Three-dimensional multilevel fast multipole algorithm from static to electrodynamic

Abstract

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. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 26: 43–48, 2000.

A Scalable Parallel Wideband MLFMA for Efficient Electromagnetic Simulations on Large Scale Clusters

“…Hence, the classical MLFMA is inefficient or numerically unstable when applied to sub-wavelength problems, where the domain is discretized at a rate higher than to capture the geometric details. These limitations have been reported in detail in [36] and several alternatives have been proposed to overcome them [5], [8]- [10]. In this work we employ the accelerated Cartesian expansion (ACE) [11].…”

A Low Frequency Vector Fast Multipole Algorithm with Vector Addition Theorem

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In the low-frequency fast multipole algorithm (LF-FMA) [19,20], scalar addition theorem has been used to factorize the scalar Green's function. Instead of this traditional factorization of the scalar Green's function by using scalar addition theorem, we adopt the vector addition theorem for the factorization of the dyadic Green's function to realize memory savings.

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“…In addition, we know that the floating-point operations for applying the basis rearrangement also scale as O(N R ) [19,21]. Therefore, the computational complexity of the LF-VFMA is clearly O(N R ), which is the same as that of the LF-FMA.…”

Efficient fast multipole method for low-frequency scattering

“…0), numerical instabilities may occur at very low frequency. This procedure is described in [13,14]. See [15] for an application of LF-MLFMA to low-frequency problems.…”