Trefftz-based methods for time-harmonic acoustics

Archives of Computational Methods in Engineering

Volumn 14, Issue 4, 2007, Pages 343-381

  Pluymers, B ^a   Van Hal, B ^a   Vandepitte, D ^a   Desmet, W ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38149084686     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11831-007-9010-x     Document Type: Article

References (159)

1. Morse P, Ingard K (1968) Theoretical acoustics. McGraw-Hill, New York
2. Pierce A (1981) Acoustics: an introduction to its physical principles and applications. McGraw-Hill series in mechanical engineering. McGraw-Hill, New York
3. Zienkiewicz OC, Taylor RL, Zhu JZ, Nithiarasu P (2005) The finite element method-the three volume set, 6th edn. Butterworth-Heinemann, London
4. Ihlenburg F (1998) Finite element analysis of acoustic scattering. Applied Mathematical Sciences, vol 132. Springer, New York
5. Brebbia CA, Telles JCF, Wrobel LCL (1984) Boundary element techniques: theory and applications in engineering. Springer, New York
6. Kirkup S (1998) The boundary element method in acoustics. Integrated Sound Software
7. Von Estorff O (2000) Boundary elements in acoustics: advances and applications. WIT Press
8. Zienkiewicz OC (2000) Achievements and some unsolved problems of the finite element method. Int J Num Methods Eng 47:9-28
9. Proceedings of the fifth world congress on computational mechanics, Vienna, Austria, 2002
10. Proceedings of the European congress on computational methods in applied sciences and engineering, Jyvaskyla, Finland, 2004
11. Proceedings of the 2004 international conference on noise and vibration engineering, Leuven, Belgium, 2004
12. Proceedings of the 13th international congress on sound and vibration, Vienna, Austria, 2006
13. Proceedings of the 2006 international conference on noise and vibration engineering, Leuven, Belgium, 2006
14. Desmet W (2002) Mid-frequency vibro-acoustic modelling: challenges and potential solutions. In: Proceedings of the 2002 international conference on noise and vibration engineering, Leuven, Belgium, pp 835-862
15. Harari I (2006) A survey of finite element methods for time-harmonic acoustics. Comput Methods Appl Mech Eng 195:1594-1607
16. Thompson LL (2006) A review of finite element methods for time-harmonic acoustics. J Acoust Soc Am 119:1315-1330
17. Trefftz E (1926) Ein Gegenstück zum Ritzschen Verfahren. In: Proceedings of the 2nd international congress on applied mechanics, Zürich, Switzerland, pp 131-137
18. Jirousek J, Wróblewski A (1996) T-elements: state of the art and future trends. Arch Comput Methods Eng 3:323-434
19. Kita E, Kamiya N (1995) Trefftz method: an overview. Adv Eng Softw 24:3-12
20. Desmet W, Van Hal B, Sas P, Vandepitte D (2002) A computationally efficient prediction technique for the steady-state dynamic analysis of coupled vibro-acoustic systems. Adv Eng Softw 33:527-540
21. Van Hal B, Desmet W, Vandepitte D, Sas P (2003) A coupled finite element-wave based approach for the steady-state dynamic analysis of acoustic systems. J Comput Acoust 11:255-283
22. Pluymers B, Desmet W, Vandepitte D, Sas P (2004) Application of an efficient wave based prediction technique for the analysis of vibro-acoustic radiation problems. J Comput Appl Math 168:353-364
23. Pluymers B, Desmet W, Vandepitte D, Sas P (2005) On the use of a wave based prediction technique for steady-state structural-acoustic radiation analysis. J Comput Model Eng Sci 7(2):173-184
24. Van Hal B, Desmet W, Vandepitte D (2005) Hybrid finite element-wave based method for steady-state interior structural-acoustic problems. Comput Struct 83:167-180
25. Colton D, Kress R (1998) Inverse acoustic and electromagnetic scattering theory, 2nd edn. Springer, New York
26. Desmet W (2006) Boundary element method in acoustics. Course notes ISAAC17: seminar on advanced techniques in applied and numerical acoustics, Leuven, Belgium, September 2006
27. Wolf JP, Song C (1996) Finite element modelling of unbounded media. Wiley, Chichester
28. Thompson LL, Pinsky PM (2004) Acoustics. Encyclopedia of computational mechanics
29. Shirron JJ, Babuška I (1998) A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems. Comput Methods Appl Mech Eng 164:121-139
30. Givoli D (2004) High-order local non-reflecting boundary conditions: a review. Wave Motion 39:319-326
31. Keller JB, Givoli D (1989) Exact non-reflecting boundary conditions. J Comput Phys 82:172-192
32. Harari I, Patlashenko I, Givoli D (1998) Dirichlet-to-Neumann maps for unbounded wave guides. J Comput Phys 143:200-223
33. Nicholls DP, Nigam N (2004) Exact non-reflecting boundary conditions on general domains. J Comput Phys 194:278-303
34. Bettess P (1992) Infinite elements. Penshaw
35. Gerdes K (2000) A review of infinite element methods for exterior Helmholtz problems. J Comput Acoust 8:43-62
36. Burnett DS, Holford RL (1998) Prolate and oblate spheroidal acoustic infinite elements. Comput Methods Appl Mech Eng 158:117-141
37. Burnett DS, Holford RL (1998) An ellipsoidal acoustic infinite element. Comput Methods Appl Mech Eng 164:49-76
38. Astley RJ, Macaulay GJ, Coyette JP (1994) Mapped wave envelope elements for acoustical radiation and scattering. J Sound Vib 170:97-118
39. Astley RJ, Macaulay GJ, Coyette JP, Cremers L (1998) Three-dimensional wave-envelope elements of variable order for acoustic radiation and scattering. Part I. Formulation in the frequency domain. J Acoust Soc Am 103:49-63
40. Astley RJ, Coyette JP (2001) The performance of spheroidal infinite elements. Int J Numer Methods Eng 52:1379-1396
41. Berenger J-P (1994) A perfectly matched layer for the absorption of electromagnetic waves. J Comput Phys 114:185-200
42. Collino F, Monk P (1998) The perfectly matched layer in curvilinear coordinates. SIAM J Sci Comput 19:2061-2090
43. Bouillard P, Ihlenburg F (1999) Error estimation and adaptivity for the finite element method in acoustics: 2D and 3D applications. Comput Methods Appl Mech Eng 176:147-163
44. Bartsch G, Wulf C (2003) Adaptive multigrid for Helmholtz problems. J Comput Acoust 11:341-350
45. Harari I, Avraham D (1997) High-order finite element methods for acoustic problems. J Comput Acoust 5:33-51
46. Dey S, Datta DK, Shirron JJ, Shephard MS (2006) p-Version FEM for structural acoustics with a posteriori error estimation. Comput Methods Appl Mech Eng 195:1946-1957
47. Burnett DS (2004) 3D Structural acoustic modelling with hp-adaptive finite elements. In: Proceedings of the XXI international congress of theoretical and applied mechanics ICTAM, Warsaw, Poland
48. Ainsworth M, Oden TJ (1997) Posteriori error estimation in finite element analysis. Comput Methods Appl Mech Eng 142:1-88
49. Zienkiewicz OC (2006) The background of error estimation and adaptivity in finite element computations. Comput Methods Appl Mech Eng 195:207-213
50. Oden JT, Prudhomme S, Demkowicz L (2005) A posteriori error estimation for acoustic wave propagation. Arch Comput Methods Eng 12:343-390
51. Thompson LL, Kunthong P (2005) A residual based variational method for reducing dispersion error in finite element methods. In: Proceedings of the 2005 ASME international mechanical engineering congress and exposition, Orlando, Florida, USA, paper IMECE2005-80551
52. Guddati MN, Yue B (2004) Modified integration rules for reducing dispersion error in finite element methods. Comput Methods Appl Mech Eng 193:275-287
53. Duff I (1998) Direct methods. Technical Report RAL-TR-1998-054, Rutherford Appleton Laboratory, Oxon, USA
54. Saad Y (2003) Iterative methods for sparse linear systems, 2nd edn. SIAM, Philadelphia
55. Craig RR Jr (1981) Structural dynamics: an introduction to computer methods. Wiley, New York
56. Bennighof JK, Kaplan MF (1998) Frequency window implementation of adaptive multi-level substructuring. J Vib Acoust 120:409-418
57. Bennighof JK, Kaplan MF, Muller MB, Kim M (2000) Meeting the NVH computational challenge: automated multi-level substructuring. In: Proceedings of the international modal analysis conference XVIII, San Antonio, USA, pp 909-915
58. Kropp A, Heiserer D (2003) Efficient broadband vibro-acoustic analysis of passenger car bodies using an FE-based component mode synthesis approach. J Comput Acoust 11:139-157
59. Stryczek R, Kropp A, Wegner S (2004) Vibro-acoustic computations in the mid-frequency range: efficiency, evaluation and validation. In: Proceedings of the international conference on noise and vibration engineering ISMA2004, Leuven, Belgium, pp 1603-1612
60. Després B (1991) Méthodes de décomposition de domaine pour les problémes de propagation d'ondes en régime harmonique. PhD thesis, Paris IX Dauphine, Paris, France
61. Cai X, Casarin M, Elliott F Jr, Widlund O (1998) Overlapping Schwartz algorithms for solving Helmholtz's equation. Contemp Math 218:391-399
62. Farhat C, Macedo A, Lesoinne M (2000) A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems. Numer Math 85:283-308
63. Farhat C, Roux F-X (1991) A method of finite element tearing and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng 32:1205-1227
64. Farhat C, Macedo A, Lesoinne M, Roux F-X, Magoules F, de La Bourdonnaie A (2000) Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems. Comput Methods Appl Mech Eng 184:213-239
65. Datta DK, Dey S, Shirron JJ (2005) Scalable three-dimensional acoustics using hp-finite/infinite elements and FETI-DP. In: Proceedings of the 16th international domain decomposition conference, New York, USA
66. Magoules F (2006) Decomposition of domains in acoustics. http://www.iecn.u-nancy.fr/~magoules/pai/greenwich/aeroacoustics2/
67. Mandel J (2002) An iterative substructuring method for coupled fluid-solid acoustic problems. J Comput Phys 177:95-116
68. Harari I, Magoules F (2004) Numerical investigations of stabilized finite element computations for acoustics. Wave Motion 39:339-349
69. Harari I, Hughes TJR (1992) Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains. Comput Methods Appl Mech Eng 98:411-454
70. Thompson LL, Pinsky PM (1995) A Galerkin least squares finite element method for the two-dimensional Helmholtz equation. Int J Numer Methods Eng 38:371-397
71. Franca LP, Dutra do Carmo EG (1989) Galerkin gradient least-squares method. Comput Methods Appl Mech Eng 74:41-54
72. Harari I (1997) Reducing spurious dispersion, anisotropy and reflection in finite element analysis of time-harmonic acoustics. Comput Methods Appl Mech Eng 140:39-58
73. Babuška I, Ihlenburg F, Paik ET, Sauter SA (1995) A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution. Comput Methods Appl Mech Eng 128:325-359
74. Babuška I, Sauter SA (1997) Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM J Numer Anal 34:2392-2423
75. Yue B, Guddati MN (2003) Highly accurate local mesh-dependent augmented Galerkin (L-MAG) FEM for simulation of time-harmonic wave propagation. In: Proceedings of the 16th ASCE engineering mechanics conference, Seattle, USA
76. Melenk JM (1995) On generalized finite element methods. PhD thesis, University of Maryland at College Park
77. Babuška I, Melenk JM (1997) The partition of unity method. Int J Numer Methods Eng 40:727-758
78. Melenk JM, Babuška I (1996) The partition of unity finite element method: basic theory and applications. Comput Methods Appl Mech Eng 139:289-314
79. Laghrouche O, Bettess P (2000) Short wave modelling using special finite elements. J Comput Acoust 8:189-210
80. Strouboulis T, Babuška I, Copps K (2000) The design and analysis of the generalized finite element method. Comput Methods Appl Mech Eng 181:43-69
81. Strouboulis T, Copps K, Babuška I (2001) The generalized finite element method. Comput Methods Appl Mech Eng 190:4081-4193
82. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139:3-47
83. Bouillard P, Suleau S (1998) Element-free Galerkin solutions for Helmholtz problems: formulation and numerical assessment of the polution effect. Comput Methods Appl Mech Eng 162:317-335
84. Suleau S, Deraemaeker A, Bouillard P (2000) Dispersion and pollution of meshless solutions for the Helmholtz equation. Comput Methods Appl Mech Eng 190:639-657
85. Lacroix V, Bouillard P, Villon P (2003) An iterative defect-correction type meshless method for acoustics. Int J Numer Methods Eng 57:2131-2146
86. Lancaster P, Salkauskas K (1981) Surfaces generated by moving least squares methods. Math Comput 37:141-158
87. Hughes TJR (1995) Multiscale phenomena: Green's functions, Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Comput Methods Appl Mech Eng 127:387-401
88. Hughes TJR, Feijoo GR, Mazzei L, Quincy J-B (1998) The variational multiscale method-a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166:3-24
89. Franca L, Farhat C, Macedo A, Lesoinne M (1997) Residual-free bubbles for Helmholtz equation. Int J Numer Methods Eng 40:4003-4009
90. Brezzie F, Franca LP, Hughes TJR, Russo A (1997) b = f g. Comput Methods Appl Mech Eng 145:329-339
91. Cipolla JL (1999) Subgrid modeling in a Galerkin method for the Helmholtz equation. Comput Methods Appl Mech Eng 177:35-49
92. Oberai AA, Pinsky PM (1998) A multiscale finite element method for the Helmholtz equation. Comput Methods Appl Mech Eng 154:281-297
93. Farhat C, Harari I, Franca LP (2001) The discontinuous enrichment method. Comput Methods Appl Mech Eng 190:6455-6479
94. Farhat C, Harari I, Hetmaniuk U (2003) The discontinuous enrichment method for multiscale analysis. Comput Methods Appl Mech Eng 192:3195-3209
95. Marburg S (2002) Six boundary elements per wavelength: is that enough? J Comput Acoust 10:25-51
96. Harari I, Hughes TJR (1992) A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics. Comput Methods Appl Mech Eng 98:77-102
97. Herrin DW, Martinus F, Wu TW, Seybert AF (2006) An assessment of the high frequency boundary element and Rayleigh integral approximations. Appl Acoust 67:819-833
98. Nagy AB, Fiala P, Marki F, Augustinovicz F, Degrande G, Jacobs S, Brassenx D (2006) Prediction of interior noise in buildings generated by underground rail traffic. J Sound Vib 293:680-690
99. DeBiesme FX, Verheij JW, Verbeek G (2003) Lumped parameter BEM for faster calculations of sound radiation from vibrating structures. In: Proceedings of the tenth international congress on sound and vibration, Stockholm, Sweden, pp 1515-1522
100. DeBiesme FX, Verheij JW (2004) Speed gains of the lumped parameter boundary element method for vibroacoustics. In: Proceedings of the international conference on noise and vibration engineering ISMA2004, Leuven, Belgium, pp 3765-3778
101. Fahnline JB, Koopman GH (1996) A lumped parameter model for the acoustic power output from a vibrating structure. J Acoust Soc Am 100:3539-3547
102. Perrey-Debain E, Trevelyan J, Bettess P (2004) Wave boundary elements: a theoretical overview presenting applications in scattering of short waves. J Eng Anal Bound Elem 28:131-141
103. Perrey-Debain E, Laghrouche O, Bettess P, Trevelyan J (2004) Plane wave basis finite elements and boundary elements for three dimensional wave scattering. Phil Trans R Soc A 362:561-577
104. Chandler-Wilde NS, Langdon S, Ritter L (2004) A high-wavenumber boundary-element method for an acoustic scattering problem. Phil Trans R Soc A 362:647-671
105. Arden S, Chandler-Wilde NS, Langdon S (2005) A collocation method for high frequency scattering by convex polygons. Technical Report Numerical Analysis Report 7/05, Reading University
106. Huybrechs D, Vandewalle S (2006) On the evaluation of highly oscillatory integrals by analytic continuation. SIAM J Numer Anal 44:1026-1048
107. Huybrechs D, Vandewalle S (2005) The construction of cubature rules for multivariate highly oscillatory integrals. Technical Report Technisch rapport TW-442, KU Leuven
108. Huybrechs D, Vandewalle S (2006) A sparse discretisation for integral equation formulations of high frequency scattering problems. Technical Report Technisch rapport TW-447, KU Leuven
109. Huybrechs D (2006) Multiscale and hybrid methods for the solution of oscillatory integral equations. PhD thesis, KU Leuven, Leuven, Belgium. http://www.cs.kuleuven.be/~daan/phd/thesis.pdf
110. Sakuma T, Yasuda Y (2002) Fast multipole boundary element method for large-scale steady-state sound field analysis. Part I: setup and validation. Acustica 88:513-525
111. Yasuda Y, Sakuma T (2002) Fast multipole boundary element method for large-scale steady-state sound field analysis. Part I: examination of numerical items. Acustica 89:28-38
112. Schneider S (2003) Application of fast methods for acoustic scattering and radiation problems. J Comput Acoust 11:387-401
113. Fischer M, Gauger U, Gaul L (2004) A multipole Galerkin boundary element method for acoustics. Eng Anal Bound Elem 28:155-162
114. Yasuda Y, Sakuma T (2005) An effective setting of hierarchical cell structure for the fast multipole boundary element method. J Comput Acoust 13:47-70
115. Yasuda Y, Sakuma T (2005) A technique for plane-symmetric sound field analysis in fast multipole boundary element method. J Comput Acoust 13:71-86
116. Fischer M, Gaul L (2005) Fast BEM-FEM mortar coupling for acoustic-structure interaction. Int J Numer Methods Eng 62:1677-1690
117. Cheung YK, Jin WG, Zienkiewicz OC (1991) Solution of Helmholtz problems by Trefftz method. Int J Numer Methods Eng 32:63-78
118. Herrera I (1984) Boundary methods: an algebraic theory. Pitman, London
119. Masson P, Redon E, Priou J-P, Gervais Y (1994) The application of the Trefftz method for acoustics. In: Proceedings of the third international congress on sound and vibration, Montreal, Canada, pp 1809-1816
120. Sladek J, Sladek V, Van Keer R (2002) Global and local Trefftz boundary integral formulations for sound vibration. Adv Eng Softw 33:469-476
121. Zielinski AP, Zienkiewicz OC (1985) Generalized finite element analysis with T-complete boundary solution functions. Int J Numer Methods Eng 21:509-528
122. Zielinski AP, Herrera I (1987) Trefftz method: fitting boundary conditions. Int J Numer Methods Eng 24:871-891
123. Qin Q-H (2000) The Trefftz finite and boundary element method. WIT Press, Southampton
124. Kompis V, Stiavnicky M (2005) Trefftz functions in FEM, BEM and meshless methods. In: Proceedings of the 10th international conference on numerical methods for continuum mechanics & the 4th international workshop on Trefftz methods, Zilina, Slovak Republic
125. Ochmann M (1995) The source simulation technique for acoustic radiation problems. Acustica 81:512-527
126. Cessenat O, Deprés B (1998) Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem. SIAM J Numer Anal 35:255-299
127. Kansa EJ (1990) Multiquadrics: a scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to parabolic, hyperbolic and elliptic partial differential equations. Comput Math Appl 19:147-161
128. Van Hal B (2004) Automation and performance optimization of the wave based method for interior structural-acoustic problems. PhD thesis, KU Leuven, Leuven, Belgium. http://www.mech.kuleuven.be/dept/resources/docs/vanhal.pdf
129. Farhat C, Harari I, Hetmaniuk U (2003) A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency range. Comput Methods Appl Mech Eng 192:1389-1419
130. Tezaur R, Farhat C (2006) Three-dimensional discontinuous Galerkin elements with plane waves and Lagrange multipliers for the solution of mid-frequency Helmholtz problems. Int J Numer Methods Eng 66:796-815
131. Jirousek J, Wróblewski A (1994) Least-squares T-elements: equivalent FE and BE forms of substructure oriented boundary solution approach. Commun Numer Methods Eng 10:21-32
132. Stojek M (1996) Finite T-elements for the Poisson and Helmholtz equations. PhD thesis, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
133. Stojek M (1998) Least-squares Trefftz-type elements for the Helmholtz equation. Int J Numer Methods Eng 41:831-849
134. Monk P, Wang D-Q (1999) A least-squares method for the Helmholtz equation. Comput Methods Appl Mech Eng 175:121-136
135. Riou H, Ladeveze P, Rouch P (2004) Extension of the variational theory of complex rays to shells for medium-frequency vibrations. J Sound Vib 272:341-360
136. Desmet W (1998) A wave based prediction technique for coupled vibro-acoustic analysis. PhD thesis, KU Leuven, Leuven, Belgium. http://people.mech.kuleuven.ac.be/~wdesmet/desmet_phd_thesis.pdf
137. Pluymers B, Vanmaele C, Desmet W, Vandepitte D, Sas P (2004) Application of a novel wave based prediction technique for acoustic cavity analysis. In: Proceedings of the 30th German convention on acoustics (DAGA) together with the 7th congrès Francais d'acoustique (CFA), Strasbourg, France, pp 313-314
138. Pluymers B (2006) Wave based modelling methods for steady-state vibro-acoustics. PhD thesis, KU Leuven, Leuven, Belgium. http://people.mech. kuleuven.be/~bpluymer/docs/thesis_bpluymers.pdf
139. Pluymers B, Vanmaele C, Desmet W, Vandepitte D (2005) Application of a hybrid finite element-Trefftz approach for acoustic analysis. In: Proceedings of the 10th international conference on numerical methods for continuum mechanics & the 4th international workshop on Trefftz methods, Zilina, Slovak Republic
140. Van Genechten B, Pluymers B, Vanmaele C, Vandepitte D, Desmet W (2006) On the coupling of wave based models with modally reduced finite element models for structural-acoustic analysis. In: Proceedings of the international conference on noise and vibration engineering ISMA2006, Leuven, Belgium, pp 2383-2404
141. Benamou JD, Depres B (1997) A domain decomposition method for the Helmholtz equation and related optimal control problems. J Comput Phys 136:68-82
142. Koopmann GH, Song L, Fahnline JB (1989) A method for computing acoustic fields based on the principle of wave superposition. J Acoust Soc Am 86:2433-2438
143. Stupfel B, Lavie A, Decarpigny JH (1988) Combined integral equation formulation and null-field method for the exterior acoustic problem. J Acoust Soc Am 83:927-941
144. Reutskiy SY (2006) The method of fundamental solutions for Helmholtz eigenvalue problems in simply and multiply connected domains. Eng Anal Bound Elem 30:150-159
145. Ochmann M (1999) The full-field equations for acoustic radiation and scattering. J Acoust Soc Am 105:2574-2584
146. Ochmann M (2004) The complex equivalent source method for sound propagation over an impedance plane. J Acoust Soc Am 116:3304-3311
147. Pavic G (2005) An engineering technique for the computation of sound radiation by vibrating bodies using substitute sources. Acustica 91:1-16
148. Pavic G (2005) A technique for the computation of sound radiation by vibrating bodies using multipole substitute sources. In: Proceedings of the international congress on noise and vibration emerging methods (NOVEM2005), Saint-Raphael, France
149. Bouchet L, Loyau T, Hamzaoui N, Boisson C (2000) Calculation of acoustic radiation using equivalent-sphere methods. J Acoust Soc Am 107:2387-2397
150. Reboul E, Perret-Liaudet J, Le Bot A (2005) Vibroacoustic prediction of mechanisms using a hybrid method. In: Proceedings of the international congress on noise and vibration emerging methods (NOVEM2005), Saint-Raphael, France
151. Herrin DW, Wu TW, Seybert AF (2004) The energy source simulation method. J Sound Vib 278:135-153
152. Chen W (2002) Symmetric boundary knot method. Eng Anal Bound Elem 26:489-494
153. Goldbert MA, Chen CS (1999) The MFS for potential, Helmholtz and diffusion problems. In: Golberg MA (ed) Boundary integral methods: numerical and mathematical aspects. WIT Press and Computational Mechanics Publ, Boston Southampton, Chapter 4
154. Alves CJS, Valtchev SS (2005) Numerical comparison of two meshfree methods for acoustic wave scattering. Eng Anal Bound Elem 29:371-382
155. Limic N (1981) Galerkin-Petrov method for Helmholtz equation on exterior problems. Glas Math 36:245-260
156. Fairweather G, Kargeorghis A (1998) The MFS for elliptic BVPs. Adv Comput Math 9:69-95
157. Chen CS, Golberg MA, Schaback RS (2002) Transformation of domain effects to the boundary. In: Rashed YF (ed) Recent developments of the dual reciprocity method using compactly supported radial basis functions. WIT Press, Southampton, Chapter 8
158. Huttunen T, Gamallo P, Astley RJ (2006) Comparison of two wave element methods for the Helmholtz problem. Comput Methods Appl Mech Eng
159. Sas P, Desmet W, Van Hal B, Pluymers B (2001) On the use of a wave based prediction technique for vehicle interior acoustics. In: Proceedings of the Styrian noise, vibration & harshness congress: integrated vehicle acoustics and comfort, Graz, Austria, pp 175-185