TY - JOUR A1 - Wagner, Marcus A1 - Pinsky, Peter M. A1 - Oberai, Assad A1 - Malhotra, Manish T1 - A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies JF - Computer Methods in Applied Mechanics and Engineering N2 - 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 KW - Multiple-frequency solution KW - Krylov subspace KW - Lanczos algorithm KW - Padé approximation KW - Helmholtz equation KW - Dirichlet-to-Neumann map KW - Acoustics Y1 - 2003 U6 - https://doi.org/10.1016/S0045-7825(03)00429-8 VL - 192 IS - 41-42 SP - 4609 EP - 4640 PB - Elsevier ER - TY - JOUR A1 - Sittl, Christopher A1 - Marburg, Steffen A1 - Wagner, Marcus T1 - Application of a Krylov subspace method for an efficient solution of acoustic transfer functions JF - Mechanical Systems and Signal Processing N2 - 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. KW - Lanczos algorithm KW - Krylov-subspace projection KW - Dirichlet-to-Neumann map KW - Padé approximation KW - Fluid–structure interaction KW - Acoustics Y1 - 2021 U6 - https://doi.org/10.1016/j.ymssp.2020.107135 VL - 148 PB - Elsevier ER - TY - JOUR A1 - Sittl, Christopher A1 - Marburg, Steffen A1 - Deckers, Elke A1 - Wagner, Marcus T1 - Model order reduction for unbounded second-order vibroacoustic systems using infinite elements and Dirichlet-to-Neumann map JF - Computer Methods in Applied Mechanics and Engineering N2 - This work addresses the efficient numerical simulation of time-harmonic vibroacoustic problems in unbounded domains, with a focus on fluid-structure interaction. The underlying mathematical model is a second-order dynamical system arising from the coupling of structural and acoustic domains, incorporating material damping effects, relevant in structural acoustics and noise control applications. A central novelty of the proposed method is its unified computational framework that supports two distinct strategies for treating unbounded fluid domains: (1) non-local absorbing boundary conditions based on Dirichlet-to-Neumann map, and (2) infinite elements, which extend the computational domain rather than truncate it. Both approaches are integrated into a consistent formulation that enables flexible and accurate modeling of exterior wave propagation. To efficiently evaluate frequency-domain transfer functions, the method employs model order reduction using the Padé-via-Lanczos technique. While this algorithm typically targets first-order systems, the present approach uses a Schur complement strategy to reduce the second-order system in a way that maintains computational efficiency and storage requirements comparable to first-order formulations. Importantly, the framework seamlessly embeds both interior structural damping and the additional dissipation introduced by the acoustic-domain truncation into the model-order reduction process. The exterior acoustic field is represented via spherical harmonic expansions, with expansion coefficients computed from the reduced system. Numerical results demonstrate the method’s accuracy, efficiency, and scalability, making it well-suited for high-fidelity vibroacoustic analysis in unbounded domains. KW - Lanczos algorithm KW - Krylov-subspace projection KW - Dirichlet-to-Neumann map KW - Infinite elements KW - Padé approximation KW - Fluid-structure interaction KW - Acoustics KW - Spherical harmonics Y1 - 2026 U6 - https://doi.org/10.1016/j.cma.2026.118846 VL - 453 PB - Elsevier ER -