A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies

Abstract

A Krylov subspace projection method which provides simultaneous solutions of the Helmholtz equation at multiple frequencies in one solution step is presented. The projector is obtained with an unsymmetric block Lanczos algorithm applied to a transfer function derived from a finite element discretization. This approach is equivalent to a matrix-valued Padé approximation of the transfer function. The proposed method is an extension of the formulation presented in [J. Comput. Acoust. 8 (2000) 223] to unsymmetric systems and allows the treatment of a much wider range of practical problems, including near-field and fluid–structure interaction computations.