Affiliations: [a] School of Science, Sichuan University of Science and Technology, Zigong 643000, Sichuan, P. R. China. wushulin_ylp@163.com | [b] Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, Sichuan, P. R. China. wuguocheng@gmail.com
Correspondence:
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Address for correspondence: Sichuan University of Science and Technology, Zigong 643000, Sichuan, P. R. China
Note: [†] The first author is supported by the NSF of China (No. 11301362), the China Postdoctoral Foundation (No. 2015M580777, No. 2016T90841), the NSF of Sichuan Province (No. 2014JQ0035, 15ZA0220) and the NSF of SUSE (No. 2015LX01).
Note: [‡] The second author is supported by the NSF of China (No. 11301257) and the Seed Funds for Major Science and Technology Innovation Projects of Sichuan Provincial Education Department (14CZ0026)
Abstract: 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.
