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

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.