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A stable and fast marching-on-in-time based integral-equation solver for analyzing low-frequency electromagnetic transients is presented. Stability and computational efficiency are achieved by using a frequency-normalized and diagonally balanced loop-tree decomposition scheme in concert with a novel fast Fourier transform (FFT)-based acceleration scheme. The proposed algorithm extends the time-domain adaptive integral method (TD-AIM) into the low-frequency regime by accelerating the computations of not only (discrete) "delayed" interactions due to fields observed one or more time steps after being generated but also "instantaneous" interactions due to fields observed less than one time step after being launched. This is realized by augmenting the four-dimensional blocked space-time FFTs in the TD-AIM recipe with three-dimensional space-only FFTs. Application of the extended TD-AIM accelerated integral-equation solver to the analysis of package geometries demonstrates its accuracy, stability, and efficiency.