Frequency Interpolation of the Electromagnetic Surface Currents Via Singular Value Decomposition. Application to High-Frequency Analysis

The time-harmonic electromagnetic scattering from conducting surfaces is considered. In this context, a recently published model order reduction for frequency interpolation of the surface current via singular value decomposition (SVD) is analyzed and evaluated: the exact currents computed at
Q
frequencies are arranged columnwise in a matrix, the SVD of which provides an orthonormal basis; on account of the observed exponential decrease of the singular values of this matrix, it is assumed that the dimension of the basis required for an accurate interpolation is much smaller than the number of unknowns in the original formulation. We propose in this paper a formal framework that justifies this decrease of the singular values, as well as the corresponding behavior of the interpolation error made on the current. From considerations based on high-frequency electromagnetics, it is shown that this method can be interpreted in terms of sampling criteria for the current, that yield an
a

priori
estimate for the minimum value of
Q
. Numerical examples illustrate the capacities of this technique for frequency interpolation and for high-frequency analysis of the currents.