Huang, Juntao; Cheng, Yingda; Christlieb, Andrew J.; Roberts, Luke F.; Yong, Wen-An Machine learning moment closure models for the radiative transfer equation. II: Enforcing global hyperbolicity in gradient-based closures. (English) Zbl 07705312 Multiscale Model. Simul. 21, No. 2, 489-512 (2023). MSC: 65M06 65N06 65L06 85A25 80A21 68T07 68Q32 68T09 82C70 35R09 35L02 PDFBibTeX XMLCite \textit{J. Huang} et al., Multiscale Model. Simul. 21, No. 2, 489--512 (2023; Zbl 07705312) Full Text: DOI arXiv
Anandan, Megala; Boutin, Benjamin; Crouseilles, Nicolas High order asymptotic preserving scheme for linear kinetic equations with diffusive scaling. arXiv:2305.13393 Preprint, arXiv:2305.13393 [math.NA] (2023). MSC: 82C40 85A25 65M06 65L04 65L06 BibTeX Cite \textit{M. Anandan} et al., ``High order asymptotic preserving scheme for linear kinetic equations with diffusive scaling'', Preprint, arXiv:2305.13393 [math.NA] (2023) Full Text: arXiv OA License
Kokhanovsky, Alexander Springer series in light scattering. Vol. 8. Light polarization and multiple scattering in turbid media. (English) Zbl 07727359 Springer Series in Light Scattering. Singapore: Springer (ISBN 978-3-031-10297-4/hbk; 978-3-031-10300-1/pbk; 978-3-031-10298-1/ebook). (2022). MSC: 78-02 78A25 78A40 78A45 78A46 78A48 78A55 78A57 78A60 78M20 82C41 82C43 60K35 86A08 86A10 85A25 35Q60 PDFBibTeX XML Full Text: DOI
Huang, Juntao; Cheng, Yingda; Christlieb, Andrew J.; Roberts, Luke F. Machine learning moment closure models for the radiative transfer equation. I: Directly learning a gradient based closure. (English) Zbl 1522.65143 J. Comput. Phys. 453, Article ID 110941, 21 p. (2022). MSC: 65M06 65L06 65N06 85A25 80A21 68Q32 68T07 68T09 82C70 35R09 35Q20 PDFBibTeX XMLCite \textit{J. Huang} et al., J. Comput. Phys. 453, Article ID 110941, 21 p. (2022; Zbl 1522.65143) Full Text: DOI arXiv
Graham, Ivan G.; Parkinson, Matthew J.; Scheichl, Robert Error analysis and uncertainty quantification for the heterogeneous transport equation in slab geometry. (English) Zbl 1502.65175 IMA J. Numer. Anal. 41, No. 4, 2331-2361 (2021). Reviewer: Hang Lau (Montréal) MSC: 65N06 65N75 65C05 82D75 82M31 85A25 35R09 45K05 60H35 35R60 35Q49 PDFBibTeX XMLCite \textit{I. G. Graham} et al., IMA J. Numer. Anal. 41, No. 4, 2331--2361 (2021; Zbl 1502.65175) Full Text: DOI arXiv
Jiang, Song; Xu, Kun; Sun, Wenjun; Xu, Xiaojing Unified gas kinetic schemes for the radiation transfer equations. (Chinese. English summary) Zbl 1499.65498 Sci. Sin., Math. 51, No. 6, 799-832 (2021). MSC: 65M60 65M06 65N30 78A40 85A25 82C40 35B40 78M35 PDFBibTeX XMLCite \textit{S. Jiang} et al., Sci. Sin., Math. 51, No. 6, 799--832 (2021; Zbl 1499.65498) Full Text: DOI
Mauser, Norbert J.; Zhang, Yong; Zhao, Xiaofei On the rotating nonlinear Klein-Gordon equation: nonrelativistic limit and numerical methods. (English) Zbl 1446.65074 Multiscale Model. Simul. 18, No. 2, 999-1024 (2020). MSC: 65M06 65M70 65Z99 81Q05 85A40 35Q55 35Q40 82D50 PDFBibTeX XMLCite \textit{N. J. Mauser} et al., Multiscale Model. Simul. 18, No. 2, 999--1024 (2020; Zbl 1446.65074) Full Text: DOI
Gosse, Laurent; Vauchelet, Nicolas A truly two-dimensional, asymptotic-preserving scheme for a discrete model of radiative transfer. (English) Zbl 1434.80015 SIAM J. Numer. Anal. 58, No. 2, 1092-1116 (2020). MSC: 80M20 80A21 65M06 82B40 85A25 PDFBibTeX XMLCite \textit{L. Gosse} and \textit{N. Vauchelet}, SIAM J. Numer. Anal. 58, No. 2, 1092--1116 (2020; Zbl 1434.80015) Full Text: DOI
Goyla, Ravinder; Sharma, R. P.; Gupta, D. N.; Gaur, Nidhi The proton whistler wave energization by finite frequency kinetic Alfven wave: a numerical approach. (English) Zbl 1417.82028 Proc. Jangjeon Math. Soc. 21, No. 4, 733-743 (2018). MSC: 82D10 76W05 85A25 85A30 35Q82 82-08 65M06 65N35 PDFBibTeX XMLCite \textit{R. Goyla} et al., Proc. Jangjeon Math. Soc. 21, No. 4, 733--743 (2018; Zbl 1417.82028)
Ma, Jun; Guo, Wenfeng; Yu, Zhi Simulating magnetohydrodynamic instabilities with conservative perturbed MHD model using discontinuous Galerkin method. (English) Zbl 1488.65448 Commun. Comput. Phys. 21, No. 5, 1429-1448 (2017). MSC: 65M60 65M06 65N30 65L06 65Z05 85-08 76W05 76X05 76M10 82D10 PDFBibTeX XMLCite \textit{J. Ma} et al., Commun. Comput. Phys. 21, No. 5, 1429--1448 (2017; Zbl 1488.65448) Full Text: DOI
Gil, Agnieszka; Alania, Michael V. Study of the cosmic rays transport problems using second order parabolic type partial differential equation. (English) Zbl 1449.85013 Appl. Math. Modelling 38, No. 13, 3260-3268 (2014). MSC: 85A25 65M60 35K55 78A35 82C70 85-03 01A60 PDFBibTeX XMLCite \textit{A. Gil} and \textit{M. V. Alania}, Appl. Math. Modelling 38, No. 13, 3260--3268 (2014; Zbl 1449.85013) Full Text: DOI
Lemou, Mohammed; Méhats, Florian Micro-macro schemes for kinetic equations including boundary layers. (English) Zbl 1266.82060 SIAM J. Sci. Comput. 34, No. 6, B734-B760 (2012). Reviewer: Claudia-Veronika Meister (Darmstadt) MSC: 82C70 82-08 76N20 65N06 35B25 82C80 41A60 85A25 PDFBibTeX XMLCite \textit{M. Lemou} and \textit{F. Méhats}, SIAM J. Sci. Comput. 34, No. 6, B734--B760 (2012; Zbl 1266.82060) Full Text: DOI arXiv
Sovinec, C. R.; King, J. R.; Nimrod Team Analysis of a mixed semi-implicit/implicit algorithm for low-frequency two-fluid plasma modeling. (English) Zbl 1346.82036 J. Comput. Phys. 229, No. 16, 5803-5819 (2010). MSC: 82C80 65M06 76X05 82D10 85-08 PDFBibTeX XMLCite \textit{C. R. Sovinec} et al., J. Comput. Phys. 229, No. 16, 5803--5819 (2010; Zbl 1346.82036) Full Text: DOI
Shu, Chi-Wang High order weighted essentially nonoscillatory schemes for convection dominated problems. (English) Zbl 1160.65330 SIAM Rev. 51, No. 1, 82-126 (2009). MSC: 65M06 35L65 76L05 76M20 85-08 82D37 90B20 92-08 PDFBibTeX XMLCite \textit{C.-W. Shu}, SIAM Rev. 51, No. 1, 82--126 (2009; Zbl 1160.65330) Full Text: DOI Link
Morel, Jim E. Discrete-ordinates methods for radiative transfer in the non-relativistic stellar regime. (English) Zbl 1197.82100 Graziani, Frank (ed.), Computational methods in transport. Granlibakken 2004. Selected papers of a workshop, Granlibakken, CA, USA, September 11–16, 2004. Berlin: Springer (ISBN 3-540-28122-3/pbk). Lecture Notes in Computational Science and Engineering 48, 69-81 (2006). MSC: 82C70 85A25 85A30 76M10 76M20 82-08 PDFBibTeX XMLCite \textit{J. E. Morel}, Lect. Notes Comput. Sci. Eng. 48, 69--81 (2006; Zbl 1197.82100)
Kontar, Eduard P. Numerical consideration of quasilinear electron cloud dynamics in plasma. (English) Zbl 1017.76063 Comput. Phys. Commun. 138, No. 3, 222-233 (2001). MSC: 76M20 76X05 85A30 82D10 PDFBibTeX XMLCite \textit{E. P. Kontar}, Comput. Phys. Commun. 138, No. 3, 222--233 (2001; Zbl 1017.76063) Full Text: DOI arXiv
Saatdjian, Estéban Transport phenomena. Equations and numerical solutions. (English) Zbl 1059.82037 Chichester: Wiley (ISBN 0-471-62230-3/hbk). xii, 414 p. (2000). Reviewer: Claudia-Veronika Meister (Potsdam) MSC: 82C70 82-01 76-01 80-01 80A20 85A25 PDFBibTeX XMLCite \textit{E. Saatdjian}, Transport phenomena. Equations and numerical solutions. Chichester: Wiley (2000; Zbl 1059.82037)
Lykov, V. A.; Nikolaev, V. G. A direct method for solving radiative transfer equations in the \(P_1\) approximation. (English. Russian original) Zbl 0964.82052 Comput. Math. Math. Phys. 38, No. 11, 1830-1841 (1998); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 11, 1907-1918 (1998). Reviewer: Alexey Tret’yakov (Siedlce) MSC: 82C80 82C70 65M06 82D10 85A25 PDFBibTeX XMLCite \textit{V. A. Lykov} and \textit{V. G. Nikolaev}, Comput. Math. Math. Phys. 38, No. 11, 1830--1841 (1998; Zbl 0964.82052); translation from Zh. Vychisl. Mat. Mat. Fiz. 38, No. 11, 1907--1918 (1998)
Garcia, R. D. M. On computing some functions basic to the \(F_ N\) method in radiative transfer. (English) Zbl 0866.65097 Transp. Theory Stat. Phys. 25, No. 6, 659-679 (1996). Reviewer: S.Mika (Plzeň) MSC: 65R20 85A25 45K05 65D20 33E30 82C70 PDFBibTeX XMLCite \textit{R. D. M. Garcia}, Transp. Theory Stat. Phys. 25, No. 6, 659--679 (1996; Zbl 0866.65097) Full Text: DOI
Winslow, Alan M. Multifrequency-gray method for radiation diffusion with Compton scattering. (English) Zbl 0832.65145 J. Comput. Phys. 117, No. 2, 262-273 (1995). Reviewer: S.Mika (Plzeň) MSC: 65R20 82C70 45K05 85A25 PDFBibTeX XMLCite \textit{A. M. Winslow}, J. Comput. Phys. 117, No. 2, 262--273 (1995; Zbl 0832.65145) Full Text: DOI
Berezin, Yu. A.; Fedoruk, M. P. Modeling of nonstationary plasma processes. (Modelirovanie nestatsionarnykh plazmennykh protsessov.) (Russian) Zbl 0887.76002 Novosibirsk: VO “Nauka”. 357 p. (1993). Reviewer: Yu.S.Sayasov (MR 94k:76104) MSC: 76-02 76X05 76M20 76W05 78A55 82D10 85A30 PDFBibTeX XMLCite \textit{Yu. A. Berezin} and \textit{M. P. Fedoruk}, Modelirovanie nestatsionarnykh plazmennykh protsessov (Russian). Novosibirsk: VO ``Nauka'' (1993; Zbl 0887.76002)
Gromyko, G. F. Finite difference methods of variable-direction type for solution of nonstationary transport equations. (English. Russian original) Zbl 0801.65140 Differ. Equations 28, No. 7, 960-966 (1992); translation from Differ. Uravn. 28, No. 7, 1198-1204 (1992). MSC: 65R20 45K05 85A25 82C70 PDFBibTeX XMLCite \textit{G. F. Gromyko}, Differ. Equations 28, No. 7, 1198--1204 (1992; Zbl 0801.65140); translation from Differ. Uravn. 28, No. 7, 1198--1204 (1992)
Gryn’, V. I.; Marchenko, A. I.; Urban, V. V. Numerical method for solving the radiation transfer equation in plane and spherical geometry. (Russian) Zbl 0716.65127 Zh. Vychisl. Mat. Mat. Fiz. 30, No. 8, 1210-1223 (1990). Reviewer: J.Gilewicz MSC: 65R20 45K05 85A25 82C70 PDFBibTeX XMLCite \textit{V. I. Gryn'} et al., Zh. Vychisl. Mat. Mat. Fiz. 30, No. 8, 1210--1223 (1990; Zbl 0716.65127)
Ly, L. N. An application of the pivotal-condensation method to modeling the air-sea boundary-layer structure. (English) Zbl 0692.76018 Math. Comput. Modelling 12, No. 9, 1117-1130 (1989). MSC: 76B60 85A05 85A35 PDFBibTeX XMLCite \textit{L. N. Ly}, Math. Comput. Modelling 12, No. 9, 1117--1130 (1989; Zbl 0692.76018) Full Text: DOI
Livne, E.; Glasner, A. A finite difference scheme for the heat conduction equation. (English) Zbl 0558.65075 J. Comput. Phys. 58, 59-66 (1985). MSC: 65N06 35K05 35K60 82C70 85A25 PDFBibTeX XMLCite \textit{E. Livne} and \textit{A. Glasner}, J. Comput. Phys. 58, 59--66 (1985; Zbl 0558.65075) Full Text: DOI
Kulinich, V. V.; Morozov, S. F. A variational-difference method of solving the non-stationary radiation transport equation. (English) Zbl 0509.65064 U.S.S.R. Comput. Math. Math. Phys. 22, No. 2, 121-129 (1982). MSC: 65R20 45K05 82C70 85A25 PDFBibTeX XMLCite \textit{V. V. Kulinich} and \textit{S. F. Morozov}, U.S.S.R. Comput. Math. Math. Phys. 22, No. 2, 121--129 (1982; Zbl 0509.65064) Full Text: DOI
Kulinich, V. V.; Morozov, S. F. Variational-difference method for solving the non-stationary radiation transfer equation. (Russian) Zbl 0489.65077 Zh. Vychisl. Mat. Mat. Fiz. 22, 367-374 (1982). MSC: 65R20 45J05 82C70 85A25 PDFBibTeX XMLCite \textit{V. V. Kulinich} and \textit{S. F. Morozov}, Zh. Vychisl. Mat. Mat. Fiz. 22, 367--374 (1982; Zbl 0489.65077)
Vyskrebentsev, A. I. A method for the numerical solution of the radiation transport equation in one-dimensional problems of gas dynamics. (English) Zbl 0558.76068 U.S.S.R. Comput. Math. Math. Phys. 21, No. 5, 134-142 (1981). MSC: 76N15 76M99 76N99 65D30 82C70 85A25 65N06 PDFBibTeX XMLCite \textit{A. I. Vyskrebentsev}, U.S.S.R. Comput. Math. Math. Phys. 21, No. 5, 134--142 (1981; Zbl 0558.76068) Full Text: DOI
Vyskrebentsev, A. I. A method of numerical solution of radiation transfer equation in one- dimensional problems of gas dynamics. (Russian) Zbl 0488.76080 Zh. Vychisl. Mat. Mat. Fiz. 21, 1206-1214 (1981). MSC: 76N15 76M99 85A25 76N99 82C70 65D30 65N06 PDFBibTeX XMLCite \textit{A. I. Vyskrebentsev}, Zh. Vychisl. Mat. Mat. Fiz. 21, 1206--1214 (1981; Zbl 0488.76080)
Williams, M. M. R. On two integro-differential equations arising in particle transport theory. (English) Zbl 0421.45011 J. Phys. A 13, 675-688 (1980). MSC: 45K05 45L05 81U99 82C70 85A25 PDFBibTeX XMLCite \textit{M. M. R. Williams}, J. Phys. A, Math. Gen. 13, 675--688 (1980; Zbl 0421.45011) Full Text: DOI
Laletin, N. I. Principles of construction of finite-difference analogies of the neutron- transfer equation for one class of problems. (Russian) Zbl 0438.45012 Variational-Difference Methods in Mathematical Physics, Mater. All-Union Conf., Novosibirsk 1977, 93-101 (1978). MSC: 45K05 82C70 85A25 82D45 PDFBibTeX XML
Lesaint, P. Approximation de problèmes de transport en neutronique. (French) Zbl 0404.65059 Comput. Meth. appl. Sci. Eng., 2nd int. Symp., Versailles 1975, Lect. Notes Econ. math. Syst. 134, 224-242 (1976). MSC: 65Z05 65N30 65N12 82C70 85A25 PDFBibTeX XML