An efficient method for Maxwell’s equations with a discrete double-curl operator in split quaternionic electromagnetics
Institute of Mathematics and Information Science, North-Eastern Federal University, 677000, Yakutsk, Russia
2 School of Electronic Information, Shandong Xiandai University, 250104, Jinan, Shandong, People’s Republic of China
3 School of Mathematics and Statistics, Linyi University, 276005, Linyi, Shandong, People’s Republic of China
Accepted: 3 April 2023
Published online: 18 April 2023
In theoretical studies and numerical computations of three-dimensional electromagnetics, Maxwell’s equations play important roles. With the breakthroughs made by physicists in the field of high-dimensional electromagnetics, it has become possible to use split quaternion algebraic representations and solve some classical Maxwell’s equations. Especially, Maxwell’s equations with a discrete double-curl operator, which can be discretized into a generalized eigen-problem for a Hermitian matrix pencil. This paper studies Maxwell’s equations and the generalized eigen-problem of the matrix pencil over split quaternion algebra and proposes an efficient method for solving Maxwell’s equations with a discrete double-curl operator based on an isomorphic mapping. In addition, this paper obtains an algebraic method for the split quaternion generalized eigen-problem. Finally, numerical experiments show the feasibility of the proposed method in this paper.
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