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 equati on for a continuous magnetic medium, including all interactions in sta ndard micromagnetic theory in three-dimensional regions of arbitrary g eometry and physical properties. The magnetization is linearly interpo lated in each tetrahedral element in a finite element mesh from its va lue on the nodes, and the Galerkin method is used to discretize the dy namic equation, We compute the demagnetizing field by solution of Poss ion's equation and treat the external region by means of an asymptotic boundary condition. The procedure is implemented in the general purpo se dynamical micromagnetic code (GDM). GDM uses a backward differentia l formula to solve the stiff ordinary differential equations system an d the generalized minimum residual method with an incomplete Cholesky conjugate gradient preconditioner to solve the linear equations. GDM i s fully parallelized using MPI and runs on massively parallel processo r supercomputers, clusters of workstations, and single processor compu ters. We have successfully applied GDM. to studies of the switching pr ocesses in isolated prolate ellipsoidal particles, and in a system of multiple particles.