Fast and efficient low-frequency algorithms for multiscale structure modeling

This paper reviews our recently developed fast and efficient algorithms for multiscale structure modeling. Low-frequency electromagnetic analysis becomes indispensable for multi-scale structures because of the involved minute length-scale compared to wavelength and mid length-scale on the order of wavelength or larger, where wave physics meets circuit physics. We are currently investigating stable low-frequency solutions in solving integral equations without the need for loop-tree decomposition, including the augmented EFIE, equivalence principle based algorithms, and perturbation-based Calderon multiplicative preconditioning methods.