Convergent finite element methods for antiferromagnetic and ferrimagnetic materials
Normington, Hywel and Ruggeri, Michele (2023) Convergent finite element methods for antiferromagnetic and ferrimagnetic materials. Other. arXiv.org, Ithaca, NY. (https://doi.org/10.48550/arXiv.2312.04939)
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Abstract
We consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations averaging the spins of two sublattices. For the static setting, which requires the solution of a constrained energy minimization problem, we introduce a discretization based on first-order finite elements and prove its Γ-convergence. Then, we propose and analyze two iterative algorithms for the computation of low-energy stationary points. The algorithms are obtained from (semi-)implicit time discretizations of gradient flows of the energy. Finally, we extend the algorithms to the dynamic setting, which consists of a nonlinear system of two Landau-Lifshitz-Gilbert equations solved by the two fields, and we prove unconditional stability and convergence of the finite element approximations toward a weak solution of the problem. Numerical experiments assess the performance of the algorithms and demonstrate their applicability for the simulation of physical processes involving antiferromagnetic and ferrimagnetic materials.
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Item type: Monograph(Other) ID code: 88194 Dates: DateEvent8 December 2023PublishedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 15 Feb 2024 11:32 Last modified: 09 Apr 2024 04:48 URI: https://strathprints.strath.ac.uk/id/eprint/88194