A CONVERGENT NUMERICAL APPROXIMATION FOR THE COUPLED MAXWELL-LANDAU-LIFSHITZ-GILBERT EQUATIONS WITH INERTIA EFFECTS

Raymond Kitengeso; Zhoushun Zheng

doi:10.11948/20240364

2025 Volume 15 Issue 3

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Article navigation > Journal of Applied Analysis & Computation > 2025 > 15(3): 1719-1741

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Raymond Kitengeso, Zhoushun Zheng. A CONVERGENT NUMERICAL APPROXIMATION FOR THE COUPLED MAXWELL-LANDAU-LIFSHITZ-GILBERT EQUATIONS WITH INERTIA EFFECTS[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1719-1741. doi: 10.11948/20240364

Citation:

Raymond Kitengeso, Zhoushun Zheng. A CONVERGENT NUMERICAL APPROXIMATION FOR THE COUPLED MAXWELL-LANDAU-LIFSHITZ-GILBERT EQUATIONS WITH INERTIA EFFECTS[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1719-1741. doi: 10.11948/20240364

A CONVERGENT NUMERICAL APPROXIMATION FOR THE COUPLED MAXWELL-LANDAU-LIFSHITZ-GILBERT EQUATIONS WITH INERTIA EFFECTS

Raymond Kitengeso^1, ,,
Zhoushun Zheng^1,

1.
School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, China

Author Bio: Email: zszheng@csu.edu.cn(Z. Zheng)
Corresponding author: Email: kitengeso@csu.edu.cn(R. Kitengeso)
Fund Project: The authors were supported by the China Scholarship Council (2020GBJ00921) and the National Natural Science Foundation of China (51974377)

Abstract

Abstract

This study aims to analyze the coupled finite element and boundary element (FEM-BEM) solution to the nonlinear system of Maxwell and inertia Landau–Lifshitz–Gilbert equations. An algorithm is proposed to numerically solve the weak form of this problem, which requires solving coupled linear systems per time step. The algorithm is coupled in the sense that it consists of the sequential computation of the magnetic and electric fields in both the interior and boundary domains, and magnetization afterward. Under some mild assumptions on the effective field, the findings show that the algorithm converges towards a weak solution of the Maxwell-Inertia Landau–Lifshitz–Gilbert system. Numerical experiments demonstrate the algorithm's applicability for a theoretical micromagnetic example.
- Maxwell /
- Landau–Lifshitz–Gilbert /
- convergence /
- FEM-BEM
MSC: 35Q61, 65M12, 65M38, 65M60

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References

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