Projection-Based model-order reduction of large-scale Maxwell systems

Abstract

In this paper we present a structure-preserving model-order reduction technique to efficiently compute electromagnetic wave fields on unbounded domains. As an approximation space, we take the span of the real and imaginary parts of frequency-domain solutions of Maxwell's equations. Reduced-order models for the electromagnetic field belong to this space and the expansion coefficients of these models are determined from a Galerkin condition. We show that the models constructed in this manner are structure-preserving and interpolate the electromagnetic field responses at the expansion frequencies. Moreover, for monostatic field responses (coinciding sources and receivers), the first-order derivative of a reduced-order model with respect to frequency interpolates this first-order derivative of the unreduced monostatic field response as well. A two-dimensional numerical example illustrates the performance of the proposed reduction method.