{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:39:35Z","timestamp":1740123575044,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T00:00:00Z","timestamp":1637280000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T00:00:00Z","timestamp":1637280000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100007601","name":"Horizon 2020","doi-asserted-by":"publisher","award":["800897","800897"],"award-info":[{"award-number":["800897","800897"]}],"id":[{"id":"10.13039\/501100007601","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s10915-021-01669-8","type":"journal-article","created":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T05:02:25Z","timestamp":1637298145000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Seamless, Extended DG Approach for Advection\u2013Diffusion Problems on Unbounded Domains"],"prefix":"10.1007","volume":"90","author":[{"given":"Federico","family":"Vismara","sequence":"first","affiliation":[]},{"given":"Tommaso","family":"Benacchio","sequence":"additional","affiliation":[]},{"given":"Luca","family":"Bonaventura","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,19]]},"reference":[{"key":"1669_CR1","doi-asserted-by":"crossref","unstructured":"Akmaev, R.: Whole atmosphere modeling: connecting terrestrial and space weather. Rev. Geophys. 49 (2011)","DOI":"10.1029\/2011RG000364"},{"issue":"11","key":"1669_CR2","doi-asserted-by":"publisher","first-page":"4200","DOI":"10.1016\/j.jcp.2009.02.030","volume":"228","author":"D Appel\u00f6","year":"2009","unstructured":"Appel\u00f6, D., Colonius, T.: A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems. J. Comput. Phys. 228(11), 4200\u20134217 (2009)","journal-title":"J. Comput. Phys."},{"key":"1669_CR3","doi-asserted-by":"publisher","first-page":"742","DOI":"10.1137\/0719052","volume":"19","author":"D Arnold","year":"1982","unstructured":"Arnold, D.: An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19, 742\u2013760 (1982)","journal-title":"SIAM J. Numer. Anal."},{"key":"1669_CR4","doi-asserted-by":"publisher","first-page":"1749","DOI":"10.1137\/S0036142901384162","volume":"39","author":"D Arnold","year":"2002","unstructured":"Arnold, D., Brezzi, F., Cockburn, B., Marini, L.: Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749\u20131779 (2002)","journal-title":"SIAM J. Numer. Anal."},{"issue":"7","key":"1669_CR5","doi-asserted-by":"publisher","first-page":"951","DOI":"10.1002\/1097-0207(20001110)49:7<951::AID-NME989>3.0.CO;2-T","volume":"49","author":"R Astley","year":"2000","unstructured":"Astley, R.: Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. Int. J. Numer. Methods Eng. 49(7), 951\u2013976 (2000)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"9","key":"1669_CR6","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1002\/fld.3768","volume":"72","author":"T Benacchio","year":"2013","unstructured":"Benacchio, T., Bonaventura, L.: Absorbing boundary conditions: a spectral collocation approach. Int. J. Numer. Methods Fluids 72(9), 913\u2013936 (2013). https:\/\/doi.org\/10.1002\/fld.3768","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"1669_CR7","first-page":"266","volume":"350","author":"T Benacchio","year":"2019","unstructured":"Benacchio, T., Bonaventura, L.: An extension of DG methods for hyperbolic problems to one-dimensional semi-infinite domains. Appl. Math. Comput. 350, 266\u2013282 (2019)","journal-title":"Appl. Math. Comput."},{"key":"1669_CR8","doi-asserted-by":"publisher","first-page":"1667","DOI":"10.1137\/S1064827596301418","volume":"19","author":"K Black","year":"1998","unstructured":"Black, K.: Spectral elements on infinite domains. SIAM J. Sci. Comput. 19, 1667\u20131681 (1998)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"1669_CR9","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1006\/jcph.1999.6414","volume":"158","author":"L Bonaventura","year":"2000","unstructured":"Bonaventura, L.: A semi-implicit semi-Lagrangian scheme using the height coordinate for a nonhydrostatic and fully elastic model of atmospheric flows. J. Comput. Phys. 158(2), 186\u2013213 (2000)","journal-title":"J. Comput. Phys."},{"key":"1669_CR10","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/j.jcp.2018.03.017","volume":"364","author":"L Bonaventura","year":"2017","unstructured":"Bonaventura, L., Fern\u00e1ndez-Nieto, E., Garres-D\u00edaz, J., Narbona-Reina, G.: Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization. J. Comput. Phys. 364, 209\u2013234 (2017)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"1669_CR11","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1137\/0719044","volume":"19","author":"C Canuto","year":"1982","unstructured":"Canuto, C., Quarteroni, A.: Error estimates for spectral and pseudospectral approximations of hyperbolic equations. SIAM J. Numer. Anal. 19(3), 629\u2013642 (1982)","journal-title":"SIAM J. Numer. Anal."},{"key":"1669_CR12","doi-asserted-by":"publisher","first-page":"1354","DOI":"10.1016\/j.cam.2010.08.023","volume":"235","author":"J Dea","year":"2011","unstructured":"Dea, J.: An experimental adaptation of Higdon-type non-reflecting boundary conditions to linear first-order systems. J. Comput. Appl. Math. 235, 1354\u20131366 (2011)","journal-title":"J. Comput. Appl. Math."},{"issue":"139","key":"1669_CR13","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1090\/S0025-5718-1977-0436612-4","volume":"31","author":"B Engquist","year":"1977","unstructured":"Engquist, B., Majda, A.: Absorbing boundary conditions for numerical simulation of waves. Math. Comput. 31(139), 629\u2013651 (1977)","journal-title":"Math. Comput."},{"issue":"1","key":"1669_CR14","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1142\/S0218396X00000042","volume":"8","author":"K Gerdes","year":"2000","unstructured":"Gerdes, K.: A review of infinite element methods for exterior Helmholtz problems. J. Comput. Acoust. 8(1), 43\u201362 (2000)","journal-title":"J. Comput. Acoust."},{"key":"1669_CR15","doi-asserted-by":"crossref","unstructured":"Giraldo, F., Kelly, J., Constantinescu, E.: Implicit-explicit formulations of a three-dimensional nonhydrostatic unified model of the atmosphere (NUMA). SIAM J. Sci. Comput. 35 (2013)","DOI":"10.1137\/120876034"},{"issue":"1","key":"1669_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-021-01519-7","volume":"88","author":"D Gu","year":"2021","unstructured":"Gu, D., Wang, Z.: Orthogonal Jacobi rational functions and spectral methods on the half line. J. Sci. Comput. 88(1), 1\u201327 (2021)","journal-title":"J. Sci. Comput."},{"key":"1669_CR17","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/0021-9991(81)90082-6","volume":"41","author":"M Israeli","year":"1981","unstructured":"Israeli, M., Orszag, S.: Approximation of radiation boundary conditions. J. Comput. Phys. 41, 115\u2013135 (1981)","journal-title":"J. Comput. Phys."},{"key":"1669_CR18","doi-asserted-by":"publisher","first-page":"1342","DOI":"10.1029\/2019SW002267","volume":"17","author":"D Jackson","year":"2019","unstructured":"Jackson, D., Fuller-Rowell, T., Griffin, D., Griffith, M., Kelly, C., Marsh, D., Walach, M.: Future directions for whole atmosphere modeling: developments in the context of space weather. Space Weather 17, 1342\u20131350 (2019)","journal-title":"Space Weather"},{"key":"1669_CR19","first-page":"430","volume":"111","author":"J Klemp","year":"1983","unstructured":"Klemp, J., Durran, D.: An upper boundary condition permitting internal gravity wave radiation in numerical mesoscale models. J. Atmos. Sci. 111, 430\u2013444 (1983)","journal-title":"J. Atmos. Sci."},{"key":"1669_CR20","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1175\/1520-0469(1978)035<0078:NSOHMW>2.0.CO;2","volume":"35","author":"J Klemp","year":"1978","unstructured":"Klemp, J., Lilly, D.: Numerical simulation of hydrostatic mountain waves. J. Atmos. Sci. 35, 78\u2013107 (1978)","journal-title":"J. Atmos. Sci."},{"key":"1669_CR21","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1002\/qj.49711247415","volume":"112","author":"P Rasch","year":"1986","unstructured":"Rasch, P.: Toward atmospheres without tops: absorbing upper boundary conditions for numerical models. Q. J. R. Meteorol. Soc. 112, 1195\u20131218 (1986)","journal-title":"Q. J. R. Meteorol. Soc."},{"key":"1669_CR22","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717440","volume-title":"Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation","author":"B Rivi\u00e8re","year":"2008","unstructured":"Rivi\u00e8re, B.: Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations: Theory and Implementation. SIAM, Philadelphia (2008)"},{"key":"1669_CR23","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1137\/S0036142999362936","volume":"38","author":"J Shen","year":"2001","unstructured":"Shen, J.: Stable and efficient spectral methods in unbounded domains using Laguerre functions. SIAM J. Numer. Anal. 38, 1113\u20131133 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"1669_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71041-7","volume-title":"Spectral Methods: Algorithms, Analysis and Applications, Springer Series in Computational Mathematics","author":"J Shen","year":"2011","unstructured":"Shen, J., Tang, T., Wang, L.L.: Spectral Methods: Algorithms, Analysis and Applications, Springer Series in Computational Mathematics, vol. 40. Springer, Berlin (2011)"},{"key":"1669_CR25","first-page":"1381","volume":"6","author":"J Shen","year":"2006","unstructured":"Shen, J., Wang, L.L.: Laguerre and composite Legendre-Laguerre dual-Petrov-Galerkin methods for third-order equations. Discrete Contin. Dyn. Syst. B 6, 1381\u20131402 (2006)","journal-title":"Discrete Contin. Dyn. Syst. B"},{"key":"1669_CR26","doi-asserted-by":"publisher","first-page":"3785","DOI":"10.1016\/j.cma.2006.10.031","volume":"196","author":"J Shen","year":"2007","unstructured":"Shen, J., Wang, L.L.: Legendre and Chebyshev dual-Petrov-Galerkin methods for Hyperbolic equations. Comput. Methods Appl. Mech. Eng. 196, 3785\u20133797 (2007)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1669_CR27","first-page":"195","volume":"5","author":"J Shen","year":"2009","unstructured":"Shen, J., Wang, L.L.: Some recent advances on spectral methods for unbounded domains. Commun. Comput. Phys. 5, 195\u2013241 (2009)","journal-title":"Commun. Comput. Phys."},{"key":"1669_CR28","doi-asserted-by":"crossref","unstructured":"Tatari, M., Haghighi, M.: A generalized Laguerre-Legendre spectral collocation method for solving initial-boundary value problems. Appl. Math. Model. 38(4), 1351\u20131364 (2014)","DOI":"10.1016\/j.apm.2013.08.008"},{"key":"1669_CR29","unstructured":"Vismara, F.: A coupled scheme for the solution of parabolic problems on unbounded domains. Master\u2019s thesis, Politecnico di Milano (2020). https:\/\/www.politesi.polimi.it\/handle\/10589\/166694 (last accessed 7 December 2020)"},{"issue":"4","key":"1669_CR30","first-page":"1019","volume":"11","author":"ZQ Wang","year":"2009","unstructured":"Wang, Z.Q., Guo, B.Y., Wu, Y.N.: Pseudospectral method using generalized Laguerre functions for singular problems on unbounded domains. Discrete Contin. Dyn. Syst. Ser. B 11(4), 1019\u20131038 (2009)","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"1669_CR31","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1137\/0715010","volume":"15","author":"M Wheeler","year":"1978","unstructured":"Wheeler, M.: An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15, 152\u2013161 (1978)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1669_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10915-009-9313-1","volume":"42","author":"Q Zhuang","year":"2010","unstructured":"Zhuang, Q., Shen, J., Xu, C.: A coupled Legendre-Laguerre spectral-element method for the Navier\u2013Stokes equations in unbounded domains. J. Sci. Comput. 42(1), 1\u201322 (2010)","journal-title":"J. Sci. Comput."},{"key":"1669_CR33","doi-asserted-by":"crossref","unstructured":"Zhuang, Q., Xu, C.: Legendre-Laguerre coupled spectral element methods for second-and fourth-order equations on the half line. J. Comput. Appl. Math. 235(3), 615\u2013630 (2010)","DOI":"10.1016\/j.cam.2010.06.013"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01669-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01669-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01669-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T23:06:53Z","timestamp":1642460813000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01669-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,19]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["1669"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01669-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2021,11,19]]},"assertion":[{"value":"10 December 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 November 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"5"}}