A preconditioning strategy for microwave susceptibility in ferromagnets

Abstract

3D numerical simulations of ferromagnetic materials can be compared with experimental results via microwave susceptibility. In this paper, an optimised computation of this microwave susceptibility for large meshes is proposed. The microwave susceptibility is obtained by linearisation of the Landau and Lifchitz equations near equilibrium states and the linear systems to be solved are very ill-conditionned. Solutions are computed using the Conjugate Gradient method for the Normal equation (CGN Method). An efficient preconditioner is developed consisting of a projection and an approximation of an ``exact'' preconditioner in the set of circulant matrices. Control of the condition number due to the preconditioning and evolution of the singular value decomposition are shown in the results.