  Surface integral equation (SIE) methods are of great interest for the
efficient electromagnetic modeling of various devices, from integrated circuits
to antenna arrays. Existing acceleration algorithms for SIEs, such as the
adaptive integral method (AIM), enable the fast approximation of interactions
between well-separated mesh elements. Nearby interactions involve the
singularity of the kernel, and must instead be computed accurately with direct
integration at each frequency of interest, which can be computationally
expensive. We propose a novel algorithm for reducing the cost-per-frequency of
near-region computations for both homogeneous and layered background media. In
the proposed extended AIM (AIMx), the SIE operators are decomposed into a
frequency-independent term containing the singularity of the kernel, and a
nonsingular frequency-dependent term. Direct integration is only required for
the frequency-independent term, and can be reused at each frequency, leading to
significantly faster frequency sweeps. The frequency-dependent term is captured
with good accuracy via fast Fourier transform (FFT)-based acceleration even in
the near region, as confirmed with an error analysis. The accuracy and
efficiency of the proposed method are demonstrated through numerical examples
drawn from several applications, and CPU times are significantly reduced by
factors ranging from three to 16.
