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A convergence theorem for the fast multipole method for 2 dimensional scattering problems

Author: Christophe Labreuche
Journal: Math. Comp. 67 (1998), 553-591
MSC (1991): Primary 41A58, 35J05, 65N30
MathSciNet review: 1458223
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Abstract: The Fast Multipole Method (FMM) designed by V. Rokhlin rapidly computes the field scattered from an obstacle. This computation consists of solving an integral equation on the boundary of the obstacle. The main result of this paper shows the convergence of the FMM for the two dimensional Helmholtz equation. Before giving the theorem, we give an overview of the main ideas of the FMM. This is done following the papers of V. Rokhlin. Nevertheless, the way we present the FMM is slightly different. The FMM is finally applied to an acoustic problem with an impedance boundary condition. The moment method is used to discretize this continuous problem.

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Additional Information

Christophe Labreuche
Affiliation: Thomson CSF-LCR, Domaine de Corbeville, 91404 Orsay cedex, France

Keywords: Fast Multipole Method, Helmholtz equation, Hankel function
Received by editor(s): December 11, 1995
Received by editor(s) in revised form: October 7, 1996
Article copyright: © Copyright 1998 American Mathematical Society