{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T21:58:18Z","timestamp":1648504698058},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2007,1,10]],"date-time":"2007-01-10T00:00:00Z","timestamp":1168387200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Mech"],"published-print":{"date-parts":[[2008,7]]},"DOI":"10.1007\/s00466-006-0153-7","type":"journal-article","created":{"date-parts":[[2007,1,9]],"date-time":"2007-01-09T12:16:53Z","timestamp":1168345013000},"page":"317-326","source":"Crossref","is-referenced-by-count":3,"title":["Some challenges in computational vibro-acoustics: verification, validation and medium frequencies"],"prefix":"10.1007","volume":"42","author":[{"given":"Ph.","family":"Bouillard","sequence":"first","affiliation":[]},{"given":"J. P. M.","family":"Almeida","sequence":"additional","affiliation":[]},{"given":"V.","family":"Decouvreur","sequence":"additional","affiliation":[]},{"given":"T.","family":"Mertens","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,1,10]]},"reference":[{"key":"153_CR1","doi-asserted-by":"crossref","unstructured":"Allard J-F (1993) Propagation of sound in porous media. Elsevier, ISBN 185166887","DOI":"10.1007\/978-94-011-1866-8"},{"key":"153_CR2","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.cma.2004.09.012","volume":"195","author":"JP Almeida","year":"2006","unstructured":"Almeida JP, Pereira O (2006) Upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems. Comput Methods Appl Mech Eng 195:279\u2013296","journal-title":"Comput Methods Appl Mech Eng"},{"key":"153_CR3","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1121\/1.421106","volume":"103","author":"R Astley","year":"1998","unstructured":"Astley R, Macaulay G, Coyette J-P, 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\u201363","journal-title":"J Acoust Soc Am"},{"key":"153_CR4","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/0045-7825(95)00890-X","volume":"128","author":"I Babu\u0161ka","year":"1995","unstructured":"Babu\u0161ka 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\u2013359","journal-title":"Comput Methods Appl Mech Eng"},{"key":"153_CR5","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1002\/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N","volume":"40","author":"I Babu\u0161ka","year":"1997","unstructured":"Babu\u0161ka I, Melenk J (1997) The partition of unity method. Int J Numer Methods Eng 40:727\u2013758","journal-title":"Int J Numer Methods Eng"},{"issue":"18","key":"153_CR6","doi-asserted-by":"crossref","first-page":"3443","DOI":"10.1002\/(SICI)1097-0207(19970930)40:18<3443::AID-NME221>3.0.CO;2-1","volume":"40","author":"I Babuska","year":"1997","unstructured":"Babuska I, Ihlenburg F, Strouboulis T et\u00a0al (1997) A posteriori error estimation for finite element solutions of Helmholtz\u2019 equation .1. The quality of local indicators and estimators. Int J Numer Methods Eng 40(18):3443\u20133462","journal-title":"Int J Numer Methods Eng"},{"key":"153_CR7","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1002\/nme.1620370205","volume":"37","author":"T Belytschko","year":"1994","unstructured":"Belytschko T, Lu Y.Y, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37:229\u2013256","journal-title":"Int J Numer Methods Eng"},{"issue":"1816","key":"153_CR8","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1098\/rsta.2003.1341","volume":"362","author":"P Bettess","year":"2004","unstructured":"Bettess P, Laghrouche O, Perrey-Debain E (2004) Short-wave scattering\u2014Introduction. Philos Trans Roy Soc London Ser A Math Phys Eng Sci 362(1816):417\u2013419","journal-title":"Philos Trans Roy Soc London Ser A Math Phys Eng Sci"},{"key":"153_CR9","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0045-7825(97)00350-2","volume":"162","author":"Ph Bouillard","year":"1998","unstructured":"Bouillard Ph, Suleau S (1998) Element-free Galerkin solutions for Helmholtz problems: formulation and numerical assessment of the pollution effect. Comput Methods Appl Mech Eng 162:317\u2013335","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"1\u20134","key":"153_CR10","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/S0045-7825(98)00334-X","volume":"176","author":"Ph Bouillard","year":"1999","unstructured":"Bouillard Ph, Ihlenburg F (1999) Error estimation and adaptivity for the finite element solution in acoustics: 2D and 3D applications. Comput Methods Appl Mech Eng 176(1\u20134): 147\u2013163","journal-title":"Comput Methods Appl Mech Eng"},{"key":"153_CR11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1002\/nme.1620320105","volume":"32","author":"YK Cheung","year":"1991","unstructured":"Cheung YK, Jin WG, Zienkiewicz OC (1991) Solution of Helmholtz equation by Trefftz method. Int J Numer Methods Eng 32:63\u201378","journal-title":"Int J Numer Methods Eng"},{"key":"153_CR12","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1002\/nme.1202","volume":"62","author":"E De Bel","year":"2005","unstructured":"De Bel E, Villon P, Bouillard Ph (2005) Forced vibrations in the medium frequency range solved by a partition of unity method with local information. Int J Numer Methods Eng 62:1105\u20131126","journal-title":"Int J Numer Methods Eng"},{"key":"153_CR13","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0045-7825(94)00726-4","volume":"122","author":"JF Debongnie","year":"1995","unstructured":"Debongnie JF, Zhong HG, Beckers P (1995) Dual analysis with general boundary conditions. Comput Methods Appl Mech Eng 122:183\u2013192","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"4\u20135","key":"153_CR14","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/j.jsv.2003.10.027","volume":"278","author":"V Decouvreur","year":"2004","unstructured":"Decouvreur V, Bouillard Ph, Deraemaeker A, Ladev\u00e8ze P (2004) Validation of 2D acoustic models based on the error in constitutive relation. J Sound Vibration 278(4\u20135):773\u2013787","journal-title":"J Sound Vibration"},{"key":"153_CR15","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.cma.2004.10.012","volume":"195","author":"V Decouvreur","year":"2006","unstructured":"Decouvreur V, De Bel E, Bouillard Ph (2006) On the effect of the dispersion error when updating acoustic models. Comput Methods Appl Mecha Eng 195:394\u2013405","journal-title":"Comput Methods Appl Mecha Eng"},{"key":"153_CR16","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1002\/(SICI)1097-0207(19991010)46:4<471::AID-NME684>3.0.CO;2-6","volume":"46","author":"A Deraemaeker","year":"1999","unstructured":"Deraemaeker A, Babu\u0161ka I, Bouillard Ph (1999) Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. Int J Numer Methods Eng 46:471\u2013500","journal-title":"Int J Numer Methods Eng"},{"key":"153_CR17","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/S0965-9978(02)00062-5","volume":"33","author":"W Desmet","year":"2002","unstructured":"Desmet W, van Hal B, Sas P, Vandepitte D (2002) A computationally efficient prediction technique for the steady-state dynamics analysis of coupled vibro-acoustic systems. Adv Eng Softw 33:527\u2013540","journal-title":"Adv Eng Softw"},{"key":"153_CR18","doi-asserted-by":"crossref","first-page":"6455","DOI":"10.1016\/S0045-7825(01)00232-8","volume":"190","author":"C Farhat","year":"2001","unstructured":"Farhat C, Harari I, Franca LP (2001) The discontinuous enrichment method. Comput Methods Appl Mech Eng 190:6455\u20136479","journal-title":"Comput Methods Appl Mech Eng"},{"key":"153_CR19","doi-asserted-by":"crossref","first-page":"4003","DOI":"10.1002\/(SICI)1097-0207(19971115)40:21<4003::AID-NME199>3.0.CO;2-Z","volume":"40","author":"L Franca","year":"1997","unstructured":"Franca L, Farhat C, Macedo A, Lesoinne M (1997) Residual-free bubbles for the Helmholtz equation. Int J Numer Methods Eng 40:4003\u20134009","journal-title":"Int J Numer Methods Eng"},{"issue":"3","key":"153_CR20","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1002\/nme.1571","volume":"66","author":"G Gabard","year":"2006","unstructured":"Gabard G (2006) Discontinuous Galerkin methods with plane waves for the displacement-based acoustic equation. Int J Numer Methods Eng 66(3):549\u2013569","journal-title":"Int J Numer Methods Eng"},{"key":"153_CR21","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/0045-7825(95)00987-6","volume":"137","author":"K Gerdes","year":"1996","unstructured":"Gerdes K, Demkowicz L (1996) Solution of the 3D Helmholtz equation in arbitrary exterior domains using hp-FEM and IFEM. Comput Methods Appl Mech Eng 137: 239\u2013273","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"3","key":"153_CR22","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1016\/0045-7825(92)90006-6","volume":"98","author":"I Harari","year":"1992","unstructured":"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(3):411\u2013454","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"13\u201316","key":"153_CR23","doi-asserted-by":"crossref","first-page":"1594","DOI":"10.1016\/j.cma.2005.05.030","volume":"195","author":"I Harari","year":"2006","unstructured":"Harari I (2006) A survey of finite element methods for time-harmonic acoustics. Comput Methods App Mech Eng 195(13\u201316):1594\u20131607","journal-title":"Comput Methods App Mech Eng"},{"key":"153_CR24","unstructured":"Hazard L, De Bel E, Bouillard Ph, Sener J-Y, Migeot J-L (2004) Design of viscoelastic damping treatments in the medium frequency range. ISMA29. International Conference on noise and vibration engineering, Leuven"},{"issue":"9","key":"153_CR25","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/0898-1221(95)00144-N","volume":"38","author":"F Ihlenburg","year":"1995","unstructured":"Ihlenburg F, Babu\u0161ka I (1995) Finite element solution of the Helmholtz equation with high wave number. Part 1: The h-version of the FEM. Comput Math Appl 38(9):9\u201337","journal-title":"Comput Math Appl"},{"issue":"15","key":"153_CR26","doi-asserted-by":"crossref","first-page":"2131","DOI":"10.1002\/nme.757","volume":"57","author":"V Lacroix","year":"2003","unstructured":"Lacroix V, Bouillard Ph, Villon P (2003) An iterative defect-correction type meshless method for acoustics. Int J Numer Methods Eng 57(15):2131\u20132146","journal-title":"Int J Numer Methods Eng"},{"issue":"12","key":"153_CR27","first-page":"849","volume":"322","author":"P Ladev\u00e8ze","year":"1996","unstructured":"Ladev\u00e8ze P (1996) A new computational approach for structure vibrations in the medium frequency range. C R Acad Sci S\u00e9rie IIb 322(12):849\u2013856","journal-title":"C R Acad Sci S\u00e9rie IIb"},{"key":"153_CR28","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0922-5382(98)80009-3","volume-title":"On new advances in adaptative computational methods in mechanics","author":"P Ladev\u00e8ze","year":"1998","unstructured":"Ladev\u00e8ze P (1998) A modelling error estimator for dynamic model updating. In: Ladev\u00e8ze P Oden JT (eds) On new advances in adaptative computational methods in mechanics. Elsevier, Amsterdam, pp 135\u2013151"},{"issue":"1\/2","key":"153_CR29","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1108\/02644400110365879","volume":"18","author":"P Ladev\u00e8ze","year":"2001","unstructured":"Ladev\u00e8ze P, Arnaud L, Rouch P, Blanz\u00e9 C (2001) The variational theory of complex rays for the calculation of medium-frequency vibrations. Eng Comput 18(1\/2):193\u2013214","journal-title":"Eng Comput"},{"key":"153_CR30","unstructured":"Mertens T, Bouillard Ph, Astley J, Gamallo P, Hazard L (2006) Acoustic convected radiation using a partition of unity formulation, ICSV13, International Conference on sound and vibration, Vienna"},{"key":"153_CR31","volume-title":"Fluid-Structure Interaction","author":"P Morand","year":"1995","unstructured":"Morand P, Ohayon R (1995) Fluid-Structure Interaction. Wiley, Chichester"},{"key":"153_CR32","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1016\/S0045-7825(02)00616-3","volume":"192","author":"JT Oden","year":"2003","unstructured":"Oden JT, Belytschko T, Babu\u0161ka I, Hughes TJR (2003) Research directions in computational mechanics. Comput Methods Appl Mech Eng 192:913\u2013922","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"4","key":"153_CR33","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/BF02736190","volume":"12","author":"JT Oden","year":"2005","unstructured":"Oden JT, Prudhomme S, Demkowicz L (2005) A posteriori error estimation for acoustic wave propagation problems. Arch Comput Meth Eng 12(4):343\u2013389","journal-title":"Arch Comput Meth Eng"},{"key":"153_CR34","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0045-7825(98)00328-4","volume":"176","author":"O Pereira","year":"1999","unstructured":"Pereira O, Almeida JP, Maunder E (1999) Adaptive methods for hybrid equilibrium finite element models. Comput Methods Appl Mech Eng 176:19\u201339","journal-title":"Comput Methods Appl Mech Eng"},{"issue":"3","key":"153_CR35","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1090\/qam\/25902","volume":"5","author":"W Prager","year":"1947","unstructured":"Prager W, Synge J (1947) Approximations in elasticity based on the concept of function space. Qu Appl Math 5(3): 241\u2013269","journal-title":"Qu Appl Math"},{"issue":"3","key":"153_CR36","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1121\/1.2164987","volume":"119","author":"LL Thompson","year":"2006","unstructured":"Thompson LL (2006), A review of finite element methods for time-harmonic acoustics. J Acoust Soc Am 119(3): 1315\u20131330","journal-title":"J Acoust Soc Am"},{"key":"153_CR37","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1002\/sapm1953321117","volume":"32","author":"K Washizu","year":"1953","unstructured":"Washizu K (1953) Bounds for solutions of boundary value problems in elasticity. J Math Phys 32:117\u2013128","journal-title":"J Math Phys"},{"issue":"3","key":"153_CR38","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/S0003-682X(96)00048-5","volume":"50","author":"D Wilson","year":"1997","unstructured":"Wilson D (1997) Simple relaxational models for the acoustical properties of porous media. Appl Acoust 50(3):171\u2013188","journal-title":"Appl Acoust"},{"key":"153_CR39","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1002\/(SICI)1097-0207(20000110\/30)47:1\/3<9::AID-NME793>3.0.CO;2-P","volume":"47","author":"OC Zienkiewicz","year":"2000","unstructured":"Zienkiewicz OC (2000) Achievements and some unsolved problems of the finite element method. Int J Numer Methods Eng 47:9\u201328","journal-title":"Int J Numer Methods Eng"}],"container-title":["Computational Mechanics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00466-006-0153-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00466-006-0153-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00466-006-0153-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T00:29:13Z","timestamp":1559089753000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00466-006-0153-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,10]]},"references-count":39,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["153"],"URL":"https:\/\/doi.org\/10.1007\/s00466-006-0153-7","relation":{},"ISSN":["0178-7675","1432-0924"],"issn-type":[{"value":"0178-7675","type":"print"},{"value":"1432-0924","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1,10]]}}}