Reduced-Order Models for Electromagnetic Scattering Problems

We consider model-order reduction of systems occurring in electromagnetic scattering problems, where the inputs are current distributions operating in the presence of a scatterer, and the outputs are their corresponding scattered fields. Using the singular-value decomposition (SVD), we formally derive minimal-order models for such systems. We then use a discrete empirical interpolation method (DEIM) to render the minimal-order models more suitable to numerical computation. These models consist of a set of elementary sources and a set of observation points, both interior to the scatterer, and located automatically by the DEIM. A single matrix then maps the values of any incident field at the observation points to the amplitudes of the sources needed to approximate the corresponding scattered field. Similar to a Green's function, these models can be used to quickly analyze the interaction of the scatterer with other nearby scatterers or antennas.