{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,9]],"date-time":"2025-03-09T16:40:04Z","timestamp":1741538404537,"version":"3.38.0"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,3,9]],"date-time":"2025-03-09T00:00:00Z","timestamp":1741478400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,9]],"date-time":"2025-03-09T00:00:00Z","timestamp":1741478400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2021YFB0300101","2021YFB0300101"],"award-info":[{"award-number":["2021YFB0300101","2021YFB0300101"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"DOI":"10.1007\/s11227-025-07087-z","type":"journal-article","created":{"date-parts":[[2025,3,9]],"date-time":"2025-03-09T16:04:32Z","timestamp":1741536272000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A heterogeneous parallel algorithm for the Cartesian discrete ordinates for multizone heterogeneous system"],"prefix":"10.1007","volume":"81","author":[{"given":"Runhua","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinglin","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,9]]},"reference":[{"key":"7087_CR1","doi-asserted-by":"publisher","DOI":"10.1063\/1.5043860","volume":"1978","author":"C-J Hu","year":"2018","unstructured":"Hu C-J, Wang A, Yang W (2018) An overview of high-performance numerical reactor design. AIP Conf Proc 1978:230005 (AIP Publishing LLC)","journal-title":"AIP Conf Proc"},{"key":"7087_CR2","unstructured":"Carlson BG (1955) Solution of the transport equation by Sn approximations. Technical report, Los Alamos National Lab.(LANL), Los Alamos, NM (United States)"},{"key":"7087_CR3","volume-title":"Deterministic numerical methods for unstructured-mesh neutron transport calculation","author":"L Cao","year":"2020","unstructured":"Cao L, Wu H (2020) Deterministic numerical methods for unstructured-mesh neutron transport calculation. Woodhead Publishing, Cambridge, UK"},{"issue":"9","key":"7087_CR4","doi-asserted-by":"publisher","first-page":"2192","DOI":"10.3390\/en13092192","volume":"13","author":"A Gunnarsson","year":"2020","unstructured":"Gunnarsson A, Andersson K, Adams BR, Fredriksson C (2020) Discrete-ordinates modelling of the radiative heat transfer in a pilot-scale rotary kiln. Energies 13(9):2192","journal-title":"Energies"},{"issue":"6","key":"7087_CR5","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1016\/S0022-4073(00)00055-8","volume":"68","author":"R Spurr","year":"2001","unstructured":"Spurr R, Kurosu T, Chance K (2001) A linearized discrete ordinate radiative transfer model for atmospheric remote-sensing retrieval. J Quant Spectrosc Radiat Transfer 68(6):689\u2013735","journal-title":"J Quant Spectrosc Radiat Transfer"},{"issue":"1","key":"7087_CR6","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0149-1970(01)00023-3","volume":"40","author":"ML Adams","year":"2002","unstructured":"Adams ML, Larsen EW (2002) Fast iterative methods for discrete-ordinates particle transport calculations. Prog Nucl Energy 40(1):3\u2013159","journal-title":"Prog Nucl Energy"},{"key":"7087_CR7","doi-asserted-by":"publisher","DOI":"10.3389\/fenrg.2022.935648","author":"B Liu","year":"2022","unstructured":"Liu B, Tan Y, Jing F, Hu G, Yan M (2022) Study on multi-objective optimization for nuclear reactor radiation shield design coupling genetic algorithm with paralleling discrete ordinate code. Front Energy Res. https:\/\/doi.org\/10.3389\/fenrg.2022.935648","journal-title":"Front Energy Res"},{"key":"7087_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2021\/6633366","volume":"2021","author":"J Hu","year":"2021","unstructured":"Hu J, Zhang B, Zong Z, Liu C, Chen Y (2021) Verification of CENDL-3.2 nuclear data on VENUS-3 shielding benchmark by ARES transport code. Sci Technol Nucl Install 2021:1\u201313","journal-title":"Sci Technol Nucl Install"},{"issue":"5","key":"7087_CR9","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1016\/j.pnucene.2006.01.007","volume":"48","author":"A Seubert","year":"2006","unstructured":"Seubert A, Zwermann W, Langenbuch S (2006) Solution of the C5G7 3-D extension benchmark by the SN code TORT. Prog Nucl Energy 48(5):432\u2013438","journal-title":"Prog Nucl Energy"},{"key":"7087_CR10","doi-asserted-by":"publisher","first-page":"06023","DOI":"10.1051\/epjconf\/202124706023","volume":"247","author":"Z Ruan","year":"2021","unstructured":"Ruan Z, Guo H (2021) A high-fidelity simulation of the C5G7 benchmark by using the parallel enter code. EPJ Web Conf 247:06023 (EDP Sciences)","journal-title":"EPJ Web Conf"},{"key":"7087_CR11","doi-asserted-by":"publisher","DOI":"10.1016\/j.anucene.2022.109042","volume":"171","author":"ZI B\u00f6r\u00f6czki","year":"2022","unstructured":"B\u00f6r\u00f6czki ZI, Aranyosy A, Szieberth M (2022) Comparison of calculation methods for lead cooled fast reactor reactivity effects. Ann Nucl Energy 171:109042","journal-title":"Ann Nucl Energy"},{"key":"7087_CR12","unstructured":"Brunett AJ, Fanning TH (2017) Us sodium fast reactor codes and methods: current capabilities and path forward. Technical report, Argonne National Lab.(ANL), Argonne, IL (United States)"},{"issue":"20","key":"7087_CR13","doi-asserted-by":"publisher","first-page":"5410","DOI":"10.3390\/en13205410","volume":"13","author":"M Hashim","year":"2020","unstructured":"Hashim M, Cao L, Zhou S, Ma R, Shao Y, Chen R (2020) Spark-nc: a lead-bismuth-cooled small modular fast reactor with natural circulation and load following capabilities. Energies 13(20):5410","journal-title":"Energies"},{"key":"7087_CR14","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/j.ces.2019.04.034","volume":"205","author":"J Moreno","year":"2019","unstructured":"Moreno J, Casado C, Marugan J (2019) Improved discrete ordinate method for accurate simulation radiation transport using solar and led light sources. Chem Eng Sci 205:151\u2013164","journal-title":"Chem Eng Sci"},{"issue":"10","key":"7087_CR15","doi-asserted-by":"publisher","first-page":"3131","DOI":"10.1175\/2009JAS3137.1","volume":"66","author":"R Pincus","year":"2009","unstructured":"Pincus R, Evans KF (2009) Computational cost and accuracy in calculating three-dimensional radiative transfer: results for new implementations of monte Carlo and SHDOM. J Atmos Sci 66(10):3131\u20133146","journal-title":"J Atmos Sci"},{"key":"7087_CR16","doi-asserted-by":"crossref","unstructured":"Roy S, Cai J, Ge W, Modest MF (2015) Computational cost and accuracy comparison of radiation solvers with emphasis on combustion simulations. In: Proceedings of CHT-15. 6 Th International Symposium on ADVANCES IN COMPUTATIONAL HEAT TRANSFER. Begel House Inc","DOI":"10.1615\/ICHMT.2015.IntSympAdvComputHeatTransf.1460"},{"issue":"4","key":"7087_CR17","doi-asserted-by":"publisher","first-page":"527","DOI":"10.13182\/NSE15-53","volume":"184","author":"J Liu","year":"2016","unstructured":"Liu J, Lihua C, Qing Lin W, Chunye G, Jie J, Xinbiao G, Shengguo L, Hu Q, Masterson T (2016) Parallel SN sweep scheduling algorithm on unstructured grids for multigroup time-dependent particle transport equations. Nucl Sci Eng 184(4):527\u2013536. https:\/\/doi.org\/10.13182\/NSE15-53","journal-title":"Nucl Sci Eng"},{"key":"7087_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109892","volume":"425","author":"JI Vermaak","year":"2021","unstructured":"Vermaak JI, Ragusa JC, Adams ML, Morel JE (2021) Massively parallel transport sweeps on meshes with cyclic dependencies. J Comput Phys 425:109892","journal-title":"J Comput Phys"},{"issue":"3","key":"7087_CR19","doi-asserted-by":"publisher","first-page":"312","DOI":"10.13182\/NSE98-1","volume":"128","author":"RS Baker","year":"1998","unstructured":"Baker RS, Koch KR (1998) An SNAlgorithm for the massively parallel CM-200 computer. Nucl Sci Eng 128(3):312\u2013320. https:\/\/doi.org\/10.13182\/NSE98-1","journal-title":"Nucl Sci Eng"},{"key":"7087_CR20","unstructured":"Bailey TS, Falgout RD (2008) Analysis of massively parallel discrete-ordinates transport sweep algorithms with collisions. Technical report, Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States)"},{"key":"7087_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109234","volume":"407","author":"MP Adams","year":"2020","unstructured":"Adams MP, Adams ML, Hawkins WD, Smith T, Rauchwerger L, Amato NM, Bailey TS, Falgout RD, Kunen A, Brown P (2020) Provably optimal parallel transport sweeps on semi-structured grids. J Comput Phys 407:109234","journal-title":"J Comput Phys"},{"key":"7087_CR22","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/j.anucene.2018.03.003","volume":"116","author":"L Xu","year":"2018","unstructured":"Xu L, Cao L, Zheng Y, Wu H (2018) Hybrid MPI-communication for the multi-angular SN parallel sweep on 3-D regular grids. Ann Nucl Energy 116:407\u2013416","journal-title":"Ann Nucl Energy"},{"key":"7087_CR23","unstructured":"Evans TM, Joubert W, Hamilton SP, Johnson SR, Turner JA, Davidson GG, Pandya TM (2015) Three-dimensional discrete ordinates reactor assembly calculations on GPUs. Technical report, Oak Ridge National Lab.(ORNL), Oak Ridge, TN (United States). Oak Ridge"},{"key":"7087_CR24","unstructured":"Alcouffe RE, Baker RS, Dahl JA, Turner SA, Ward R (2005) PARTISN: A time-dependent, parallel neutral particle transport code system. Los Alamos National Laboratory, LA-UR-05-3925 (May 2005)"},{"key":"7087_CR25","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1016\/j.anucene.2018.02.049","volume":"116","author":"J Chen","year":"2018","unstructured":"Chen J, Liu Z, Zhao C, He Q, Zu T, Cao L, Wu H (2018) A new high-fidelity neutronics code NECP-X. Ann Nucl Energy 116:417\u2013428","journal-title":"Ann Nucl Energy"},{"key":"7087_CR26","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/j.nucengdes.2017.04.011","volume":"318","author":"L Zhang","year":"2017","unstructured":"Zhang L, Zhang B, Liu C, Zheng J, Zheng Y, Chen Y (2017) Calculation of the C5G7 3-D extension benchmark by ARES transport code. Nucl Eng Des 318:231\u2013238","journal-title":"Nucl Eng Des"},{"key":"7087_CR27","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.anucene.2014.08.034","volume":"82","author":"S Moustafa","year":"2015","unstructured":"Moustafa S, Dutka-Malen I, Plagne L, Pon\u00e7ot A, Ramet P (2015) Shared memory parallelism for 3D Cartesian discrete ordinates solver. Ann Nucl Energy 82:179\u2013187","journal-title":"Ann Nucl Energy"},{"key":"7087_CR28","first-page":"004","volume":"51463","author":"T Cheng","year":"2018","unstructured":"Cheng T, Mo Z, Yang C, Wen L, Deng L (2018) Jsnt-s: A parallel 3d discrete ordinates radiation transport code on structured mesh. Int Conf Nuclear Eng 51463:004\u201315017 (American Society of Mechanical Engineers)","journal-title":"Int Conf Nuclear Eng"},{"key":"7087_CR29","doi-asserted-by":"crossref","unstructured":"Wang Q, Xing Z, Liu J, Qiang X, Gong C, Jiang J (2014) Parallel 3d deterministic particle transport on intel mic architecture. In: 2014 International conference on high performance computing & simulation (HPCS), pp 186\u2013192. IEEE","DOI":"10.1109\/HPCSim.2014.6903685"},{"issue":"1","key":"7087_CR30","doi-asserted-by":"publisher","first-page":"63","DOI":"10.3745\/JIPS.2011.7.1.063","volume":"7","author":"C Gong","year":"2011","unstructured":"Gong C, Liu J, Chen H, Xie J, Gong Z (2011) Accelerating the Sweep3D for a graphic processor unit. J Inf Process Syst 7(1):63\u201374","journal-title":"J Inf Process Syst"},{"issue":"15","key":"7087_CR31","doi-asserted-by":"publisher","first-page":"6010","DOI":"10.1016\/j.jcp.2011.04.010","volume":"230","author":"C Gong","year":"2011","unstructured":"Gong C, Liu J, Chi L, Huang H, Fang J, Gong Z (2011) GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method. J Comput Phys 230(15):6010\u20136022","journal-title":"J Comput Phys"},{"key":"7087_CR32","doi-asserted-by":"publisher","DOI":"10.3389\/fenrg.2021.701437","author":"B Li","year":"2021","unstructured":"Li B, Liu J, Zhu X, Ding S (2021) Large-scale heterogeneous computing for 3D deterministic particle transport on Tianhe-2A supercomputer. Front Energy Res. https:\/\/doi.org\/10.3389\/fenrg.2021.701437","journal-title":"Front Energy Res"},{"key":"7087_CR33","doi-asserted-by":"crossref","unstructured":"Plimpton S, Hendrickson B, Burns S, McLendon W (2000) Parallel algorithms for radiation transport on unstructured grids. In: SC\u201900: Proceedings of the 2000 ACM\/IEEE conference on supercomputing, pp 25\u201325. IEEE","DOI":"10.1109\/SC.2000.10030"},{"key":"7087_CR34","unstructured":"Yan J, Yang Z, Zhang A, Mo Z (2018) JSweep: a patch-centric data-driven approach for parallel sweeps on large-scale meshes"},{"issue":"2","key":"7087_CR35","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/s42514-022-00095-y","volume":"4","author":"K Lu","year":"2022","unstructured":"Lu K, Wang Y, Guo Y, Huang C, Liu S, Wang R, Fang J, Tang T, Chen Z, Liu B (2022) MT-3000: a heterogeneous multi-zone processor for HPC. CCF Trans High Perform Comput 4(2):150\u2013164","journal-title":"CCF Trans High Perform Comput"},{"key":"7087_CR36","doi-asserted-by":"publisher","first-page":"108806","DOI":"10.1016\/j.cpc.2023.108806","volume":"292","author":"R Li","year":"2023","unstructured":"Li R, Liu J, Zhang G, Gong C, Yang B, Liang Y (2023) An efficient heterogeneous parallel algorithm of the 3D MOC for multizone heterogeneous systems. Comput Phys Commun 292:108806. https:\/\/doi.org\/10.1016\/j.cpc.2023.108806","journal-title":"Comput Phys Commun"},{"key":"7087_CR37","volume-title":"Modelling of nuclear reactor multi-physics: from local balance equations to macroscopic models in neutronics and thermal-hydraulics","author":"C Demazi\u00e8re","year":"2019","unstructured":"Demazi\u00e8re C (2019) Modelling of nuclear reactor multi-physics: from local balance equations to macroscopic models in neutronics and thermal-hydraulics. Academic Press, Cambridge, MA, USA"},{"issue":"2","key":"7087_CR38","doi-asserted-by":"publisher","first-page":"171","DOI":"10.13182\/NT171-171","volume":"171","author":"TM Evans","year":"2010","unstructured":"Evans TM, Stafford AS, Slaybaugh RN, Clarno KT (2010) Denovo: a new three-dimensional parallel discrete ordinates code in scale. Nucl Technol 171(2):171\u2013200","journal-title":"Nucl Technol"},{"key":"7087_CR39","unstructured":"Rhoades WA, Engle WWJ (1977) New weighted-difference formulation for discrete-ordinates calculations. Trans Am Nucl Soc 27"},{"key":"7087_CR40","doi-asserted-by":"crossref","unstructured":"Rhoades WA, Simpson D (1997) The tort three-dimensional discrete ordinates neutron\/photon transport code (tort version 3). Technical report, Oak Ridge National Lab.(ORNL), Oak Ridge, TN (United States)","DOI":"10.2172\/582265"},{"key":"7087_CR41","unstructured":"Zerr RJ (2011) Solution of the within-group multidimensional discrete ordinates transport equations on massively parallel architectures. PhD thesis, Pennsylvania State University, University Park, PA, USA"},{"issue":"1","key":"7087_CR42","doi-asserted-by":"publisher","first-page":"107","DOI":"10.13182\/NSE15-124","volume":"185","author":"RS Baker","year":"2017","unstructured":"Baker RS (2017) An SNalgorithm for modern architectures. Nucl Sci Eng 185(1):107\u2013116. https:\/\/doi.org\/10.13182\/NSE15-124","journal-title":"Nucl Sci Eng"},{"key":"7087_CR43","doi-asserted-by":"crossref","unstructured":"Deakin T, McIntosh-Smith S, Gaudin W (2016) Many-core acceleration of a discrete ordinates transport mini-app at extreme scale. In: High performance computing: 31st International conference, ISC high performance 2016, Frankfurt, Germany, June 19-23, 2016, Proceedings, pp. 429\u2013448. Springer","DOI":"10.1007\/978-3-319-41321-1_22"},{"issue":"3","key":"7087_CR44","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s42514-023-00146-y","volume":"5","author":"Y Luo","year":"2023","unstructured":"Luo Y, Yang B, Liu J, Wang R, Wen J, Xiao T, Chen X, Gong C (2023) MT-office: parallel password recovery program for office on domestic heterogeneous multi-core processor. CCF Trans High Perform Comput 5(3):231\u2013244","journal-title":"CCF Trans High Perform Comput"},{"key":"7087_CR45","doi-asserted-by":"crossref","unstructured":"Yang J, Yang W, Qi R, Tsai Q, Lin S, Dong F, Li K, Li K (2023) Parallel algorithm design and optimization of geodynamic numerical simulation application on the tianhe new-generation high-performance computer. J Supercomput 1\u201332","DOI":"10.1007\/s11227-023-05469-9"},{"key":"7087_CR46","doi-asserted-by":"crossref","unstructured":"Zhang Q, Xu L, Chen R, Chen L, Chen X, Wang Q, Liu J, Yang B (2022) Improving the performance of lattice Boltzmann method with pipelined algorithm on a heterogeneous multi-zone processor. In: International conference on parallel and distributed computing: applications and technologies, pp 28\u201341. Springer","DOI":"10.1007\/978-3-031-29927-8_3"},{"key":"7087_CR47","doi-asserted-by":"crossref","unstructured":"Xie A, Hu Y, Cheng A, Tang Z, Liu P, Zhang X (2023) Advancing matrix decomposition efficiency: a study on ft-matrix dsp based svd optimization. In: 2023 IEEE 10th International conference on cyber security and cloud computing (CSCloud)\/2023 IEEE 9th International conference on edge computing and scalable cloud (EdgeCom), pp 464\u2013469. IEEE","DOI":"10.1109\/CSCloud-EdgeCom58631.2023.00085"},{"key":"7087_CR48","unstructured":"Pescarini M, Orsi R, Borgia M, Martinelli T (2001) Enea nuclear data centre neutron transport analysis of the venus-3 shielding benchmark experiment. KTSCG-00013, ENEA-Bologna"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07087-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-025-07087-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-07087-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,9]],"date-time":"2025-03-09T16:04:41Z","timestamp":1741536281000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-025-07087-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,9]]},"references-count":48,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["7087"],"URL":"https:\/\/doi.org\/10.1007\/s11227-025-07087-z","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,9]]},"assertion":[{"value":"17 February 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2025","order":2,"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 no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"593"}}