Dynamical micromagnetics by the finite element method

We developed a new numerical procedure to study dynamical behavior in micromagnetic systems. This procedure solves the damped Gilbert equation for a continuous magnetic medium, including all interactions in standard micromagnetic theory in three-dimensional regions of arbitrary geometry and physical properties. The magnetization is linearly interpolated in each tetrahedral element in a finite element mesh from its value on the nodes, and the Galerkin method is used to discretize the dynamic equation. We compute the demagnetizing field by solution of Poisson's equation and treat the external region by means of an asymptotic boundary condition. The procedure is implemented in the general purpose dynamical micromagnetic code (GDM). GDM uses a backward differential formula to solve the stiff ordinary differential equations system and the generalized minimum residual method with an incomplete Cholesky conjugate gradient preconditioner to solve the linear equations. GDM is fully parallelized using MPI and runs on massively parallel processor supercomputers, clusters of workstations, and single processor computers. We have successfully applied GDM to studies of the switching processes in isolated prolate ellipsoidal particles and in a system of multiple particles.