AIMx: An Extended Adaptive Integral Method for the Fast Electromagnetic Modeling of Complex Structures
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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. In this work, a novel algorithm is proposed for reducing the cost-per-frequency associated with 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, which contains the singularity of the kernel, and a frequency-dependent term, which is a smooth function. The expensive near-region computations are only required for the frequency-independent term, and can be reused at each frequency point, leading to significantly faster frequency sweeps. The frequency-dependent term is accurately captured via the AIM even in the near region, as confirmed through 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.
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