A Trefftz based method for solving Helmholtz problems in semi-infinite domains

Engineering Analysis with Boundary Elements - Tập 36 - Trang 30-38 - 2012
Bart Bergen1, Bert Pluymers1, Bert Van Genechten1, Dirk Vandepitte1, Wim Desmet1
1K.U.Leuven, Department of Mechanical Engineering, division PMA, Celestijnenlaan 300B - box 2420, B-3001 Leuven, Belgium

Tài liệu tham khảo

Zienkiewicz, 2005 Harari, 2006, A survey of finite element methods for time-harmonic acoustics, Computer Methods in Applied Mechanics and Engineering, 195, 1594, 10.1016/j.cma.2005.05.030 Thompson, 2006, A review of finite element methods for time-harmonic acoustics, Journal of the Acoustical Society of America, 119, 1315, 10.1121/1.2164987 Givoli, 1993, Artificial boundary conditions for 2d problems in geophysics, Computer Methods in Applied Mechanics and Engineering, 110, 87, 10.1016/0045-7825(93)90021-O Coyette, 2000, A conjugated infinite element method for half-space acoustic problems, Journal of the Acoustical Society of America, 108, 1464, 10.1121/1.1289921 Zschiedrich, 2006, A new finite element realization of the perfectly matched layer method for Helmholtz scattering problems on polygonal domains in two dimensions, Journal of Computational and Applied Mathematics, 188, 12, 10.1016/j.cam.2005.03.047 Von Estorff, 2000 Bouillard, 1999, Error estimation and adaptivity for the finite element method in acoustics: 2D and 3D applications, Computer Methods in Applied Mechanics and Engineering, 176, 147, 10.1016/S0045-7825(98)00334-X Marburg, 2002, Six boundary elements per wavelength: Is that enough?, Journal of Computational Acoustics, 10, 25, 10.1142/S0218396X02001401 Boyd, 2001 Bialecki, 2008, Spectral Chebyshev–Fourier collocation for the Helmholtz and variable coefficient equations in a disk, Journal of Computational Physics, 227, 8588, 10.1016/j.jcp.2008.06.009 Trefftz E. Ein Gegenstück zum Ritzschen Verfahren. In: Proceedings of the 2nd international congress on applied mechanics, Zurich, Switzerland, 1926. p. 131–7. Koopmann, 1989, A method for computing acoustic fields based on the principle of wave superposition, Journal of the Acoustical Society of America, 86, 2433, 10.1121/1.398450 Chen, 2009, Equivalence between the Trefftz method and the method of fundamental solution for the annular Green's function using the addition theorem and image concept, Engineering Analysis with Boundary Elements, 33, 678, 10.1016/j.enganabound.2008.10.003 Alves, 2005, Numerical comparison of two meshfree methods for acoustic wave scattering, Engineering Analysis with Boundary Elements, 29, 371, 10.1016/j.enganabound.2004.09.008 Li, 2010, Comparisons of fundamental solutions and particular solutions for Trefftz methods, Engineering Analysis with Boundary Elements, 34, 248, 10.1016/j.enganabound.2009.10.001 Reutskiy, 2004, A Trefftz type method for time-dependent problems, Engineering Analysis with Boundary Elements, 28, 13, 10.1016/S0955-7997(03)00115-2 Kita, 2003, Indirect Trefftz method for boundary value problem of Poisson equation, Engineering Analysis with Boundary Elements, 27, 825, 10.1016/S0955-7997(03)00042-0 Desmet W. A wave based prediction technique for coupled vibro-acoustic analysis. PhD thesis 98D12, KULeuven, division PMA; 1998 URL 〈http://www.mech.kuleuven.be/mod/wbm/phd_dissertations〉. Vanmaele, 2009, An efficient wave based prediction technique for dynamic plate bending problems with corner stress singularities, Computer Methods in Applied Mechanics and Engineering, 198, 2227, 10.1016/j.cma.2009.01.015 Pluymers, 2007, Trefftz-based methods for time-harmonic acoustics, Archives of Computational Methods in Engineering, 14, 343, 10.1007/s11831-007-9010-x Desmet, 2002, A computationally efficient prediction technique for the steady-state dynamic analysis of coupled vibro-acoustic systems, Advances in Engineering Software, 33, 527, 10.1016/S0965-9978(02)00062-5 Sas, 1998, A wave-based prediction technique for vibroacoustics: comparison with the finite-element technique and experimental validation, Journal of the Acoustical Society of America, 103, 2770, 10.1121/1.421900 Pluymers, 2004, Application of an efficient wave based prediction technique for the analysis of vibro-acoustic radiation problems, Journal of Computational and Applied Mathematics, 168, 353, 10.1016/j.cam.2003.05.020 Pluymers, 2005, On the use of a wave based prediction technique for steady-state structural-acoustic radiation analysis, Journal of Computer Modeling in Engineering & Sciences, 7, 173 Van Genechten, 2010, A Trefftz-based numerical modelling framework for Helmholtz problems with complex multiple scatterer configurations, Journal of Computational Physics, 229, 6623, 10.1016/j.jcp.2010.05.016 Bergen, 2010, An efficient Trefftz-based method for three-dimensional Helmholtz problems in unbounded domains, Computer Modeling in Engineering & Sciences, 61, 155 Pierce, 1981 Colton, 1998 Pluymers B. Wave based modelling methods for steady-state vibro-acoustics. PhD thesis 2006D04, KULeuven, division PMA; 2006. URL 〈http://www.mech.kuleuven.be/mod/wbm/phd_dissertations〉. van Hal, 2005, Hybrid finite element—wave-based method for steady-state interior structural-acoustic problems, Computers & Structures, 83, 167, 10.1016/j.compstruc.2004.04.019 Van Genechten, 2009, A hybrid wave based—modally reduced finite element method for the efficient analysis of low- and mid-frequency car cavity acoustics, SAE International Journal of Passenger Cars—Mechanical Systems, 2, 1494, 10.4271/2009-01-2214 Genechten, 2010, A multi-level wave based numerical modelling framework for the steady-state dynamic analysis of bounded Helmholtz problems with multiple inclusions, Computer Methods in Applied Mechanics and Engineering, 199, 1881, 10.1016/j.cma.2010.01.013 Herrera, 1984 Bergen B, Van Genechten B, Pluymers B, Vandepitte D, Desmet W. Efficient wave based models for acoustic scattering and transmission problems using point source and plane wave excitation. In: Proceedings of the fourteenth international congress on sound and vibration (ICSV14), Cairns, Australia, 2007. Deckers, 2011, Spline-based boundaries: a first step towards generic geometric domain descriptions for efficient mid-frequency acoustic analysis using the wave based method, Journal of Computational and Applied Mathematics, 235, 2679, 10.1016/j.cam.2010.11.020 Li, 2008, Study on effective condition number for collocation methods, Engineering Analysis with Boundary Elements, 32, 839, 10.1016/j.enganabound.2008.02.001 Varah, 1979, A practical examination of some numerical methods for linear discrete ill-posed problems, SIAM Review, 21, 100, 10.1137/1021007