A two-level domain decomposition method for the iterative solution of highfrequency exterior Helmholtz problems

We present a Lagrange multiplier based two-level domain decomposition metho d for solving iteratively large-scale systems of equations arising from the finite element discretization of high-frequency exterior Helmholtz problem s. The proposed method is essentially an extension of the regularized FETI (Finite Element Tearing and Interconnecting) method to indefinite problems. Its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix, and the preconditioning of the int erface problem by an auxiliary coarse problem constructed to enforce at eac h iteration the orthogonality of the residual to a set of carefully chosen planar waves. We show numerically that the proposed method is scalable with respect to the mesh size, the subdomain size, and the wavenumber. We repor t performance results for a submarine application that highlight the effici ency of the proposed method for the solution of high frequency acoustic sca ttering problems discretized by finite elements. Mathematics Subject Classi fication (1991): 65N55.