A normalized three-dimensional (3-D) multilevel fast multipole algorithm (M
LFMA) with a computational complexity of O(N)for very low-frequency (LF) pr
oblems is developed. This 3-D LF-MLFMA can be used nor only independently f
or very low-frequency cases or very small structures compared to the wavele
ngth, but also to solve large-scale structures with rapidly varying areas w
hen merged with a general dynamic algorithm. From the LF-MLFMA, a more expl
icit and succinct representation of the static MLFMA is also derived. (C) 2
000 John Wiley & Sons, Inc.