Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems

We present two different but related Lagrange multiplier based domain decom position (DD) methods for solving iteratively large-scale systems of equati ons arising from the finite element discretization of high-frequency exteri or Helmholtz problems. The proposed methods are essentially two distinct ex tensions of the regularized finite element tearing and interconnecting (FET I) method to indefinite or complex problems. The first method employs a sin gle Lagrange multiplier held to glue the local solutions at the subdomain i nterface boundaries. The second method employs two Lagrange multiplier fiel ds for that purpose. The key ingredients of both of these FETI methods are the regularization of each subdomain matrix by a complex lumped mass matrix defined on the subdomain interface boundary, and the preconditioning of th e global interface problem by a coarse second-level problem constructed wit h planar waves. We show numerically that both methods are scalable with res pect to the mesh size, the subdomain size, and the wavenumber, but that the FETI method with a single Lagrange multiplier field - labeled FETI-H (H fo r Helmholtz) in this paper - delivers superior computational performances. We apply the FETI-H method to the parallel solution on a 24-processor Origi n 2000 of an acoustic scattering problem with a submarine shaped obstacle, and report performance results that highlight the unique efficiency of this DD method for the solution of high frequency acoustic scattering problems. (C) 2000 Elsevier Science S.A. All rights reserved. MSG: 57; 49; 18; 20.