Accurate error estimates in the fast multipole method for electromagnetics

Author

Carayol, Q. ; Collino, F.

Author_Institution

Dassault Aviation, Saint-Cloud, France

Volume

3

fYear

2004

fDate

20-25 June 2004

Firstpage

3381

Abstract

The fast multipole method (FMM) is useful for solving electromagnetic scattering problems through integral equations. Some asymptotic laws are given for the truncation of the series involved in the FMM. Those laws were rigorously proved in Carayol (2002). For the first time, the accuracy of the widely used empirical formulas was studied mathematically. Our results also give some elements to understand the difference of FMM error due to the configuration of points in FMM boxes (connected to the term u&capped;· v&capped;). We also derived in Carayol some consequences on the number of quadrature points needed for the numerical integrations in the FMM.

Keywords

computational electromagnetics; electromagnetic wave scattering; error analysis; integral equations; integration; series (mathematics); FMM boxes; FMM error; electromagnetic scattering; electromagnetics; error estimates; fast multipole method; integral equations; numerical integrations; point configuration; quadrature points; series truncation; Finite wordlength effects; H infinity control; Jacobian matrices; Polynomials; Testing;

fLanguage

English

Publisher

ieee

Conference_Titel

Antennas and Propagation Society International Symposium, 2004. IEEE

Print_ISBN

0-7803-8302-8

Type

conf

DOI

10.1109/APS.2004.1332105

Filename

1332105