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Respectively scaled splitting iteration method for a class of block 4-by-4 linear systems from eddy current electromagnetic problems

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Abstract

In this paper, we present a respectively scaled splitting (RSS) iteration method for the block 4-by-4 linear system from eddy current electromagnetic problems. Unconditional convergence properties of the RSS iteration method are established. Theoretical results show that the quasi-optimal iterative parameter that minimizes the spectral radius is \(\alpha _{opt}=1\) and the corresponding convergence factor is no more than \(\frac{1}{2}\). The validity of theoretical analysis and the effectiveness of RSS methods are verified by numerical experiments.

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Acknowledgements

The authors would like to thank the referees for the comments and constructive suggestions, which were valuable for improving the quality of the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Finance, Putian University, Putian, 351100, Fujian, People’s Republic of China

    Min-Li Zeng

  2. Key Laboratory of Financial Mathematics (Putian University), Fujian Province University, Putian, 351100, Fujian, People’s Republic of China

    Min-Li Zeng

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  1. Min-Li Zeng
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Correspondence to Min-Li Zeng.

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This work was supported by the National Natural Science Foundation of China (No. 11901324), the Natural Science Foundation of Fujian Province (No. 2020J01906) and the Program for Innovative Research Team in Science and Technology in Fujian Province University (No. 2018-39)

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Zeng, ML. Respectively scaled splitting iteration method for a class of block 4-by-4 linear systems from eddy current electromagnetic problems. Japan J. Indust. Appl. Math. 38, 489–501 (2021). https://doi.org/10.1007/s13160-020-00446-8

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  • DOI: https://doi.org/10.1007/s13160-020-00446-8

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