INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer.Meth. Engng 2001; 51:1175–1193 (DOI: 10.1002/nme.212) Iterative solution of large-scale acoustic scattering problems with multiple right hand-sides by a domain decomposition method with Lagrange multipliers Radek Tezaur, AntoniniMacedo and Charbel Farhat ∗; † Department of Aerospace Engineering; Center for Aerospace Structures; University of Colorado at Boulder; Boulder;CO80309;U.S.A. SUMMARY An extension of the FETI-H method is designed for the solution of acoustic scattering problems with multiple right-hand sides. A new localpre-conditioning of this domain decomposition method is also presented. The potential of the resulting iterative solver is demonstrated by numerical experiments for two-dimensional problems with high wavenumbers, as many as 2:5 million complex degrees of freedom, and a sweep on the angle of the incident wave.Preliminary results for a three-dimensional submarine problem are also included. The FETI-H method, whose numerical scalability with respect to the mesh and subdomain sizes was previously established, is shown here to be also numerically scalable with respect to the wavenumber. Copyright ? 2001 John Wiley & Sons, Ltd. KEY WORDS: acousticscattering; domain decomposition; FETI; multipleright-hand-sides; parallel processing 1. INTRODUCTION We considerthe scattering of time-harmonic acoustic waves by an impenetrable obstacle embedded in a homogeneous medium e ⊂ R d . This can be modelled by the following exterior Helmholtz boundary value problem −u − k 2 u = f in e u = u 0 on B D ∗ Correspondence to: CharbelFarhat,Department of AerospaceEngineering, CenterforAerospaceStructures, University of Colorado at Boulder,Boulder,CO 80309, U.S.A. † E-mail:charbel.farhat@colorado.edu Contract=grant sponsor: Oce of Naval Research; contract=grant number: N-00014-95-1-0663 Contract=grant sponsor: Brazilian CAPES Fellowship; contract=grant number: 1233=95-2 Received 7 July 1999 Copyright ? 2001 John Wiley & Sons, Ltd. Revised 7 November 2000