Time domain electromagnetic field computation with a semi-discrete scheme as an alternative to implicit FDTD methods

A novel semi-discrete scheme is presented as an alternative to the implicit FDTD methods. This new scheme is also unconditionally stable, with much better numerical dispersion and no truncation errors in time-domain. A preliminary numerical experiment for one-dimensional propagation in free space shows that this semi-discrete scheme is still accurate even when the time step size is equal to or larger than the Nyquist rate, which outperforms the alternate-direction-implicit (ADI) FDTD and the Crank-Nicolson (CN) FDTD methods. The efficiency of this new scheme depends on the algorithm of computing the matrix exponential of a sparse matrix. A MATLAB implementation of this scheme is slow, but can be improved in the future