מושגי ליבה
The authors construct a new class of higher-order implicit-explicit (IMEX) schemes for the Landau-Lifshitz equation that preserve the pointwise length constraint, satisfy a modified energy dissipation law, and have rigorous error estimates.
תקציר
The authors present a new class of higher-order IMEX schemes for the Landau-Lifshitz equation. The key features of these schemes are:
They are purely linear and only require solving decoupled or coupled elliptic equations at each time step.
They preserve the pointwise length constraint of the magnetization field.
They satisfy a modified energy dissipation law, and the numerical solutions are uniformly bounded.
The authors carry out a rigorous error analysis for the semi-discretized schemes up to fifth-order in a unified framework, establishing error estimates in l^∞(0, T; H^1(Ω)) ∩ l^2(0, T; H^2(Ω)) under mild conditions on the time step size and the exchange parameter.
The authors first reformulate the Landau-Lifshitz equation into an equivalent form that is more amenable to numerical treatment. They then construct the IMEX-GSAV (Generalized Scalar Auxiliary Variable) schemes and prove that the numerical solutions are uniformly bounded. Finally, they perform a detailed error analysis, deriving rigorous error estimates for the semi-discretized schemes up to fifth-order.