{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T19:56:15Z","timestamp":1760730975103,"version":"3.41.0"},"reference-count":48,"publisher":"Association for Computing Machinery (ACM)","issue":"5","license":[{"start":{"date-parts":[[2017,7,25]],"date-time":"2017-07-25T00:00:00Z","timestamp":1500940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"National High Technology Research and Development Program of China","award":["2015AA016404"],"award-info":[{"award-number":["2015AA016404"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61373085 and 61173105"],"award-info":[{"award-number":["61373085 and 61173105"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2017,10,31]]},"abstract":"<jats:p>\n            We present an algorithmically efficient and parallelized domain decomposition based approach to solving Poisson\u2019s equation on irregular domains. Our technique employs the Schur complement method, which permits a high degree of parallel efficiency on multicore systems. We create a novel Schur complement preconditioner which achieves faster convergence, and requires less computation time and memory. This domain decomposition method allows us to apply different linear solvers for different regions of the flow. Subdomains with regular boundaries can be solved with an FFT-based Fast Poisson Solver. We can solve systems with 1,024\n            <jats:sup>3<\/jats:sup>\n            degrees of freedom, and demonstrate its use for the pressure projection step of incompressible liquid and gas simulations. The results demonstrate considerable speedup over preconditioned conjugate gradient methods commonly employed to solve such problems, including a multigrid preconditioned conjugate gradient method.\n          <\/jats:p>","DOI":"10.1145\/3092818","type":"journal-article","created":{"date-parts":[[2017,7,26]],"date-time":"2017-07-26T12:10:35Z","timestamp":1501071035000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["A Schur Complement Preconditioner for Scalable Parallel Fluid Simulation"],"prefix":"10.1145","volume":"36","author":[{"given":"Jieyu","family":"Chu","sequence":"first","affiliation":[{"name":"Shanghai Jiao Tong University, Oriental DreamWorks"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nafees Bin","family":"Zafar","sequence":"additional","affiliation":[{"name":"Oriental DreamWorks"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xubo","family":"Yang","sequence":"additional","affiliation":[{"name":"Shanghai Jiao Tong University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,7,25]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461982"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276502"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01639.x"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(84)90073-1"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/0723075"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461991"},{"volume-title":"Patrick Le Tallec, and Marina Vidrascu","year":"1989","author":"Bourgat Jean-Francois","key":"e_1_2_2_8_1"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.2307\/2008084"},{"volume-title":"Fluid Simulation for Computer Graphics","author":"Bridson Robert","key":"e_1_2_2_10_1"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/040620047"},{"volume-title":"Overlapping domain decomposition methods. Advanced Topics in Computational Partial Differential Equations","author":"Cai X","key":"e_1_2_2_12_1"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1137\/0613018"},{"volume-title":"Proceedings of the 2007 ACM SIGGRAPH\/Eurographics Symposium on Computer Animation (SCA\u201907)","author":"Chentanez Nuttapong","key":"e_1_2_2_14_1"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2012.86"},{"volume-title":"Proceedings of the ACM SIGGRAPH\/Eurographics Symposium on Computer Animation (SCA\u201914)","year":"2014","author":"Chentanez Nuttapong","key":"e_1_2_2_16_1"},{"volume-title":"Applied Numerical Linear Algebra","author":"Demmel James W.","key":"e_1_2_2_17_1"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2511734"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2485895.2485897"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2006.105"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12825"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2014.2307873"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1996.0039"},{"key":"e_1_2_2_24_1","unstructured":"Jean Gallier. 2010. The Schur complement and symmetric positive semidefinite (and definite) matrices. Retrieved from http:\/\/www.cis.upenn.edu\/&sim;jean\/schur-comp.pdf.  Jean Gallier. 2010. The Schur complement and symmetric positive semidefinite (and definite) matrices. Retrieved from http:\/\/www.cis.upenn.edu\/&sim;jean\/schur-comp.pdf."},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366167"},{"key":"e_1_2_2_26_1","series-title":"Proc. Eurographics 2016","volume-title":"A practical method for high-resolution embedded liquid surfaces. Comput. Graph. Forum","author":"Goldade Ryan","year":"2016"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595285299"},{"volume-title":"Van Loan","year":"1996","author":"Golub Gene H.","key":"e_1_2_2_28_1"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112097007465"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/2370919.2370927"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/1273440.1250690"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/1618452.1618466"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141961"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982430"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015745"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1002\/cnm.1640090307"},{"volume-title":"Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations","author":"Mathew Tarek","key":"e_1_2_2_37_1"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.5555\/1921427.1921438"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.5555\/1632592.1632595"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1145\/2487228.2487235"},{"key":"e_1_2_2_42_1","volume-title":"Numerical Recipes: The Art of Scientific Computing","author":"Press William H.","year":"2007","edition":"3"},{"edition":"1","volume-title":"Intel Threading Building Blocks","author":"Reinders James","key":"e_1_2_2_43_1"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.1680010405"},{"key":"e_1_2_2_45_1","unstructured":"Nicole Spillane. 2016. An Adaptive Multipreconditioned Conjugate Gradient Algorithm. (2016). https:\/\/hal.archives-ouvertes.fr\/hal-01170059 working paper or preprint.  Nicole Spillane. 2016. An Adaptive Multipreconditioned Conjugate Gradient Algorithm. (2016). https:\/\/hal.archives-ouvertes.fr\/hal-01170059 working paper or preprint."},{"key":"e_1_2_2_46_1","doi-asserted-by":"publisher","DOI":"10.1145\/311535.311548"},{"volume-title":"Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. NASA Conference Publication, 621--634","year":"1993","author":"Tatebe Osamu","key":"e_1_2_2_47_1"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1137\/0912082"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2446474"},{"key":"e_1_2_2_50_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073298"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3092818","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3092818","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:37:27Z","timestamp":1750217847000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3092818"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,25]]},"references-count":48,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,10,31]]}},"alternative-id":["10.1145\/3092818"],"URL":"https:\/\/doi.org\/10.1145\/3092818","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2017,7,25]]},"assertion":[{"value":"2016-09-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-04-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-07-25","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}