A Plane-Wave Least-Squares Method for Time-Harmonic Maxwell's Equations in Absorbing Media

In this paper we discuss numerical methods for solving time-harmonic Maxwell equations in three-dimensional absorbing media. We propose a new variational problem on the space spanned by the plane-wave basis functions for the discretization of these types of equations. The variational problem is derived mathematically from a minimization problem, and the resulting stiffness matrix is Hermitian positive definite. A simple domain decomposition preconditioner is introduced for the system generated by the proposed variational formula. Numerical results indicate that the approximate solution generated by the proposed discretization method is clearly more accurate than that generated by the ultra weak variational formulation method, and the proposed preconditioner is effective.