A normalized three-dimensional (3-D) multilevel fast multipole algorithm (MLFMA) with a computational complexity of O(N) for very low-frequency (LF) problems is developed. This 3-D LF-MLFMA can be used not only independently for very low-frequency cases or very small structures compared to the wavelength, but also to solve large-scale structures with rapidly varying areas when merged with a general dynamic algorithm. From the LF–MLFMA, a more explicit and succinct representation of the static MLFMA is also derived.
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Zhao et al. (2000) studied this question.
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