{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T07:28:13Z","timestamp":1742974093532,"version":"3.40.3"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030558734"},{"type":"electronic","value":"9783030558741"}],"license":[{"start":{"date-parts":[[2020,8,22]],"date-time":"2020-08-22T00:00:00Z","timestamp":1598054400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,22]],"date-time":"2020-08-22T00:00:00Z","timestamp":1598054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-55874-1_34","type":"book-chapter","created":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T11:52:51Z","timestamp":1620042771000},"page":"353-361","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Energy Preserving High-Order Discretizations for Nonlinear Acoustics"],"prefix":"10.1007","author":[{"given":"Herbert","family":"Egger","sequence":"first","affiliation":[]},{"given":"Vsevolod","family":"Shashkov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,22]]},"reference":[{"key":"34_CR1","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/s00211-011-0363-6","volume":"118","author":"G Akrivis","year":"2011","unstructured":"G. Akrivis, C. Makridakis, and R. N. Nochetto. Galerkin and Runge-Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence. Numer. Math., 118:429\u2013456, 2011.","journal-title":"Numer. Math."},{"key":"34_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04823-8","volume-title":"Higher-Order Numerical Methods for Transient Wave Equations","author":"G Cohen","year":"2002","unstructured":"G. Cohen. Higher-Order Numerical Methods for Transient Wave Equations. Springer, 2002."},{"key":"34_CR3","doi-asserted-by":"publisher","first-page":"1266","DOI":"10.1137\/S0036142993246445","volume":"33","author":"G Cohen","year":"1996","unstructured":"G. Cohen and P. Joly. Construction analysis of fourth-order finite difference schemes for the acoustic wave equation in nonhomogeneous media. SIAM J. Numer. Anal., 33:1266\u20131302, 1996.","journal-title":"SIAM J. Numer. Anal."},{"key":"34_CR4","unstructured":"H. Egger. Energy stable Galerkin approximation of Hamiltonian and gradient systems. 2018. arXive:1812.04253."},{"key":"34_CR5","doi-asserted-by":"crossref","unstructured":"K. Fagnan, R. J. LeVeque, T. J. Matula, and B. MacConaghy. High-resolution finite volume methods for extracorporeal shock wave therapy. In Hyperbolic Problems: Theory, Numerics, Applications, pages 503\u2013510. Springer, New York, 2008.","DOI":"10.1007\/978-3-540-75712-2_48"},{"key":"34_CR6","doi-asserted-by":"publisher","first-page":"A2830","DOI":"10.1137\/18M1175549","volume":"40","author":"S Geevers","year":"2018","unstructured":"S. Geevers, W. A. Mulder, and J. J. W. van der Vegt. New higher-order mass-lumped tetrahedral elements for wave propagation modelling. SIAM J. Sci. Comput., 40:A2830\u2013A2857, 2018.","journal-title":"SIAM J. Sci. Comput."},{"key":"34_CR7","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1007\/BF02440162","volume":"6","author":"O Gonzales","year":"1996","unstructured":"O. Gonzales. Time integration and discrete Hamiltonian systems. J. Nonl. Sci., 6:449\u2013467, 1996.","journal-title":"J. Nonl. Sci."},{"key":"34_CR8","doi-asserted-by":"publisher","first-page":"452","DOI":"10.1093\/imanum\/drt031","volume":"34","author":"E Hairer","year":"2014","unstructured":"E. Hairer and C. Lubich. Energy-diminishing integration of gradient systems. IMA J. Numer. Anal., 34:452\u2013461, 2014.","journal-title":"IMA J. Numer. Anal."},{"key":"34_CR9","volume-title":"Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations; 2nd ed","author":"E Hairer","year":"2006","unstructured":"E. Hairer, C. Lubich, and G. Wanner. Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations; 2nd ed. Springer, 2006."},{"key":"34_CR10","doi-asserted-by":"publisher","first-page":"L7","DOI":"10.1121\/1.426776","volume":"105","author":"I M Hallaj","year":"1999","unstructured":"I. M. Hallaj and R. O. Cleveland. FDTD simulation of finite-amplitude pressure and temperature fields for biomedical ultrasound. J. Acoust. Soc. Am., 105:L7, 1999.","journal-title":"J. Acoust. Soc. Am."},{"key":"34_CR11","volume-title":"Nonlinear Acoustics","author":"M F Hamilton","year":"1998","unstructured":"M. F. Hamilton and D. T. Blackstock. Nonlinear Acoustics. Academic Press, 1998."},{"key":"34_CR12","doi-asserted-by":"publisher","first-page":"779","DOI":"10.1109\/58.920712","volume":"48","author":"J Hoffelner","year":"2001","unstructured":"J. Hoffelner, H. Landes, M. Kaltenbacher, and R. Lerch. Finite element simulation of nonlinear wave propagation in thermoviscous fluids including dissipation. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 48:779\u2013786, 2001.","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"34_CR13","first-page":"503","volume":"2","author":"B Kaltenbacher","year":"2009","unstructured":"B. Kaltenbacher and I. Lasiecka. Global existence and exponential decay rates for the Westervelt equation. Discr. Cont. Dyn. Sys. Ser. S, 2:503\u2013523, 2009.","journal-title":"Discr. Cont. Dyn. Sys. Ser. S"},{"key":"34_CR14","doi-asserted-by":"crossref","unstructured":"A. Karamalis, W. Wein, and N. Navab. Fast ultrasound image simulation using the Westervelt equation. In Medical Image Computing and Computer-Assisted Intervention \u2013 MICCAI 2010, pages 243\u2013250. Springer, New York, 2010.","DOI":"10.1007\/978-3-642-15705-9_30"},{"key":"34_CR15","volume-title":"Simulating Hamiltonian Dynamics","author":"B Leimkuhler","year":"2004","unstructured":"B. Leimkuhler and S. Reich. Simulating Hamiltonian Dynamics. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 2004."},{"key":"34_CR16","doi-asserted-by":"publisher","first-page":"1021","DOI":"10.1098\/rsta.1999.0363","volume":"357","author":"R I McLachlan","year":"1999","unstructured":"R. I. McLachlan, G. R. W. Quispel, and N. Robidoux. Geometric integration using discrete gradients. R. Soc. Lond. Philos. Trans. Ser. A: Math. Phys. Eng. Sci., 357:1021\u20131045, 1999.","journal-title":"R. Soc. Lond. Philos. Trans. Ser. A: Math. Phys. Eng. Sci."},{"key":"34_CR17","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1002\/fld.2470","volume":"65","author":"K Okita","year":"2011","unstructured":"K. Okita, K. Ono, S. Takagi, and Y. Matsumoto. Development of high intensity focused ultrasound simulator for large-scale computing. Int. J. Numer. Meth. Fluids, 65:43\u201366, 2011.","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"34_CR18","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1250\/ast.13.223","volume":"13","author":"T Tsuchiya","year":"1992","unstructured":"T. Tsuchiya and Y. Kagawa. A simulation study on nonlinear sound propagation by finite element approach. J. Acoust. Soc. Jpn., 13:223\u2013230, 1992.","journal-title":"J. Acoust. Soc. Jpn."},{"key":"34_CR19","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/j.wavemoti.2015.05.006","volume":"58","author":"R Velasco-Segura","year":"2015","unstructured":"R. Velasco-Segura and P. L. Rend\u00f2n. A finite volume approach for the simulation of nonlinear dissipative acoustic wave propagation. Wave Motion, 58:180\u2013195, 2015.","journal-title":"Wave Motion"},{"key":"34_CR20","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1121\/1.1918525","volume":"35","author":"P J Westervelt","year":"1963","unstructured":"P. J. Westervelt. Parametric acoustic array. J. Acoust. Soc. Am., 35:535\u2013537, 1963.","journal-title":"J. Acoust. Soc. Am."}],"container-title":["Lecture Notes in Computational Science and Engineering","Numerical Mathematics and Advanced Applications ENUMATH 2019"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-55874-1_34","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T00:06:30Z","timestamp":1651795590000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-55874-1_34"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,22]]},"ISBN":["9783030558734","9783030558741"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-55874-1_34","relation":{},"ISSN":["1439-7358","2197-7100"],"issn-type":[{"type":"print","value":"1439-7358"},{"type":"electronic","value":"2197-7100"}],"subject":[],"published":{"date-parts":[[2020,8,22]]},"assertion":[{"value":"22 August 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}