The Fast Multipole Method I: Error Analysis and Asymptotic Complexity

Authors:
Eric Darve
Affiliations:
-
Venue:
SIAM Journal on Numerical Analysis
Year:
2000

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Abstract

This paper is concerned with the application of the fast multipole method (FMM) to the Maxwell equations. This application differs in many aspects from other applications such as the N-body problem, Laplace equation, and quantum chemistry, etc. The FMM leads to a significant speed-up in CPU time with a major reduction in the amount of computer memory needed when performing matrix-vector products. This leads to faster resolution of scattering of harmonic plane waves from perfectly conducting obstacles. Emphasis here is on a rigorous mathematical approach to the problem. We focus on the estimation of the error introduced by the FMM and a rigorous analysis of the complexity (O(n log n)) of the algorithm. We show that error estimates reported previously are not entirely satisfactory and provide sharper and more precise estimates.