{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T22:55:07Z","timestamp":1777676107726,"version":"3.51.4"},"reference-count":39,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T00:00:00Z","timestamp":1734048000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/T000414\/1"],"award-info":[{"award-number":["EP\/T000414\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of High Performance Computing Applications"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p>\n                    Reduction multigrids have recently shown good performance in hyperbolic problems without the need for Gauss-Seidel smoothers. When applied to the hyperbolic limit of the Boltzmann Transport Equation (BTE), these methods result in very close to\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">O<\/mml:mi>\n                        <mml:mrow>\n                          <mml:mo stretchy=\"false\">(<\/mml:mo>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:mo stretchy=\"false\">)<\/mml:mo>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    growth in work with problem size on unstructured grids. This scalability relies on the CF splitting producing an\n                    <jats:bold>A<\/jats:bold>\n                    <jats:sub>ff<\/jats:sub>\n                    block that is easy to invert. We introduce a parallel two-pass CF splitting designed to give diagonally dominant\n                    <jats:bold>A<\/jats:bold>\n                    <jats:sub>ff<\/jats:sub>\n                    . The first pass computes a maximal independent set in the symmetrized strong connections. The second pass converts F-points to C-points based on the row-wise diagonal dominance of\n                    <jats:bold>A<\/jats:bold>\n                    <jats:sub>ff<\/jats:sub>\n                    . We find this two-pass CF splitting outperforms common CF splittings available in\n                    <jats:italic toggle=\"yes\">hypre<\/jats:italic>\n                    . Furthermore, parallelisation of reduction multigrids in hyperbolic problems is difficult as we require both long-range grid-transfer operators and slow coarsenings (with rates of \u223c1\/2 in both 2D and 3D). We find that good parallel performance in the setup and solve is dependent on several factors: repartitioning the coarse grids, reducing the number of active MPI ranks as we coarsen, truncating the multigrid hierarchy and applying a GMRES polynomial as a coarse-grid solver. We compare the performance of two different reduction multigrids, AIRG (that we developed previously) and the\n                    <jats:italic toggle=\"yes\">hypre<\/jats:italic>\n                    implementation of\n                    <jats:italic toggle=\"yes\">\u2113<\/jats:italic>\n                    AIR. In the streaming limit with AIRG, we demonstrate 81% weak scaling efficiency in the solve from 2 to 64 nodes (256 to 8196 cores) with only 8.8k unknowns per core, with solve times up to 5.9\u00d7 smaller than the\n                    <jats:italic toggle=\"yes\">\u2113<\/jats:italic>\n                    AIR implementation in\n                    <jats:italic toggle=\"yes\">hypre<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1177\/10943420241304759","type":"journal-article","created":{"date-parts":[[2024,12,13]],"date-time":"2024-12-13T11:07:17Z","timestamp":1734088037000},"page":"364-384","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Coarsening and parallelism with reduction multigrids for hyperbolic Boltzmann transport"],"prefix":"10.1177","volume":"39","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8890-7437","authenticated-orcid":false,"given":"Steven","family":"Dargaville","sequence":"first","affiliation":[{"name":"Imperial College London"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Richard","family":"Smedley-Stevenson","sequence":"additional","affiliation":[{"name":"AWE"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Smith","sequence":"additional","affiliation":[{"name":"Imperial College London"},{"name":"ANSWERS Software Service"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christopher C","family":"Pain","sequence":"additional","affiliation":[{"name":"Imperial College London"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2024,12,13]]},"reference":[{"key":"e_1_3_5_2_1","doi-asserted-by":"crossref","unstructured":"Adams M Bayraktar H Keaveny T et al. 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