A POD reduced-order finite difference time-domain extrapolating scheme for the 2D Maxwell equations in a lossy medium

This paper is concerned with establishing a reduced-order finite difference time-domain (FDTD) extrapolating scheme based on proper orthogonal decomposition (POD) method for the two-dimensional (2D) Maxwell equations in a lossy medium. For this purpose, we first review the classical FDTD scheme and associated results for the 2D Maxwell equations in a lossy medium. And then, we formulate three sets of POD bases by means of the solutions obtained from the classical FDTD scheme on the very short time interval, establish the POD reduced-order FDTD extrapolating scheme, and furnish the error estimates among the POD reduced-order FDTD solutions and the classical FDTD solutions as well as the accuracy solution for the 2D Maxwell equations in a lossy medium. Finally, we enumerate two numerical examples to confirm that the POD reduced-order FDTD extrapolating scheme is feasible and efficient for simulating the phenomena for the electric and magnetic fields in a lossy medium.