Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The LLGE is obtained by assuming small deviation around the equilibrium state of system. Inserting such expansion into and keeping only first order terms gives LLGE, which frequency domain solution complex magnetization amplitudes an external applied field given frequency. solve linear system with iterative using generalized minimal residual method. construct preconditioner matrix to effectively validity, effectiveness, speed, scalability are demonstrated via numerical examples.