Issue |
ESAIM: M2AN
Volume 38, Number 2, March-April 2004
|
|
---|---|---|
Page(s) | 371 - 394 | |
DOI | https://doi.org/10.1051/m2an:2004017 | |
Published online | 15 March 2004 |
Error estimates in the fast multipole method for scattering problems Part 1: Truncation of the Jacobi-Anger series
1
Dassault Aviation, 78, quai Marcel Dassault, Cedex 300,
92552 Saint-Cloud Cedex, France, quentin.carayol@dassault-aviation.fr.
2
CERFACS, 42 avenue G. Coriolis, 31057
Toulouse, France, Collino@cerfacs.fr.
Received:
1
July
2003
We perform a complete study
of the truncation error of the Jacobi-Anger series.
This series expands every
plane wave in terms of
spherical harmonics
.
We consider the truncated series where the summation is
performed over the
's satisfying
.
We prove that if
is large enough,
the truncated series gives rise to an error lower than ϵ
as soon as L satisfies
where W is the Lambert function and
are pure positive constants.
Numerical experiments show that this
asymptotic is optimal. Those results are
useful to provide sharp estimates for the
error in the fast multipole method for
scattering computation.
Mathematics Subject Classification: 33C10 / 33C55 / 41A80
Key words: Jacobi-Anger / fast multipole method / truncation error.
© EDP Sciences, SMAI, 2004
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