A convergent linear finite element scheme for the Maxwell-Landau-Lifshitz-Gilbert equation
For researchers in computational micromagnetics, this provides convergent and efficient linear schemes for a challenging nonlinear system.
The paper proposes two linear finite element schemes for the Maxwell-Landau-Lifshitz-Gilbert equations, requiring only two linear solves per timestep, and proves convergence to weak solutions. Numerical tests on a benchmark problem show the methods' performance.
We consider a lowest-order finite element discretization of the nonlinear system of Maxwell's and Landau-Lifshitz-Gilbert equations (MLLG). Two algorithms are proposed to numerically solve this problem, both of which only require the solution of at most two linear systems per timestep. One of the algorithms is fully decoupled in the sense that each timestep consists of the sequential computation of the magnetization and afterwards the magnetic and electric field. Under some mild assumptions on the effective field, we show that both algorithms converge towards weak solutions of the MLLG system. Numerical experiments for a micromagnetic benchmark problem demonstrate the performance of the proposed algorithms.