Convergence of numerical solution for the inhomogeneous Landau-Lifshitz equations with Gilbert damping

In this paper, we discuss the inhomogeneous Landau-Lifshitz equation with nonuniform Gilbert damping term by numerical method. First, we establish a semi-discrete form for the inhomogeneous Landau-Lifshitz equation with nonuniform Gilbert damping, which is continuous in time. Then we study the temporal discretization. It proposes a simple projection method to solve our issue. Finally, we prove that it is unconditionally stable.

Automated summary

The paper discusses the inhomogeneous Landau-Lifshitz equation with nonuniform Gilbert damping term using a numerical method. A semi-discrete form of the equation is established, which is continuous in time. The temporal discretization is studied and a simple projection method is proposed to solve the problem. It is proved that the method is unconditionally stable.