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

DOI10.1016/S0045-7825(03)00429-8zbMath1054.65031OpenAlexW2073910384MaRDI QIDQ1420986

Marcus M. Wagner, Manish Malhotra, Peter M. Pinsky, Assad A. Oberai

Publication date: 23 January 2004

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(03)00429-8

zbMATH Keywords

Padé approximationHelmholtz equationLanczos algorithmDirichlet-to-Neumann mapKrylov subspaceAcousticsMultiple-frequency solution

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Iterative numerical methods for linear systems (65F10) Hydro- and aero-acoustics (76Q05) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items

Review and assessment of interpolatory model order reduction methods for frequency response structural dynamics and acoustics problems, Acoustical topology optimization of Zwicker's loudness with Padé approximation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides
• The nonsymmetric Lanczos algorithm and controllability
• Matrix Padé approximation: Definitions and properties
• Exact non-reflecting boundary conditions
• Analysis of continuous formulations underlying the computation of time- harmonic acoustics in exterior domains
• Matrix interpretations and applications of the continued fraction algorithm
• Finite element analysis of acoustic scattering
• Error estimation on the Padé approximation of transfer functions via the Lanczos process
• On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation
• Asymptotic waveform evaluation via a Lanczos method
• Krylov-subspace methods for reduced-order modeling in circuit simulation
• On nonreflecting boundary conditions
• Finite element solution of electromagnetic problems over a wide frequency range via the Padé approximation
• A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems
• EFFICIENT COMPUTATION OF MULTI-FREQUENCY FAR-FIELD SOLUTIONS OF THE HELMHOLTZ EQUATION USING PADÉ APPROXIMATION
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• Boundary Conditions for the Numerical Solution of Elliptic Equations in Exterior Regions
• A Lanczos-type method for multiple starting vectors
• An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
• Numerical treatment of acoustic problems with the hybrid boundary element method
• A fast method for solving acoustic scattering problems in frequency bands