{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T03:05:03Z","timestamp":1791860703505,"version":"4.3.4"},"reference-count":54,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"Research Foundation - Flanders","award":["1SB1919N"],"award-info":[{"award-number":["1SB1919N"]}]},{"name":"Flemish Government - department EWI"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of an infinite collision rate. Despite this well-defined limit, numerical simulation is expensive when the collision rate is high but finite, as small time steps are then required. In this work, we present an asymptotic-preserving multilevel Monte Carlo particle scheme that makes use of this diffusive limit to accelerate computations. In this scheme, we first sample the diffusive limiting model to compute a biased initial estimate of a quantity of interest, using large time steps. We then perform a limited number of finer simulations with transport and collision dynamics to correct the bias. The efficiency of the multilevel method depends on being able to perform correlated simulations of particles on a hierarchy of discretization levels. We present a method for correlating particle trajectories and present both an analysis and numerical experiments. We demonstrate that our approach significantly reduces the cost of particle simulations in high-collisional regimes, compared with prior work, indicating significant potential for adopting these schemes in various areas of active research.<\/jats:p>\n                  <jats:p>Reproducibility of computational results. This paper has been awarded the \u201cSIAM Reproducibility Badge: code and data available\u201d, as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https:\/\/github.com\/ELoevbak\/APMLMC . [Formula: see text]<\/jats:p>","DOI":"10.1137\/22m1498498","type":"journal-article","created":{"date-parts":[[2023,7,21]],"date-time":"2023-07-21T09:32:20Z","timestamp":1689931940000},"page":"A1862-A1889","source":"Crossref","is-referenced-by-count":6,"title":["Accelerated Simulation of Boltzmann-BGK Equations near the Diffusive Limit with Asymptotic-Preserving Multilevel Monte Carlo"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1520-4922","authenticated-orcid":true,"given":"Emil","family":"L\u00f8vbak","sequence":"first","affiliation":[{"name":"NUMA Section, Department of Computer Science, KU Leuven, Heverlee, 3001, Belgium."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giovanni","family":"Samaey","sequence":"additional","affiliation":[{"name":"NUMA Section, Department of Computer Science, KU Leuven, Heverlee, 3001, Belgium."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,21]]},"reference":[{"key":"ref1","unstructured":"D. Belomestny , \nL. Szpruch , and \nS. Tan , Iterative Multilevel Density Estimation for McKean-Vlasov SDEs via Projections, preprint, https:\/\/arxiv.org\/abs\/1909.11717, 2019."},{"key":"ref2","unstructured":"N. Ben Rached , \nA.L. Haji-Ali , \nS. M. S. Pillai , and \nR. Tempone , Multilevel Importance Sampling for McKean-Vlasov Stochastic Differential Equation, preprint, https:\/\/arxiv.org\/abs\/2208.03225, 2022."},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.11.032"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.94.511"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/110842855"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2018.v16.n4.a1"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.3934\/krm.2011.4.441"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1002\/fld.2345"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0141"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/070680916"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/080730585"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1137\/100811052"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2012.05.010"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492914000063"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/17M1140741"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110353"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/21M1392772"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1994.10476841"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1070.0496"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1017\/S096249291500001X"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(02)02257-4"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-017-9771-5"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-45346-6_5"},{"key":"ref24","unstructured":"R. Illner  and \nH. Neunzert , Domain Decomposition: Linking Kinetic and Aerodynamic Descriptions, Technical report 90, Technische Universit\u00e4t Kaiserslautern, 1993."},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598334599"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492922000010"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997315962"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142998347978"},{"key":"ref29","first-page":"203","volume":"15","author":"Klar A.","year":"1995","journal-title":"European J. Mech. B Fluids"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996305558"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997321765"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597319258"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12616-5"},{"key":"ref34","series-title":"Oxf. Texts Appl. Eng. Math. 6","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198525929.001.0001","volume-title":"Introduction to Monte Carlo Methods for Transport and Diffusion Equations","author":"Lapeyre B.","year":"2003"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90229-5"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90170-7"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1137\/07069479X"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-50433-5_29"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-43465-6_19"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-021-01201-y"},{"key":"ref41","unstructured":"B. Mortier , Advanced Monte Carlo Simulation and Estimation for Kinetic Neutral Particles in the Plasma Edge of Fusion Reactors, Ph.D. thesis, KU Leuven, Leuven, Belgium, 2020,"},{"key":"ref42","first-page":"e201900134","author":"Mortier B.","year":"2019","journal-title":"Contrib. Plasm. Phys."},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1051\/proc:2005024"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6301"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1051\/proc:2001004"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1002\/fld.969"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1080\/00102208108547500"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.13182\/FST47-172"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.05.030"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202513500292"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2010.07.014"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1002\/ctpp.2150340246"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1214\/18-AAP1452"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2017.09.030"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1498498","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:56:50Z","timestamp":1787327810000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1498498"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,21]]},"references-count":54,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8,31]]}},"alternative-id":["10.1137\/22M1498498"],"URL":"https:\/\/doi.org\/10.1137\/22m1498498","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,21]]}}}