Second-order absorbing boundary conditions for marching-on-in-order scheme

In this letter, we derive second-order absorbing boundary conditions (ABCs) for a marching-on-in-order scheme, which is a time-domain method with weighted Laugerre polynomials and free of stability constraint. This method does not have to deal with time steps, and may be computationally much more efficient than conventional finite-difference time-domain (FDTD)methods with too many time steps to complete a solution. Starting from the three-dimensional (3-D) case of the marching-on-in-order scheme, we deduce a second-order ABC and apply it to a 3-D microstrip line example. The results show the second-order ABC performs better than the first-order one for guided wave problems.