{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,24]],"date-time":"2025-05-24T04:10:30Z","timestamp":1748059830027,"version":"3.41.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T00:00:00Z","timestamp":1744675200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T00:00:00Z","timestamp":1744675200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12131005","12471348","U2230402"],"award-info":[{"award-number":["12131005","12471348","U2230402"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012165","name":"Key Technologies Research and Development Program","doi-asserted-by":"publisher","award":["2021YFB0300203"],"award-info":[{"award-number":["2021YFB0300203"]}],"id":[{"id":"10.13039\/501100012165","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":[[2025,6]]},"DOI":"10.1007\/s10915-025-02890-5","type":"journal-article","created":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T11:44:53Z","timestamp":1744717493000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Spectral Method for 1-D Neutron Transport Equation"],"prefix":"10.1007","volume":"103","author":[{"given":"Haonan","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6326-9926","authenticated-orcid":false,"given":"Huiyuan","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhimin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,15]]},"reference":[{"issue":"6","key":"2890_CR1","doi-asserted-by":"publisher","first-page":"2143","DOI":"10.1016\/j.nucengdes.2011.03.048","volume":"241","author":"M Abbassi","year":"2011","unstructured":"Abbassi, M., Zolfaghari, A., Minuchehr, A., Yousefi, M.: An adaptive finite element approach for neutron transport equation. Nucl. Eng. Des. 241(6), 2143\u20132154 (2011)","journal-title":"Nucl. Eng. Des."},{"issue":"4","key":"2890_CR2","doi-asserted-by":"publisher","first-page":"1299","DOI":"10.1137\/S0036142992238119","volume":"35","author":"M Asadzadeh","year":"1998","unstructured":"Asadzadeh, M.: A finite element method for the neutron transport equation in an infinite cylindrical domain. SIAM J. Numer. Anal. 35(4), 1299\u20131314 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"2890_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-30728-0","volume-title":"Spectral Methods: Fundamentals in Single Domains","author":"C Canuto","year":"2007","unstructured":"Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods: Fundamentals in Single Domains. Springer (2007)"},{"issue":"6","key":"2890_CR4","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1515\/kern-1994-590611","volume":"59","author":"A Cardona","year":"1994","unstructured":"Cardona, A., Vilhena, M.: Eine L\u00f6sung der linearen Transportgleichung mit Hilfe Tschebyscheffscher Polynome und der Laplace-Transformation. Kerntechnik 59(6), 278\u2013281 (1994)","journal-title":"Kerntechnik"},{"key":"2890_CR5","volume-title":"Mathematical Analysis and Numerical Methods for Science and Technology: Volume 6 Evolution Problems II","author":"R Dautray","year":"2012","unstructured":"Dautray, R., Lions, J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology: Volume 6 Evolution Problems II. Springer (2012)"},{"key":"2890_CR6","unstructured":"Dudouit, Y.: Efficient high-dimension high-order matrix-free discontinuous Galerkin methods for high-fidelity physics. In: CEED Meeting. Lawrence Livermore National Laboratory (2023)"},{"issue":"2","key":"2890_CR7","doi-asserted-by":"publisher","first-page":"A936","DOI":"10.1137\/110844581","volume":"35","author":"D Fournier","year":"2013","unstructured":"Fournier, D., Herbin, R., Tellier, R.L.: Discontinuous Galerkin discretization and hp-refinement for the resolution of the neutron transport equation. SIAM J. Sci. Comput. 35(2), A936\u2013A956 (2013)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"2890_CR8","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/0306-4549(79)90075-6","volume":"6","author":"J Galliara","year":"1979","unstructured":"Galliara, J., Williams, M.: A finite element method for neutron transport-II. Some practical considerations. Ann. Nucl. Energy 6(4), 205\u2013223 (1979)","journal-title":"Ann. Nucl. Energy"},{"issue":"2","key":"2890_CR9","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1108\/03684920710741242","volume":"36","author":"A Kadem","year":"2007","unstructured":"Kadem, A.: Solution of the three-dimensional transport equation using the spectral methods. Kybernetes 36(2), 236\u2013252 (2007)","journal-title":"Kybernetes"},{"key":"2890_CR10","first-page":"1","volume":"S4","author":"P Lesaint","year":"1974","unstructured":"Lesaint, P., Raviart, P.A.: On a finite element method for solving the neutron transport equation. Publications des s\u00e9minaires de math\u00e9matiques et informatique de Rennes S4, 1\u201340 (1974)","journal-title":"Publications des s\u00e9minaires de math\u00e9matiques et informatique de Rennes"},{"key":"2890_CR11","volume-title":"Computational Methods of Neutron Transport","author":"EE Lewis","year":"1984","unstructured":"Lewis, E.E., Miller, W.F.: Computational Methods of Neutron Transport. Wiley, New York (1984)"},{"issue":"9","key":"2890_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02724346","volume":"7","author":"EE Lewis","year":"1984","unstructured":"Lewis, E.E., Miller, W.F.: Monte Carlo calculations of the transport of high-energy nucleons. La Rivista del Nuovo Cimento 7(9), 1\u201348 (1984)","journal-title":"La Rivista del Nuovo Cimento"},{"issue":"25\u201326","key":"2890_CR13","doi-asserted-by":"publisher","first-page":"5887","DOI":"10.1016\/j.ijheatmasstransfer.2008.04.048","volume":"51","author":"B-W Li","year":"2008","unstructured":"Li, B.-W., Sun, Y.-S., Yu, Y.: Iterative and direct Chebyshev collocation spectral methods for one-dimensional radiative heat transfer. Int. J. Heat Mass Transf. 51(25\u201326), 5887\u20135894 (2008)","journal-title":"Int. J. Heat Mass Transf."},{"issue":"1","key":"2890_CR14","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.jcp.2006.08.020","volume":"223","author":"E Machorro","year":"2007","unstructured":"Machorro, E.: Discontinuous Galerkin finite element method applied to the 1-D spherical neutron transport equation. J. Comput. Phys. 223(1), 67\u201381 (2007)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"2890_CR15","doi-asserted-by":"publisher","first-page":"371","DOI":"10.13182\/NSE77-A26979","volume":"62","author":"WR Martin","year":"1977","unstructured":"Martin, W.R., Duderstadt, J.J.: Finite element solutions of the neutron transport equation with applications to strong heterogeneities. Nucl. Sci. Eng. 62(3), 371\u2013390 (1977)","journal-title":"Nucl. Sci. Eng."},{"issue":"2","key":"2890_CR16","doi-asserted-by":"publisher","first-page":"148","DOI":"10.13182\/NSE73-A26590","volume":"51","author":"W Miller Jr","year":"1973","unstructured":"Miller, W., Jr., Lewis, E., Rossow, E.: The application of phase-space finite elements to the one-dimensional neutron transport equation. Nucl. Sci. Eng. 51(2), 148\u2013156 (1973)","journal-title":"Nucl. Sci. Eng."},{"key":"2890_CR17","unstructured":"Min, M.: Spectral element methods for multiphysics transport problems. In: International Conference on Spectral and High Order Methods. Yonsei University, Seoul (2023)"},{"key":"2890_CR18","unstructured":"Reed, W.H., Hill, T.: Triangular mesh methods for the neutron transport equation. Los Alamos Report LA-UR-73-479 (1973)"},{"issue":"1","key":"2890_CR19","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s10915-022-01965-x","volume":"93","author":"Y Ren","year":"2022","unstructured":"Ren, Y., Xing, Y., Wang, D., Qiu, J.: High order asymptotic preserving Hermite WENO fast sweeping method for the steady-state $${S_N}$$ transport equations. J. Sci. Comput. 93(1), 3 (2022)","journal-title":"J. Sci. Comput."},{"key":"2890_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-71041-7","volume-title":"Spectral Methods: Algorithms, Analysis and Applications","author":"J Shen","year":"2011","unstructured":"Shen, J., Tang, T., Wang, L.-L.: Spectral Methods: Algorithms, Analysis and Applications, vol. 41. Springer (2011)"},{"issue":"9","key":"2890_CR21","first-page":"815","volume":"31","author":"G Verdu","year":"1994","unstructured":"Verdu, G.: Review of the Monte Carlo method for particle transport. J. Nucl. Sci. Technol. 31(9), 815\u2013834 (1994)","journal-title":"J. Nucl. Sci. Technol."},{"issue":"3\u20134","key":"2890_CR22","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/S0149-1970(99)00019-0","volume":"35","author":"M Vilhena","year":"1999","unstructured":"Vilhena, M., Barichello, L.B., Zabadal, J., Segatto, C.F., Cardona, A.V., Pazos, R.: Solutions to the multidimensional linear transport equation by the spectral method. Prog. Nucl. Energy 35(3\u20134), 275\u2013291 (1999)","journal-title":"Prog. Nucl. Energy"},{"issue":"3","key":"2890_CR23","first-page":"488","volume":"35","author":"K Wang","year":"2008","unstructured":"Wang, K., Long, P.-C., Wu, H.-C., Ye, M.-Y.: Simulation of 3D neutron transport problems by a new method of finite difference. Ann. Nucl. Energy 35(3), 488\u2013493 (2008)","journal-title":"Ann. Nucl. Energy"},{"issue":"1\u20134","key":"2890_CR24","first-page":"41","volume":"43","author":"A Yamamoto","year":"2003","unstructured":"Yamamoto, A.: Solution of the Boltzmann transport equation for monoenergetic neutrons using the discrete ordinates and the finite difference methods. Prog. Nucl. Energy 43(1\u20134), 41\u201392 (2003)","journal-title":"Prog. Nucl. Energy"},{"issue":"5","key":"2890_CR25","doi-asserted-by":"publisher","first-page":"A2987","DOI":"10.1137\/16M1061072","volume":"38","author":"D Yuan","year":"2016","unstructured":"Yuan, D., Cheng, J., Shu, C.-W.: High order positivity-preserving discontinuous Galerkin methods for radiative transfer equations. SIAM J. Sci. Comput. 38(5), A2987\u2013A3019 (2016)","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02890-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-025-02890-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-025-02890-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,23]],"date-time":"2025-05-23T13:18:33Z","timestamp":1748006313000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-025-02890-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,15]]},"references-count":25,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["2890"],"URL":"https:\/\/doi.org\/10.1007\/s10915-025-02890-5","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2025,4,15]]},"assertion":[{"value":"23 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 January 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 April 2025","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":"73"}}