A staggered upwind embedded boundary (SUEB) method to eliminate the FDTD staircasing error

In spite of its flexibility and second-order accuracy in a homogeneous medium, Yee's finite-difference time-domain (FDTD) method suffers from serious degradation when treating material interfaces, greatly reducing its accuracy in the presence of inhomogeneous media and perfect conductors. Indeed, such so-called staircasing approximation may lead to local zeroth-order and global first-order errors. In this work, an embedded FDTD scheme, the staggered upwind embedded boundary (SUEB) method, is developed for the solution of one- and two-dimensional Maxwell's equations. This simple embedded technique uses upwind conditions in the FDTD method to correctly represent the location and physical conditions of material and metallic boundaries, hence eliminating problems caused by the staircasing approximation. Accuracy analysis has been made to show that the SUEB method maintains a second-order accuracy globally. Since the entire problem has been embedded into the simple staggered grid similar to that employed by the Yee's scheme, extra effort is only needed when treating the grid points close to the interfaces. Therefore, little additional computational cost is needed over Yee's scheme. The SUEB method has been validated by analytical solutions for plane wave normally incident to a planar boundary and for the TM wave propagation in the presence of a dielectric cylinder and a perfectly electrically conducting cylinder.