 
Summary: ALTERNATIVE INTEGRAL EQUATIONS FOR THE
ITERATIVE SOLUTION OF ACOUSTIC SCATTERING
PROBLEMS
by X. ANTOINE
(Math´ematiques pour l'Industrie et la Physique, MIP UMR5640, UFR MIG, Universit´e Paul
Sabatier, 118 route de Narbonne, 31062 Toulouse cedex, France)
and M. DARBAS
(D´epartement de G´enie Math´ematique, INSA, MIP UMR5640, Complexe Scientifique de
Rangueil, 31077, Toulouse cedex 4, France)
[Received 15 March 2003. Revises 3 November 2003 and 26 April 2004]
Summary
This paper addresses the first step of the derivation of wellconditioned integral formulations for
the iterative solution of exterior acoustic boundaryvalue problems. These new formulations are
designed to be implemented in a fast multipole method coupled to a Krylov subspace iterative
algorithm. Their construction is based on the onsurface radiation condition formalism. Both
theoretical developments and numerical aspects are examined in detail. This approach can be
viewed as a generalization of the usual BurtonMiller integral equations.
1. Introduction
A very popular method for solving the acoustic scattering problem of a timeharmonic wave in an
unbounded domain is provided by the integral equation method (1 to 3). Even if other efficient
