A local meshless collocation method for solving Landau–Lifschitz–Gilbert equation

This paper is concerned with a meshless simulation of the two dimensional Landau–Lifschitz–Gilbert (LLG) equation which describes the dynamics of the magnetization inside a ferromagnetic body. After elimination of the time variable by a suitable finite difference scheme, a combination of the meshless local RBF and the finite collocation method is used for spatial discretizations of the field variables. Three test problems are numerically investigated and the results reveal the effectiveness of the method.