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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
Application of a Krylov subspace method for an efficient solution of acoustic transfer functions
(2021)
Solving acoustic radiation problems, arising from systems including fluid–structure interaction, is of interest in many engineering applications. Computing frequency response functions over a large frequency range is a concern in such applications. A method which solves the Helmholtz equation for multiple frequencies in one step is the matrix-Padé-via-Lanczos connection for unsymmetric systems, as presented by Wagner et al. [1]. The present work is based on Ref. [1] and presents a method for efficiently computing frequency responses over a frequency range for coupled structural-acoustic problems, where the structure and the acoustic near field are discretized with finite elements and an analytical Dirichlet-to-Neumann map approximates the far field. The method is based on a Krylov-subspace projection technique which derives a matrix-valued Padé approximation for a restricted area in the near field and the pressure field on a spherical boundary. On the spherical boundary, where the finite domain is truncated, the non-local modified Dirichlet-to-Neumann operator is applied as a low-rank update matrix. The present contribution extends this method and incorporates new techniques for a more stable model reduction through the Lanczos algorithm and a novel weighted adaptive windowing technique. Further, structural damping is incorporated, for computing the acoustic radiation of a harmonically excited plate. These computed results are compared with acoustic measurements in an anechoic chamber and verified with computational results obtained with a commercial code that uses the perfectly matched layer method.