Reduction of FDTD simulation time with modal methods

In order to simulate electromagnetic phenomena at high frequencies, full wave solvers such as the FDTD method must be used. An alternative to the conventional FDTD method is to compute the zero state response with convolution. Convolution results in an increased computation time with every time step. By performing eigenmodal decomposition of the inputs, a constant time for the convolution can be achieved. We show how the solution can be constructed analytically in terms of the eigenvalues and the eigenvectors of the state transition matrix.