2
SP - 390
EP - 415
PY - 2018
DA - 2018/10
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2017-0177
UR - https://global-sci.org/intro/article_detail/cicp/12756.html
KW - Schwarz waveform relaxation, fractional Cable equation, parameter optimization, asymptotic analysis.
AB - <p style="text-align: justify;">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.</p>