Generation of FDTD subcell equations by means of reduced order modeling

Abstract

Adapted finite-difference time-domain (FDTD) update equations exist for a number of objects that are smaller than the grid step, such as wires and thin slots. We provide a technique that automatically generates new FDTD update equations for small objects. Our presentation focusses on 2D-FDTD. We start from the FDTD equations in a fine grid where the time derivative is not discretised. This yields a large state-space model that is drastically reduced with a reduced order modeling technique. The reduced state-space model is then translated into new FDTD update equations that can be used in an FDTD simulation in the same way as the existing update equations for wires and thin slots. This technique is applied to a number of numerical problems showing the accuracy and versatility of the proposed method.