{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T04:38:49Z","timestamp":1787373529600,"version":"build-2736575974"},"reference-count":39,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100006192","name":"Office of Advanced Scientific Computing Research","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100006192","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100017223","name":"National Energy Research Scientific Computing Center","doi-asserted-by":"crossref","award":["DE-AC02-05CH11231"],"award-info":[{"award-number":["DE-AC02-05CH11231"]}],"id":[{"id":"10.13039\/100017223","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100008902","name":"Los Alamos National Laboratory","doi-asserted-by":"publisher","award":["89233218CNA000001"],"award-info":[{"award-number":["89233218CNA000001"]}],"id":[{"id":"10.13039\/100008902","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008902","name":"Los Alamos National Laboratory","doi-asserted-by":"publisher","award":["20220174ER"],"award-info":[{"award-number":["20220174ER"]}],"id":[{"id":"10.13039\/100008902","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100008902","name":"Los Alamos National Laboratory","doi-asserted-by":"publisher","award":["LA-UR-23-20885"],"award-info":[{"award-number":["LA-UR-23-20885"]}],"id":[{"id":"10.13039\/100008902","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006207","name":"Fusion Energy Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006207","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2024,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization\u2019s superior accuracy over other discretizations of anisotropic heat flux, achieving error [Formula: see text] smaller for anisotropy ratio of [Formula: see text], for closed field lines. The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction, which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are nonsingular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.<\/jats:p>","DOI":"10.1137\/23m155918x","type":"journal-article","created":{"date-parts":[[2024,5,24]],"date-time":"2024-05-24T04:01:41Z","timestamp":1716523301000},"page":"A1821-A1849","source":"Crossref","is-referenced-by-count":5,"title":["A Fast Algebraic Multigrid Solver and Accurate Discretization for Highly Anisotropic Heat Flux I: Open Field Lines"],"prefix":"10.1137","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7871-1748","authenticated-orcid":true,"given":"Golo A.","family":"Wimmer","sequence":"first","affiliation":[{"name":"Corresponding author. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0283-4928","authenticated-orcid":true,"given":"Ben S.","family":"Southworth","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas J.","family":"Gregory","sequence":"additional","affiliation":[{"name":"Imperial College London, London, SW7 2BX UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xian-Zhu","family":"Tang","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,5,24]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)00242-X"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.2172\/1577437"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.21105\/joss.05495"},{"key":"ref4","unstructured":"A. Bienz and L. N. Olson, raptor-library\/raptor v0.1, Release 0.1, https:\/\/github.com\/lukeolson\/raptor (2017)."},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1804"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142903437374"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.06.064"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s00791-014-0224-9"},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"S. Dargaville, R. P. Smedley-Stevenson, P. N. Smith, and C. C. Pain, AIR Multigrid with GMRES Polynomials (AIRG) and Additive Preconditioners for Boltzmann Transport, preprint, arXiv:2301.05521, 2023.","DOI":"10.1016\/j.jcp.2024.113342"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.11.040"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/17M115205X"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1017\/S0022377814000816"},{"key":"ref13","doi-asserted-by":"crossref","unstructured":"R. D. Falgout and U. M. Yang, hypre: A library of high performance preconditioners, in International Conference on Computational Science, Springer, Berlin, 2002, pp. 632\u2013641.","DOI":"10.1007\/3-540-47789-6_66"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-0836-3"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1002\/nla.593"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2022.108333"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.07.016"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1080\/00295639.2020.1747263"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1088\/1741-4326\/abf99f"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1201\/EBK1439810958"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827598334599"},{"key":"ref22","unstructured":"D. Kuzmin, A Guide to Numerical Methods for Transport Equations, https:\/\/www.scribd.com\/doc\/146886759\/A-Guide-to-Numerical-Methods-Dmitri-Kuzmin (2010)."},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719628"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1145\/779359.779361"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1137\/18M1193761"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/16M1082706"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1137\/17M1144350"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2014.08.018"},{"key":"ref29","first-page":"123","volume":"37","author":"Notay Y.","year":"2010","journal-title":"Electron. Trans. Numer. Anal."},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1145\/2998441"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971057.ch4"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1002\/ctpp.200610001"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1805"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1137\/19M1298317"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.10.004"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1887\/0750305592"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1016\/0096-3003(83)90023-1"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2023.06.019"},{"key":"ref39","unstructured":"C. Yang, F. Deluzet, and J. Narski, Preserving the Accuracy of Numerical Methods Discretizing Anisotropic Elliptic Problems, preprint, arXiv:1911.11482, 2019."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/23M155918X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:45:41Z","timestamp":1787327141000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M155918X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,24]]},"references-count":39,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6,30]]}},"alternative-id":["10.1137\/23M155918X"],"URL":"https:\/\/doi.org\/10.1137\/23m155918x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5,24]]}}}