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Efficient Computation of Multi-Frequency Far-Field Solutions of the Helmholtz Equation Using Padé Approximation

2000; World Scientific; Volume: 8; Issue: 1 Linguagem: Inglês

10.1016/s0218-396x(00)00014-5

1793-6489

M. Malhotra,

Electromagnetic Simulation and Numerical Methods

Journal of Computational AcousticsVol. 08, No. 01, pp. 223-240 (2000) No AccessEFFICIENT COMPUTATION OF MULTI-FREQUENCY FAR-FIELD SOLUTIONS OF THE HELMHOLTZ EQUATION USING PADÉ APPROXIMATIONMANISH MALHOTRA and PETER M. PINSKYMANISH MALHOTRADepartment of Mechanical Engineering, Stanford University, CA 94305–4040, USAPresent address: Sun Microsystems, UMPK24-201, 901 San Antonio Road, Palo Alto 94303. Search for more papers by this author and PETER M. PINSKYDepartment of Mechanical Engineering, Stanford University, CA 94305–4040, USA Search for more papers by this author https://doi.org/10.1142/S0218396X00000145Cited by:19 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractFor many problems in exterior structural acoustics, the solution is required to be computed over multiple frequencies. For some classes of these problems, however, it may be sufficient to evaluate the multiple frequency solutions over restricted regions of the spatial domain. Examples include optimization and inverse problems based on the minimization of a functional defined over a specified surface or sub-region. For such problems, which include both near-field and far-field computations, we recently proposed an efficient algorithm to compute the partial-field solutions at multiple frequencies simultaneously. In this paper, we consider the particular case of far-field computations and simplify the recently proposed algorithm by exploiting the symmetry of linear operators. The approach involves a reformulation of the Dirichlet-to-Neumann (DtN) map based finite-element matrix problem into a transfer-function form that can efficiently describe the far-field solution. A multi-frequency approximation of the transfer function is developed by constructing matrix-valued Padé approximation of the transfer function via a symmetric, banded Lanczos process. Numerical tests illustrate the accuracy of the approach for a wide range of frequencies and cost reductions of an order of magnitude when compared to commonly used factorization based methods. FiguresReferencesRelatedDetailsCited By 19Efficient multi-frequency solutions of FE–BE coupled structural–acoustic problems using Arnoldi-based dimension reduction approachXiang Xie and Yijun Liu1 Dec 2021 | Computer Methods in Applied Mechanics and Engineering, Vol. 386Application of a Krylov subspace method for an efficient solution of acoustic transfer functionsChristopher Sittl, Steffen Marburg and Marcus Wagner1 Feb 2021 | Mechanical Systems and Signal Processing, Vol. 148AcousticsLonny L. Thompson and Peter M. 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Pinsky15 November 2004Application of Padé via Lanczos approximations for efficient multifrequency solution of Helmholtz problemsMarcus M. Wagner, Peter M. Pinsky and Manish Malhotra1 Jan 2003 | The Journal of the Acoustical Society of America, Vol. 113, No. 1Developments in structural-acoustic optimization for passive noise controlSteffen Marburg1 Dec 2002 | Archives of Computational Methods in Engineering, Vol. 9, No. 4Multifrequency Analysis using Matrix Padé–via–LanczosJames P. Tuck–Lee, Peter M. Pinsky and Haw–Ling Liew Recommended Vol. 08, No. 01 Metrics History Received 19 July 1999 Revised 7 December 1999 PDF download