2024/07/01 by Agus L. Soenjaya, Soenjaya, Agus L. · 2 citations
Computer Science · Engineering · #35Q60 #65M12 #65M60 #Advanced Mathematical Modeling in Engineering #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2407.01125
openalex publication_date 2024/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Landau--Lifshitz--Baryakhtar (LLBar) and the Landau--Lifshitz--Bloch (LLBloch) equations are nonlinear vector-valued PDEs which arise in the theory of micromagnetics to describe the dynamics of magnetic spin field in a ferromagnet at elevated temperatures. We consider the LLBar and the regularised LLBloch equations in a unified manner, thus allowing us to treat the numerical approximations for both problems at once. In this paper, we propose a semi-discrete mixed finite element scheme and two fully discrete mixed finite element schemes based on a semi-implicit Euler method and a semi-implicit Crank--Nicolson method to solve the problems. These numerical schemes provide accurate approximations to both the magnetisation vector and the effective magnetic field. Moreover, they are proven to be unconditionally energy-stable and preserve energy dissipativity of the system at the discrete level. Error analysis is performed which shows optimal rates of convergence in \mathbbL2, \mathbbL^∞, and ℍ1 norms. These theoretical results are further corroborated by several numerical experiments.