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math.NA2026
A linear mass-lumped finite element method for the Landau-Lifshitz-Gilbert equation: unconditional energy dissipation and length preservation
Qiumei Huang, Binghong Li, Xiaoli Li +2
We develop a linear, unconditionally energy-dissipative, mass-lumped finite element method for the highly nonlinear Landau--Lifshitz--Gilbert (LLG) equation on quasi-uniform triang…
math.NA2026
Stability and error analysis of fully discrete original energy-dissipative and length-preserving scheme for the Landau-Lifshitz-Gilbert equation
Binghong Li, Xiaoli Li, Cheng Wang +1
The Landau-Lifshitz-Gilbert (LLG) equation, regarded as a gradient flow with manifold constraint, is the fundamental model describing magnetization dynamics in ferromagnetic materi…
math.NA2026
Stability and convergence analysis of unconditionally original energy dissipative implicit-explicit Runge--Kutta methods for the phase field crystal models without Lipschitz assumptions
Xiaoli Li, Kaiyi Niu, Jiang Yang
The phase field crystal (PFC) method is an efficient technique for simulating the evolution of crystalline microstructures at atomistic length scales and diffusive time scales. Due…