{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:34:11Z","timestamp":1787337251640,"version":"build-2736575974"},"reference-count":41,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020 Framework Programme","doi-asserted-by":"publisher","award":["824158"],"award-info":[{"award-number":["824158"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We propose a new sparse matrix format which captures the matrix structure typical for discretized partial differential equations with piecewise-constant coefficients. The format uses a stencil representation for some blocks of matrix rows, typically corresponding to regions with constant coefficients, whereas other rows are encoded in the general compressed sparse row format. The stencil representation saves memory and is suitable for SIMD-like parallelism as available on GPUs. Further, this format is well suited for the implementation of algebraic multigrid methods, and we present a proof-of-concept GPU-accelerated aggregation-based algebraic multigrid solver based on this format. This solver is compared on a few model problems (2-dimension and 3-dimension Poisson-like) with the compressed sparse row\u2013based solver AmgX from NVIDIA and with the CUDA version of the BoomerAMG solver. For the considered tested problems with one million unknowns or more, the presented solver outperforms AmgX and BoomerAMG in terms of both run time and memory usage, and the performance gap increases with the system size.<\/jats:p>","DOI":"10.1137\/22m1480938","type":"journal-article","created":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T04:07:24Z","timestamp":1686542844000},"page":"C154-C178","source":"Crossref","is-referenced-by-count":3,"title":["Algebraic Multigrid Using a Stencil\u2013CSR Hybrid Format on GPUs"],"prefix":"10.1137","volume":"45","author":[{"given":"Siham","family":"Boukhris","sequence":"first","affiliation":[{"name":"Universit\u00e9 Libre de Bruxelles, Service de M\u00e9trologie Nucl\u00e9aire (CP 165-84), 50, Av. F.D. Roosevelt, B-1050 Brussels, Belgium. The first author is Research Fellow of the Fonds de la Recherche Scientifique - FNRS. The third author is Research Director of the Fonds de la Recherche Scientifique - FNRS."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Artem","family":"Napov","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Libre de Bruxelles, Service de M\u00e9trologie Nucl\u00e9aire (CP 165-84), 50, Av. F.D. Roosevelt, B-1050 Brussels, Belgium. The first author is Research Fellow of the Fonds de la Recherche Scientifique - FNRS. The third author is Research Director of the Fonds de la Recherche Scientifique - FNRS."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yvan","family":"Notay","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Libre de Bruxelles, Service de M\u00e9trologie Nucl\u00e9aire (CP 165-84), 50, Av. F.D. Roosevelt, B-1050 Brussels, Belgium. The first author is Research Fellow of the Fonds de la Recherche Scientifique - FNRS. The third author is Research Director of the Fonds de la Recherche Scientifique - FNRS."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,12]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(03)00194-3"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/100798806"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/110838844"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1002\/nla.382"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1080\/17445760701442218"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.parco.2019.102599"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882364"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-7172-1_5"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719505"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2010.08.012"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jocs.2016.07.004"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol55s687"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.parco.2021.102840"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.09.001"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2014.08.022"},{"key":"ref16","unstructured":"N. Goodnight , \nC. Woolley , \nG. Lewin , \nD. Luebke  and \nG. Humphreys , A multigrid solver for boundary value problems using programmable graphics hardware, in Proceedings of the ACM SIGGRAPH\/EUROGRAPHICS Conference on Graphics Hardware, HWWS \u201903, Eurographics Association, Goslar, Germany, 2003, pp. 102\u2013111."},{"key":"ref17","unstructured":"T. Gradl , Data Structures and Algorithms for the Optimization of Hierarchical Hybrid Multigrid Methods, Ph.D. thesis, Der Technischen Fakult\u00e4t der Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen\u2013Nuremberg, Germany, 2015."},{"key":"ref18","doi-asserted-by":"crossref","unstructured":"K. Hou , \nH. Wang  and \nW.c. Feng , GPU-UniCache: Automatic code generation of spatial blocking for stencils on GPUs, in Proceedings of the Computing Frontiers Conference, CF\u201917, Association for Computing Machinery, New York, 2017, pp. 107\u2013116, https:\/\/doi.org\/10.1145\/3075564.3075583.","DOI":"10.1145\/3075564.3075583"},{"key":"ref19","unstructured":"Hypre Software and Documentation, https:\/\/www.llnl.gov\/casc\/hypre\/."},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1080\/17445760.2018.1506453"},{"key":"ref21","doi-asserted-by":"crossref","unstructured":"M. Kreutzer , \nG. Hager , \nG. Wellein , \nH. Fehske , \nA. Basermann  and \nA. Bishop , Sparse matrix-vector multiplication on GPGPU clusters: A new storage format and a scalable implementation, in Proceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops, IPDPSW 2012, IEEE, Piscataway, NJ, 2012, pp. 1696\u20131702, https:\/\/doi.org\/10.1109\/IPDPSW.2012.211.","DOI":"10.1109\/IPDPSW.2012.211"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1137\/130930352"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1145\/3322813"},{"key":"ref24","doi-asserted-by":"crossref","unstructured":"W. Liu  and \nB. Vinter , CSR5: An efficient storage format for cross-platform sparse matrix-vector multiplication, in ICS \u201915: Proceedings of the 29th ACM International Conference on Supercomputing, 2015, pp. 339\u2013350, https:\/\/doi.org\/10.1145\/2751205.2751209.","DOI":"10.1145\/2751205.2751209"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1925"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1137\/20M1375413"},{"key":"ref27","unstructured":"MUMPS: A Parallel Sparse Direct Solver, http:\/\/graal.ens-lyon.fr\/MUMPS\/."},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1002\/nla.741"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/100818509"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/140980260"},{"key":"ref31","doi-asserted-by":"crossref","unstructured":"A. D. Nguyen , \nN. Satish , \nJ. Chhugani , \nC. Kim  and \nP. K. Dubey , 3.5-D blocking optimization for stencil computations on modern CPUs and GPUs, in SC \u201910: Proceedings of the 2010 ACM\/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis, SC \u201910, ACM, New York, 2010, pp. 1\u201313.","DOI":"10.1109\/SC.2010.2"},{"key":"ref32","doi-asserted-by":"crossref","unstructured":"Y. Niu , \nZ. Lu , \nM. Dong , \nZ. Jin , \nW. Liu  and \nG. Tan , TileSpMV: A tiled algorithm for sparse matrix-vector multiplication on GPUs, in 2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS), IEEE, Piscataway, NJ, 2021, pp. 68\u201378, https:\/\/doi.org\/10.1109\/IPDPS49936.2021.00016.","DOI":"10.1109\/IPDPS49936.2021.00016"},{"key":"ref33","unstructured":"Y. Notay , AGMG software and documentation, http:\/\/agmg.eu."},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599362314"},{"key":"ref35","first-page":"123","volume":"37","author":"Notay Y.","year":"2010","journal-title":"Electron. Trans. Numer. Anal."},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1002\/nla.542"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-87475-1_39"},{"key":"ref39","first-page":"413","volume-title":"Multigrid","author":"St\u00fcben K.","year":"2001"},{"key":"ref40","volume-title":"Multigrid","author":"Trottenberg U.","year":"2001"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1002\/cpe.1658"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1480938","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:52:43Z","timestamp":1787334763000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1480938"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,12]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,6,30]]}},"alternative-id":["10.1137\/22M1480938"],"URL":"https:\/\/doi.org\/10.1137\/22m1480938","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,12]]}}}