{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T12:12:07Z","timestamp":1774959127040,"version":"3.50.1"},"reference-count":85,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,5,12]],"date-time":"2018-05-12T00:00:00Z","timestamp":1526083200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,5,12]],"date-time":"2018-05-12T00:00:00Z","timestamp":1526083200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100006192","name":"Advanced Scientific Computing Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006192","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":[[2018,11]]},"DOI":"10.1007\/s10915-018-0726-6","type":"journal-article","created":{"date-parts":[[2018,5,12]],"date-time":"2018-05-12T02:12:25Z","timestamp":1526091145000},"page":"819-849","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration"],"prefix":"10.1007","volume":"77","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3910-2613","authenticated-orcid":false,"given":"Debojyoti","family":"Ghosh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikhail A.","family":"Dorf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Milo R.","family":"Dorr","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeffrey A. F.","family":"Hittinger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,5,12]]},"reference":[{"issue":"2\u20133","key":"726_CR1","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/S0168-9274(97)00056-1","volume":"25","author":"UM Ascher","year":"1997","unstructured":"Ascher, U.M., Ruuth, S.J., Spiteri, R.J.: Implicit\u2013explicit Runge\u2013Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25(2\u20133), 151\u2013167 (1997). \n                    https:\/\/doi.org\/10.1016\/S0168-9274(97)00056-1","journal-title":"Appl. Numer. Math."},{"issue":"3","key":"726_CR2","doi-asserted-by":"publisher","first-page":"032108","DOI":"10.1063\/1.4943194","volume":"23","author":"JW Banks","year":"2016","unstructured":"Banks, J.W., Brunner, S., Berger, R.L., Tran, T.M.: Vlasov simulations of electron-ion collision effects on damping of electron plasma waves. Phys. Plasmas 23(3), 032108 (2016). \n                    https:\/\/doi.org\/10.1063\/1.4943194","journal-title":"Phys. Plasmas"},{"issue":"1","key":"726_CR3","doi-asserted-by":"publisher","first-page":"015015","DOI":"10.1088\/0741-3335\/54\/1\/015015","volume":"54","author":"EA Belli","year":"2012","unstructured":"Belli, E.A., Candy, J.: Full linearized Fokker\u2013Planck collisions in neoclassical transport simulations. Plasma Phys. Control. Fusion 54(1), 015015 (2012). \n                    https:\/\/doi.org\/10.1088\/0741-3335\/54\/1\/015015","journal-title":"Plasma Phys. Control. Fusion"},{"issue":"1","key":"726_CR4","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/0021-9991(87)90160-4","volume":"69","author":"Y Berezin","year":"1987","unstructured":"Berezin, Y., Khudick, V., Pekker, M.: Conservative finite-difference schemes for the Fokker\u2013Planck equation not violating the law of an increasing entropy. J. Comput. Phys. 69(1), 163\u2013174 (1987). \n                    https:\/\/doi.org\/10.1016\/0021-9991(87)90160-4","journal-title":"J. Comput. Phys."},{"key":"726_CR5","first-page":"205","volume":"1","author":"SI Braginskii","year":"1965","unstructured":"Braginskii, S.I.: Transport processes in a plasma. Rev. Plasma Phys. 1, 205 (1965)","journal-title":"Rev. Plasma Phys."},{"key":"726_CR6","unstructured":"Brunner, S., Tran, T., Hittinger, J.: Numerical implementation of the non-linear Landau collision operator for Eulerian Vlasov simulations. part I: computation of the Rosenbluth potentials. Tech. Rep. LLNL-SR-459135, Lawrence Livermore National Laboratory, Livermore, CA (2010)"},{"issue":"1","key":"726_CR7","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1006\/jcph.1998.6015","volume":"145","author":"C Buet","year":"1998","unstructured":"Buet, C., Cordier, S.: Conservative and entropy decaying numerical scheme for the isotropic Fokker\u2013Planck\u2013Landau equation. J. Comput. Phys. 145(1), 228\u2013245 (1998). \n                    https:\/\/doi.org\/10.1006\/jcph.1998.6015","journal-title":"J. Comput. Phys."},{"issue":"2","key":"726_CR8","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1006\/jcph.1997.5669","volume":"133","author":"C Buet","year":"1997","unstructured":"Buet, C., Cordier, S., Degond, P., Lemou, M.: Fast algorithms for numerical, conservative, and entropy approximations of the Fokker\u2013Planck\u2013Landau equation. J. Comput. Phys. 133(2), 310\u2013322 (1997). \n                    https:\/\/doi.org\/10.1006\/jcph.1997.5669","journal-title":"J. Comput. Phys."},{"key":"726_CR9","doi-asserted-by":"publisher","DOI":"10.1002\/0470868279","volume-title":"Numerical Methods for Ordinary Differential Equations","author":"J Butcher","year":"2003","unstructured":"Butcher, J.: Numerical Methods for Ordinary Differential Equations. Wiley, New York (2003)"},{"key":"726_CR10","doi-asserted-by":"publisher","first-page":"045001","DOI":"10.1103\/PhysRevLett.91.045001","volume":"91","author":"J Candy","year":"2003","unstructured":"Candy, J., Waltz, R.E.: Anomalous transport scaling in the DIII-D tokamak matched by supercomputer simulation. Phys. Rev. Lett. 91, 045001 (2003). \n                    https:\/\/doi.org\/10.1103\/PhysRevLett.91.045001","journal-title":"Phys. Rev. Lett."},{"key":"726_CR11","doi-asserted-by":"publisher","first-page":"2143","DOI":"10.1103\/PhysRevLett.67.2143","volume":"67","author":"M Casanova","year":"1991","unstructured":"Casanova, M., Larroche, O., Matte, J.P.: Kinetic simulation of a collisional shock wave in a plasma. Phys. Rev. Lett. 67, 2143\u20132146 (1991). \n                    https:\/\/doi.org\/10.1103\/PhysRevLett.67.2143","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"726_CR12","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1006\/jcph.1999.6394","volume":"157","author":"L Chac\u00f3n","year":"2000","unstructured":"Chac\u00f3n, L., Barnes, D.C., Knoll, D.A., Miley, G.H.: An implicit energy-conservative 2D Fokker\u2013Planck algorithm: I. Difference scheme. J. Comput. Phys. 157(2), 618\u2013653 (2000). \n                    https:\/\/doi.org\/10.1006\/jcph.1999.6394","journal-title":"J. Comput. Phys."},{"issue":"2","key":"726_CR13","doi-asserted-by":"publisher","first-page":"654","DOI":"10.1006\/jcph.1999.6395","volume":"157","author":"L Chac\u00f3n","year":"2000","unstructured":"Chac\u00f3n, L., Barnes, D.C., Knoll, D.A., Miley, G.H.: An implicit energy-conservative 2D Fokker\u2013Planck algorithm: II. Jacobian-free Newton\u2013Krylov solver. J. Comput. Phys. 157(2), 654\u2013682 (2000). \n                    https:\/\/doi.org\/10.1006\/jcph.1999.6395","journal-title":"J. Comput. Phys."},{"issue":"6","key":"726_CR14","doi-asserted-by":"publisher","first-page":"062510","DOI":"10.1063\/1.2937116","volume":"15","author":"CS Chang","year":"2008","unstructured":"Chang, C.S., Ku, S.: Spontaneous rotation sources in a quiescent tokamak edge plasma. Phys. Plasmas 15(6), 062510 (2008). \n                    https:\/\/doi.org\/10.1063\/1.2937116","journal-title":"Phys. Plasmas"},{"issue":"1","key":"726_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0021-9991(70)90001-X","volume":"6","author":"J Chang","year":"1970","unstructured":"Chang, J., Cooper, G.: A practical difference scheme for Fokker\u2013Planck equations. J. Comput. Phys. 6(1), 1\u201316 (1970). \n                    https:\/\/doi.org\/10.1016\/0021-9991(70)90001-X","journal-title":"J. Comput. Phys."},{"issue":"10","key":"726_CR16","doi-asserted-by":"publisher","first-page":"2391","DOI":"10.1016\/j.cpc.2014.05.010","volume":"185","author":"G Chen","year":"2014","unstructured":"Chen, G., Chac\u00f3n, L.: An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov\u2013Darwin particle-in-cell algorithm. Comput. Phys. Commun. 185(10), 2391\u20132402 (2014). \n                    https:\/\/doi.org\/10.1016\/j.cpc.2014.05.010","journal-title":"Comput. Phys. Commun."},{"key":"726_CR17","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.cpc.2015.08.008","volume":"197","author":"G Chen","year":"2015","unstructured":"Chen, G., Chac\u00f3n, L.: A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov\u2013Darwin particle-in-cell algorithm. Comput. Phys. Commun. 197, 73\u201387 (2015). \n                    https:\/\/doi.org\/10.1016\/j.cpc.2015.08.008","journal-title":"Comput. Phys. Commun."},{"issue":"18","key":"726_CR18","doi-asserted-by":"publisher","first-page":"7018","DOI":"10.1016\/j.jcp.2011.05.031","volume":"230","author":"G Chen","year":"2011","unstructured":"Chen, G., Chac\u00f3n, L., Barnes, D.: An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm. J. Comput. Phys. 230(18), 7018\u20137036 (2011). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2011.05.031","journal-title":"J. Comput. Phys."},{"issue":"3","key":"726_CR19","doi-asserted-by":"publisher","first-page":"330","DOI":"10.1016\/0021-9991(76)90053-X","volume":"22","author":"C Cheng","year":"1976","unstructured":"Cheng, C., Knorr, G.: The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22(3), 330\u2013351 (1976). \n                    https:\/\/doi.org\/10.1016\/0021-9991(76)90053-X","journal-title":"J. Comput. Phys."},{"issue":"1\u20133","key":"726_CR20","doi-asserted-by":"publisher","first-page":"212","DOI":"10.1002\/ctpp.200810038","volume":"48","author":"RH Cohen","year":"2008","unstructured":"Cohen, R.H., Xu, X.Q.: Progress in kinetic simulation of edge plasmas. Contrib. Plasma Phys. 48(1\u20133), 212\u2013223 (2008). \n                    https:\/\/doi.org\/10.1002\/ctpp.200810038","journal-title":"Contrib. Plasma Phys."},{"issue":"8","key":"726_CR21","doi-asserted-by":"publisher","first-page":"2952","DOI":"10.1016\/j.jcp.2010.12.044","volume":"230","author":"P Colella","year":"2011","unstructured":"Colella, P., Dorr, M., Hittinger, J., Martin, D.: High-order, finite-volume methods in mapped coordinates. J. Comput. Phys. 230(8), 2952\u20132976 (2011). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2010.12.044","journal-title":"J. Comput. Phys."},{"issue":"10","key":"726_CR22","doi-asserted-by":"publisher","first-page":"1730","DOI":"10.1016\/j.cpc.2009.04.024","volume":"180","author":"N Crouseilles","year":"2009","unstructured":"Crouseilles, N., Respaud, T., Sonnendr\u00fccker, E.: A forward semi-Lagrangian method for the numerical solution of the Vlasov equation. Comput. Phys. Commun. 180(10), 1730\u20131745 (2009). \n                    https:\/\/doi.org\/10.1016\/j.cpc.2009.04.024","journal-title":"Comput. Phys. Commun."},{"key":"726_CR23","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971200","volume-title":"Numerical Methods for Unconstrained Optimization and Nonlinear Equations","author":"J Dennis","year":"1996","unstructured":"Dennis, J., Schnabel, R.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Society for Industrial and Applied Mathematics, Philadelphia (1996). \n                    https:\/\/doi.org\/10.1137\/1.9781611971200"},{"issue":"5\u20136","key":"726_CR24","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1002\/ctpp.201210042","volume":"52","author":"MA Dorf","year":"2012","unstructured":"Dorf, M.A., Cohen, R.H., Compton, J.C., Dorr, M., Rognlien, T.D., Angus, J., Krasheninnikov, S., Colella, P., Martin, D., McCorquodale, P.: Progress with the COGENT edge kinetic code: collision operator options. Contrib. Plasma Phys. 52(5\u20136), 518\u2013522 (2012). \n                    https:\/\/doi.org\/10.1002\/ctpp.201210042","journal-title":"Contrib. Plasma Phys."},{"issue":"4\u20136","key":"726_CR25","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1002\/ctpp.201410023","volume":"54","author":"MA Dorf","year":"2014","unstructured":"Dorf, M.A., Cohen, R.H., Dorr, M., Hittinger, J., Rognlien, T.D.: Progress with the COGENT edge kinetic code: implementing the Fokker\u2013Planck collision operator. Contrib. Plasma Phys. 54(4\u20136), 517\u2013523 (2014). \n                    https:\/\/doi.org\/10.1002\/ctpp.201410023","journal-title":"Contrib. Plasma Phys."},{"issue":"1","key":"726_CR26","doi-asserted-by":"publisher","first-page":"012513","DOI":"10.1063\/1.4776712","volume":"20","author":"MA Dorf","year":"2013","unstructured":"Dorf, M.A., Cohen, R.H., Dorr, M., Rognlien, T., Hittinger, J., Compton, J., Colella, P., Martin, D., McCorquodale, P.: Simulation of neoclassical transport with the continuum gyrokinetic code COGENT. Phys. Plasmas 20(1), 012513 (2013). \n                    https:\/\/doi.org\/10.1063\/1.4776712","journal-title":"Phys. Plasmas"},{"key":"726_CR27","unstructured":"Dorr, M.R., Colella, P., Dorf, M.A., Ghosh, D., Hittinger, J.A.F., Schwartz, P.O.: High-order discretization of a gyrokinetic Vlasov model in edge plasma geometry. Submitted (2017). \n                    arXiv:1712.01978"},{"issue":"4","key":"726_CR28","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1175\/MWR-D-11-00088.1","volume":"140","author":"DR Durran","year":"2012","unstructured":"Durran, D.R., Blossey, P.N.: Implicit\u2013explicit multistep methods for fast-wave-slow-wave problems. Mon. Weather Rev. 140(4), 1307\u20131325 (2012). \n                    https:\/\/doi.org\/10.1175\/MWR-D-11-00088.1","journal-title":"Mon. Weather Rev."},{"issue":"2","key":"726_CR29","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1006\/jcph.1994.1101","volume":"112","author":"E Epperlein","year":"1994","unstructured":"Epperlein, E.: Implicit and conservative difference scheme for the Fokker\u2013Planck equation. J. Comput. Phys. 112(2), 291\u2013297 (1994). \n                    https:\/\/doi.org\/10.1006\/jcph.1994.1101","journal-title":"J. Comput. Phys."},{"key":"726_CR30","doi-asserted-by":"publisher","first-page":"2453","DOI":"10.1103\/PhysRevLett.61.2453","volume":"61","author":"EM Epperlein","year":"1988","unstructured":"Epperlein, E.M., Rickard, G.J., Bell, A.R.: Two-dimensional nonlocal electron transport in laser-produced plasmas. Phys. Rev. Lett. 61, 2453\u20132456 (1988). \n                    https:\/\/doi.org\/10.1103\/PhysRevLett.61.2453","journal-title":"Phys. Rev. Lett."},{"key":"726_CR31","doi-asserted-by":"publisher","first-page":"632","DOI":"10.1007\/3-540-47789-6_66","volume-title":"hypre: A Library of High Performance Preconditioners","author":"RD Falgout","year":"2002","unstructured":"Falgout, R.D., Yang, U.M.: hypre: A Library of High Performance Preconditioners, pp. 632\u2013641. Springer, Berlin (2002). \n                    https:\/\/doi.org\/10.1007\/3-540-47789-6_66"},{"issue":"1","key":"726_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jcph.2002.7010","volume":"179","author":"F Filbet","year":"2002","unstructured":"Filbet, F., Pareschi, L.: A numerical method for the accurate solution of the Fokker\u2013Planck\u2013Landau equation in the nonhomogeneous case. J. Comput. Phys. 179(1), 1\u201326 (2002). \n                    https:\/\/doi.org\/10.1006\/jcph.2002.7010","journal-title":"J. Comput. Phys."},{"issue":"1","key":"726_CR33","doi-asserted-by":"publisher","first-page":"166","DOI":"10.1006\/jcph.2001.6818","volume":"172","author":"F Filbet","year":"2001","unstructured":"Filbet, F., Sonnendr\u00fccker, E., Bertrand, P.: Conservative numerical schemes for the Vlasov equation. J. Comput. Phys. 172(1), 166\u2013187 (2001). \n                    https:\/\/doi.org\/10.1006\/jcph.2001.6818","journal-title":"J. Comput. Phys."},{"issue":"3","key":"726_CR34","doi-asserted-by":"publisher","first-page":"A1848","DOI":"10.1137\/15M1044369","volume":"38","author":"D Ghosh","year":"2016","unstructured":"Ghosh, D., Constantinescu, E.M.: Semi-implicit time integration of atmospheric flows with characteristic-based flux partitioning. SIAM J. Sci. Comput. 38(3), A1848\u2013A1875 (2016). \n                    https:\/\/doi.org\/10.1137\/15M1044369","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"726_CR35","doi-asserted-by":"publisher","first-page":"B1162","DOI":"10.1137\/120876034","volume":"35","author":"FX Giraldo","year":"2013","unstructured":"Giraldo, F.X., Kelly, J.F., Constantinescu, E.: Implicit\u2013explicit formulations of a three-dimensional nonhydrostatic unified model of the atmosphere (NUMA). SIAM J. Sci. Comput. 35(5), B1162\u2013B1194 (2013). \n                    https:\/\/doi.org\/10.1137\/120876034","journal-title":"SIAM J. Sci. Comput."},{"issue":"6","key":"726_CR36","doi-asserted-by":"publisher","first-page":"3394","DOI":"10.1137\/090775889","volume":"32","author":"FX Giraldo","year":"2010","unstructured":"Giraldo, F.X., Restelli, M., L\u00e4uter, M.: Semi-implicit formulations of the Navier\u2013Stokes equations: application to nonhydrostatic atmospheric modeling. SIAM J. Sci. Comput. 32(6), 3394\u20133425 (2010). \n                    https:\/\/doi.org\/10.1137\/090775889","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"726_CR37","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1016\/j.jcp.2006.01.023","volume":"217","author":"V Grandgirard","year":"2006","unstructured":"Grandgirard, V., Brunetti, M., Bertrand, P., Besse, N., Garbet, X., Ghendrih, P., Manfredi, G., Sarazin, Y., Sauter, O., Sonnendr\u00fccker, E., Vaclavik, J., Villard, L.: A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation. J. Comput. Phys. 217(2), 395\u2013423 (2006). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2006.01.023","journal-title":"J. Comput. Phys."},{"issue":"12","key":"726_CR38","doi-asserted-by":"publisher","first-page":"4658","DOI":"10.1063\/1.872034","volume":"3","author":"TS Hahm","year":"1996","unstructured":"Hahm, T.S.: Nonlinear gyrokinetic equations for turbulence in core transport barriers. Phys. Plasmas 3(12), 4658\u20134664 (1996). \n                    https:\/\/doi.org\/10.1063\/1.872034","journal-title":"Phys. Plasmas"},{"issue":"2","key":"726_CR39","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1006\/jcph.2001.6891","volume":"173","author":"J Heikkinen","year":"2001","unstructured":"Heikkinen, J., Kiviniemi, T., Kurki-Suonio, T., Peeters, A., Sipil\u00e4, S.: Particle simulation of the neoclassical plasmas. J. Comput. Phys. 173(2), 527\u2013548 (2001). \n                    https:\/\/doi.org\/10.1006\/jcph.2001.6891","journal-title":"J. Comput. Phys."},{"issue":"7\u20139","key":"726_CR40","doi-asserted-by":"publisher","first-page":"490","DOI":"10.1002\/ctpp.200610035","volume":"46","author":"JA Heikkinen","year":"2006","unstructured":"Heikkinen, J.A., Henriksson, S., Janhunen, S., Kiviniemi, T.P., Ogando, F.: Gyrokinetic simulation of particle and heat transport in the presence of wide orbits and strong profile variations in the edge plasma. Contrib. Plasma Phys. 46(7\u20139), 490\u2013495 (2006). \n                    https:\/\/doi.org\/10.1002\/ctpp.200610035","journal-title":"Contrib. Plasma Phys."},{"key":"726_CR41","unstructured":"Huba, J.D.: NRL plasma formulary. Tech. rep, Naval Research Laboratory, Washington, DC (2016)"},{"issue":"6","key":"726_CR42","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1016\/j.cpc.2008.04.005","volume":"179","author":"Y Idomura","year":"2008","unstructured":"Idomura, Y., Ida, M., Kano, T., Aiba, N., Tokuda, S.: Conservative global gyrokinetic toroidal full-f five-dimensional Vlasov simulation. Comput. Phys. Commun. 179(6), 391\u2013403 (2008). \n                    https:\/\/doi.org\/10.1016\/j.cpc.2008.04.005","journal-title":"Comput. Phys. Commun."},{"issue":"1","key":"726_CR43","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1016\/j.cnsns.2007.05.015","volume":"13","author":"Y Idomura","year":"2008","unstructured":"Idomura, Y., Ida, M., Tokuda, S.: Conservative gyrokinetic Vlasov simulation. Commun. Nonlinear Sci. Numer. Simul. 13(1), 227\u2013233 (2008). \n                    https:\/\/doi.org\/10.1016\/j.cnsns.2007.05.015\n                    \n                  . (Vlasovia 2006: The Second International Workshop on the Theory and Applications of the Vlasov Equation)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"726_CR44","volume-title":"Classical Electrodynamics","author":"JD Jackson","year":"1999","unstructured":"Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999)","edition":"3"},{"issue":"10","key":"726_CR45","doi-asserted-by":"publisher","first-page":"1760","DOI":"10.1016\/j.cpc.2009.05.020","volume":"180","author":"G Jacobs","year":"2009","unstructured":"Jacobs, G., Hesthaven, J.: Implicit-explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning. Comput. Phys. Commun. 180(10), 1760\u20131767 (2009). \n                    https:\/\/doi.org\/10.1016\/j.cpc.2009.05.020","journal-title":"Comput. Phys. Commun."},{"issue":"2","key":"726_CR46","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/0021-9991(77)90013-4","volume":"25","author":"R James","year":"1977","unstructured":"James, R.: The solution of Poisson\u2019s equation for isolated source distributions. J. Comput. Phys. 25(2), 71\u201393 (1977). \n                    https:\/\/doi.org\/10.1016\/0021-9991(77)90013-4","journal-title":"J. Comput. Phys."},{"issue":"22","key":"726_CR47","doi-asserted-by":"publisher","first-page":"8313","DOI":"10.1016\/j.jcp.2010.07.019","volume":"229","author":"SY Kadioglu","year":"2010","unstructured":"Kadioglu, S.Y., Knoll, D.A., Lowrie, R.B., Rauenzahn, R.M.: A second order self-consistent IMEX method for radiation hydrodynamics. J. Comput. Phys. 229(22), 8313\u20138332 (2010). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2010.07.019","journal-title":"J. Comput. Phys."},{"issue":"1\u20132","key":"726_CR48","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/S0168-9274(02)00138-1","volume":"44","author":"CA Kennedy","year":"2003","unstructured":"Kennedy, C.A., Carpenter, M.H.: Additive Runge\u2013Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44(1\u20132), 139\u2013181 (2003). \n                    https:\/\/doi.org\/10.1016\/S0168-9274(02)00138-1","journal-title":"Appl. Numer. Math."},{"key":"726_CR49","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1103\/PhysRevA.32.666","volume":"32","author":"TH Kho","year":"1985","unstructured":"Kho, T.H.: Relaxation of a system of charged particles. Phys. Rev. A 32, 666\u2013669 (1985). \n                    https:\/\/doi.org\/10.1103\/PhysRevA.32.666","journal-title":"Phys. Rev. A"},{"issue":"1","key":"726_CR50","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jcp.2003.08.017","volume":"194","author":"R Kingham","year":"2004","unstructured":"Kingham, R., Bell, A.: An implicit Vlasov\u2013Fokker\u2013Planck code to model non-local electron transport in 2-D with magnetic fields. J. Comput. Phys. 194(1), 1\u201334 (2004). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2003.08.017","journal-title":"J. Comput. Phys."},{"issue":"2","key":"726_CR51","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.jcp.2003.08.010","volume":"193","author":"D Knoll","year":"2004","unstructured":"Knoll, D., Keyes, D.: Jacobian-free Newton\u2013Krylov methods: a survey of approaches and applications. J. Comput. Phys. 193(2), 357\u2013397 (2004). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2003.08.010","journal-title":"J. Comput. Phys."},{"issue":"2","key":"726_CR52","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/s10915-011-9554-7","volume":"52","author":"H Kumar","year":"2012","unstructured":"Kumar, H., Mishra, S.: Entropy stable numerical schemes for two-fluid plasma equations. J. Sci. Comput. 52(2), 401\u2013425 (2012). \n                    https:\/\/doi.org\/10.1007\/s10915-011-9554-7","journal-title":"J. Sci. Comput."},{"issue":"2","key":"726_CR53","first-page":"203","volume":"7","author":"LD Landau","year":"1937","unstructured":"Landau, L.D.: The kinetic equation in the case of Coulomb interaction. Zh. Eksper. i Teoret. Fiz. 7(2), 203\u2013209 (1937)","journal-title":"Zh. Eksper. i Teoret. Fiz."},{"key":"726_CR54","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1016\/j.jcp.2013.02.041","volume":"243","author":"M Landreman","year":"2013","unstructured":"Landreman, M., Ernst, D.R.: New velocity-space discretization for continuum kinetic calculations and Fokker\u2013Planck collisions. J. Comput. Phys. 243, 130\u2013150 (2013). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2013.02.041","journal-title":"J. Comput. Phys."},{"issue":"8","key":"726_CR55","doi-asserted-by":"publisher","first-page":"2816","DOI":"10.1063\/1.860670","volume":"5","author":"O Larroche","year":"1993","unstructured":"Larroche, O.: Kinetic simulation of a plasma collision experiment. Phys. Fluids B 5(8), 2816\u20132840 (1993). \n                    https:\/\/doi.org\/10.1063\/1.860670","journal-title":"Phys. Fluids B"},{"issue":"2","key":"726_CR56","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1140\/epjd\/e2003-00251-1","volume":"27","author":"O Larroche","year":"2003","unstructured":"Larroche, O.: Kinetic simulations of fuel ion transport in ICF target implosions. Eur. Phys. J. D At. Mol. Opt. Plasma Phys. 27(2), 131\u2013146 (2003). \n                    https:\/\/doi.org\/10.1140\/epjd\/e2003-00251-1","journal-title":"Eur. Phys. J. D At. Mol. Opt. Plasma Phys."},{"issue":"3","key":"726_CR57","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0021-9991(85)90070-1","volume":"61","author":"E Larsen","year":"1985","unstructured":"Larsen, E., Levermore, C., Pomraning, G., Sanderson, J.: Discretization methods for one-dimensional Fokker\u2013Planck operators. J. Comput. Phys. 61(3), 359\u2013390 (1985). \n                    https:\/\/doi.org\/10.1016\/0021-9991(85)90070-1","journal-title":"J. Comput. Phys."},{"issue":"2","key":"726_CR58","doi-asserted-by":"publisher","first-page":"556","DOI":"10.1063\/1.864140","volume":"26","author":"WW Lee","year":"1983","unstructured":"Lee, W.W.: Gyrokinetic approach in particle simulation. Phys. Fluids 26(2), 556\u2013562 (1983). \n                    https:\/\/doi.org\/10.1063\/1.864140","journal-title":"Phys. Fluids"},{"issue":"4","key":"726_CR59","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s002110050327","volume":"78","author":"M Lemou","year":"1998","unstructured":"Lemou, M.: Multipole expansions for the Fokker\u2013Planck\u2013Landau operator. Numer. Math. 78(4), 597\u2013618 (1998). \n                    https:\/\/doi.org\/10.1007\/s002110050327","journal-title":"Numer. Math."},{"issue":"10","key":"726_CR60","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1016\/j.crma.2004.03.010","volume":"338","author":"M Lemou","year":"2004","unstructured":"Lemou, M., Mieussens, L.: Fast implicit schemes for the Fokker\u2013Planck\u2013Landau equation. C. R. Math. 338(10), 809\u2013814 (2004). \n                    https:\/\/doi.org\/10.1016\/j.crma.2004.03.010","journal-title":"C. R. Math."},{"issue":"3","key":"726_CR61","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1137\/040609422","volume":"27","author":"M Lemou","year":"2005","unstructured":"Lemou, M., Mieussens, L.: Implicit schemes for the Fokker\u2013Planck\u2013Landau equation. SIAM J. Sci. Comput. 27(3), 809\u2013830 (2005). \n                    https:\/\/doi.org\/10.1137\/040609422","journal-title":"SIAM J. Sci. Comput."},{"issue":"9","key":"726_CR62","doi-asserted-by":"publisher","first-page":"1986","DOI":"10.1016\/j.cpc.2012.04.028","volume":"183","author":"S Maeyama","year":"2012","unstructured":"Maeyama, S., Ishizawa, A., Watanabe, T.H., Nakajima, N., Tsuji-Iio, S., Tsutsui, H.: A hybrid method of semi-Lagrangian and additive semi-implicit Runge\u2013Kutta schemes for gyrokinetic Vlasov simulations. Comput. Phys. Commun. 183(9), 1986\u20131992 (2012). \n                    https:\/\/doi.org\/10.1016\/j.cpc.2012.04.028","journal-title":"Comput. Phys. Commun."},{"key":"726_CR63","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.jcp.2015.01.006","volume":"288","author":"P McCorquodale","year":"2015","unstructured":"McCorquodale, P., Dorr, M., Hittinger, J., Colella, P.: High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids. J. Comput. Phys. 288, 181\u2013195 (2015). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2015.01.006","journal-title":"J. Comput. Phys."},{"issue":"1","key":"726_CR64","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/0010-4655(81)90105-3","volume":"24","author":"M McCoy","year":"1981","unstructured":"McCoy, M., Mirin, A., Killeen, J.: FPPAC: a two-dimensional multispecies nonlinear Fokker\u2013Planck package. Comput. Phys. Commun. 24(1), 37\u201361 (1981). \n                    https:\/\/doi.org\/10.1016\/0010-4655(81)90105-3","journal-title":"Comput. Phys. Commun."},{"issue":"2","key":"726_CR65","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1006\/jcph.1997.5736","volume":"136","author":"V Mousseau","year":"1997","unstructured":"Mousseau, V., Knoll, D.: Fully implicit kinetic solution of collisional plasmas. J. Comput. Phys. 136(2), 308\u2013323 (1997). \n                    https:\/\/doi.org\/10.1006\/jcph.1997.5736","journal-title":"J. Comput. Phys."},{"issue":"1\u20132","key":"726_CR66","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/BF02728986","volume":"25","author":"L Pareschi","year":"2005","unstructured":"Pareschi, L., Russo, G.: Implicit\u2013explicit Runge\u2013Kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25(1\u20132), 129\u2013155 (2005). \n                    https:\/\/doi.org\/10.1007\/BF02728986","journal-title":"J. Sci. Comput."},{"issue":"21","key":"726_CR67","doi-asserted-by":"publisher","first-page":"7840","DOI":"10.1016\/j.jcp.2011.07.005","volume":"230","author":"A Pataki","year":"2011","unstructured":"Pataki, A., Greengard, L.: Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator. J. Comput. Phys. 230(21), 7840\u20137852 (2011). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2011.07.005","journal-title":"J. Comput. Phys."},{"issue":"1","key":"726_CR68","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1137\/S1064827596303843","volume":"19","author":"M Pernice","year":"1998","unstructured":"Pernice, M., Walker, H.F.: NITSOL: a Newton iterative solver for nonlinear systems. SIAM J. Sci. Comput. 19(1), 302\u2013318 (1998). \n                    https:\/\/doi.org\/10.1137\/S1064827596303843","journal-title":"SIAM J. Sci. Comput."},{"issue":"9","key":"726_CR69","doi-asserted-by":"publisher","first-page":"3663","DOI":"10.1063\/1.1286509","volume":"7","author":"GD Porter","year":"2000","unstructured":"Porter, G.D., Isler, R., Boedo, J., Rognlien, T.D.: Detailed comparison of simulated and measured plasma profiles in the scrape-off layer and edge plasma of DIII-D. Phys. Plasmas 7(9), 3663\u20133680 (2000). \n                    https:\/\/doi.org\/10.1063\/1.1286509","journal-title":"Phys. Plasmas"},{"issue":"4","key":"726_CR70","doi-asserted-by":"publisher","first-page":"1130","DOI":"10.1016\/j.jcp.2009.10.016","volume":"229","author":"JM Qiu","year":"2010","unstructured":"Qiu, J.M., Christlieb, A.: A conservative high order semi-Lagrangian WENO method for the Vlasov equation. J. Comput. Phys. 229(4), 1130\u20131149 (2010). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2009.10.016","journal-title":"J. Comput. Phys."},{"issue":"23","key":"726_CR71","doi-asserted-by":"publisher","first-page":"8386","DOI":"10.1016\/j.jcp.2011.07.018","volume":"230","author":"JM Qiu","year":"2011","unstructured":"Qiu, J.M., Shu, C.W.: Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: theoretical analysis and application to the Vlasov\u2013Poisson system. J. Comput. Phys. 230(23), 8386\u20138409 (2011). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2011.07.018","journal-title":"J. Comput. Phys."},{"key":"726_CR72","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1103\/PhysRev.107.1","volume":"107","author":"MN Rosenbluth","year":"1957","unstructured":"Rosenbluth, M.N., MacDonald, W.M., Judd, D.L.: Fokker\u2013Planck equation for an inverse-square force. Phys. Rev. 107, 1\u20136 (1957). \n                    https:\/\/doi.org\/10.1103\/PhysRev.107.1","journal-title":"Phys. Rev."},{"issue":"16","key":"726_CR73","doi-asserted-by":"publisher","first-page":"6203","DOI":"10.1016\/j.jcp.2011.04.018","volume":"230","author":"JA Rossmanith","year":"2011","unstructured":"Rossmanith, J.A., Seal, D.C.: A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov\u2013Poisson equations. J. Comput. Phys. 230(16), 6203\u20136232 (2011). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2011.04.018","journal-title":"J. Comput. Phys."},{"key":"726_CR74","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y Saad","year":"2003","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2003)","edition":"2"},{"issue":"3","key":"726_CR75","doi-asserted-by":"publisher","first-page":"856","DOI":"10.1137\/0907058","volume":"7","author":"Y Saad","year":"1986","unstructured":"Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7(3), 856\u2013869 (1986). \n                    https:\/\/doi.org\/10.1137\/0907058","journal-title":"SIAM J. Sci. Stat. Comput."},{"issue":"5","key":"726_CR76","doi-asserted-by":"publisher","first-page":"B817","DOI":"10.1137\/130924905","volume":"36","author":"S Salmi","year":"2014","unstructured":"Salmi, S., Toivanen, J., von Sydow, L.: An IMEX-scheme for pricing options under stochastic volatility models with jumps. SIAM J. Sci. Comput. 36(5), B817\u2013B834 (2014). \n                    https:\/\/doi.org\/10.1137\/130924905","journal-title":"SIAM J. Sci. Comput."},{"issue":"5A","key":"726_CR77","doi-asserted-by":"publisher","first-page":"A387","DOI":"10.1088\/0741-3335\/48\/5A\/S39","volume":"48","author":"B Scott","year":"2006","unstructured":"Scott, B.: Gyrokinetic study of the edge shear layer. Plasma Phys. Controll. Fusion 48(5A), A387 (2006)","journal-title":"Plasma Phys. Controll. Fusion"},{"key":"726_CR78","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1016\/j.jcp.2016.03.071","volume":"318","author":"W Taitano","year":"2016","unstructured":"Taitano, W., Chac\u00f3n, L., Simakov, A.: An adaptive, conservative 0D-2V multispecies Rosenbluth\u2013Fokker\u2013Planck solver for arbitrarily disparate mass and temperature regimes. J. Comput. Phys. 318, 391\u2013420 (2016). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2016.03.071","journal-title":"J. Comput. Phys."},{"key":"726_CR79","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/j.jcp.2015.05.025","volume":"297","author":"W Taitano","year":"2015","unstructured":"Taitano, W., Chac\u00f3n, L., Simakov, A., Molvig, K.: A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth\u2013Fokker\u2013Planck equation. J. Comput. Phys. 297, 357\u2013380 (2015). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2015.05.025","journal-title":"J. Comput. Phys."},{"issue":"3","key":"726_CR80","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1016\/j.jcp.2011.09.028","volume":"231","author":"A Thomas","year":"2012","unstructured":"Thomas, A., Tzoufras, M., Robinson, A., Kingham, R., Ridgers, C., Sherlock, M., Bell, A.: A review of Vlasov\u2013Fokker\u2013Planck numerical modeling of inertial confinement fusion plasma. J. Comput. Phys. 231(3), 1051\u20131079 (2012). \n                    https:\/\/doi.org\/10.1016\/j.jcp.2011.09.028\n                    \n                  . (Special issue: computational plasma physics)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"726_CR81","doi-asserted-by":"publisher","first-page":"033001","DOI":"10.1088\/1367-2630\/11\/3\/033001","volume":"11","author":"AGR Thomas","year":"2009","unstructured":"Thomas, A.G.R., Kingham, R.J., Ridgers, C.P.: Rapid self-magnetization of laser speckles in plasmas by nonlinear anisotropic instability. New J. Phys. 11(3), 033001 (2009)","journal-title":"New J. Phys."},{"issue":"6\u20137","key":"726_CR82","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/S1364-8152(00)00034-7","volume":"15","author":"R Wolke","year":"2000","unstructured":"Wolke, R., Knoth, O.: Implicit\u2013explicit Runge\u2013Kutta methods applied to atmospheric chemistry-transport modelling. Environ. Model. Softw. 15(6\u20137), 711\u2013719 (2000). \n                    https:\/\/doi.org\/10.1016\/S1364-8152(00)00034-7","journal-title":"Environ. Model. Softw."},{"issue":"6","key":"726_CR83","doi-asserted-by":"publisher","first-page":"064003","DOI":"10.1088\/0029-5515\/50\/6\/064003","volume":"50","author":"X Xu","year":"2010","unstructured":"Xu, X., Bodi, K., Cohen, R., Krasheninnikov, S., Rognlien, T.: TEMPEST simulations of the plasma transport in a single-null tokamak geometry. Nucl. Fusion 50(6), 064003 (2010)","journal-title":"Nucl. Fusion"},{"issue":"8","key":"726_CR84","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1088\/0029-5515\/47\/8\/011","volume":"47","author":"X Xu","year":"2007","unstructured":"Xu, X., Xiong, Z., Dorr, M., Hittinger, J., Bodi, K., Candy, J., Cohen, B., Cohen, R., Colella, P., Kerbel, G., Krasheninnikov, S., Nevins, W., Qin, H., Rognlien, T., Snyder, P., Umansky, M.: Edge gyrokinetic theory and continuum simulations. Nucl. Fusion 47(8), 809 (2007)","journal-title":"Nucl. Fusion"},{"key":"726_CR85","doi-asserted-by":"publisher","first-page":"215,001","DOI":"10.1103\/PhysRevLett.100.215001","volume":"100","author":"XQ Xu","year":"2008","unstructured":"Xu, X.Q., Xiong, Z., Gao, Z., Nevins, W.M., McKee, G.R.: TEMPEST simulations of collisionless damping of the geodesic-acoustic mode in edge-plasma pedestals. Phys. Rev. Lett. 100, 215,001 (2008). \n                    https:\/\/doi.org\/10.1103\/PhysRevLett.100.215001","journal-title":"Phys. Rev. Lett."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-018-0726-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0726-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0726-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T09:32:07Z","timestamp":1589707927000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-018-0726-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,12]]},"references-count":85,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,11]]}},"alternative-id":["726"],"URL":"https:\/\/doi.org\/10.1007\/s10915-018-0726-6","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,12]]},"assertion":[{"value":"25 July 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 May 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}