{"id":"https://openalex.org/W1984863278","doi":"https://doi.org/10.1145/2661229.2661261","title":"A PPPM fast summation method for fluids and beyond","display_name":"A PPPM fast summation method for fluids and beyond","publication_year":2014,"publication_date":"2014-11-18","ids":{"openalex":"https://openalex.org/W1984863278","doi":"https://doi.org/10.1145/2661229.2661261","mag":"1984863278"},"language":"en","primary_location":{"id":"doi:10.1145/2661229.2661261","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2661229.2661261","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100375447","display_name":"Xinxin Zhang","orcid":"https://orcid.org/0000-0001-6069-5391"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xinxin Zhang","raw_affiliation_strings":["UBC Computer Science"],"affiliations":[{"raw_affiliation_string":"UBC Computer Science","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079912836","display_name":"Robert Bridson","orcid":null},"institutions":[{"id":"https://openalex.org/I4210103820","display_name":"Autodesk (Canada)","ror":"https://ror.org/01b3dk794","country_code":"CA","type":"company","lineage":["https://openalex.org/I1286353243","https://openalex.org/I4210103820"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Robert Bridson","raw_affiliation_strings":["UBC Computer Science, Autodesk Canada"],"affiliations":[{"raw_affiliation_string":"UBC Computer Science, Autodesk Canada","institution_ids":["https://openalex.org/I4210103820"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100375447"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.4153,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.94036095,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"33","issue":"6","first_page":"1","last_page":"11"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11694","display_name":"Fluid Dynamics Simulations and Interactions","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11382","display_name":"Fluid Dynamics and Heat Transfer","score":0.979200005531311,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6827989220619202},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6804856061935425},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.49297285079956055},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.48850810527801514},{"id":"https://openalex.org/keywords/rendering","display_name":"Rendering (computer graphics)","score":0.46606093645095825},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.4385416805744171},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.412389874458313},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4076499938964844},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39963728189468384},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3212825655937195},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2248077690601349},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.22405976057052612},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17785757780075073},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15921521186828613},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.09746652841567993}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6827989220619202},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6804856061935425},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.49297285079956055},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.48850810527801514},{"id":"https://openalex.org/C205711294","wikidata":"https://www.wikidata.org/wiki/Q176953","display_name":"Rendering (computer graphics)","level":2,"score":0.46606093645095825},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.4385416805744171},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.412389874458313},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4076499938964844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39963728189468384},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3212825655937195},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2248077690601349},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.22405976057052612},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17785757780075073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15921521186828613},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.09746652841567993},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2661229.2661261","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2661229.2661261","pdf_url":null,"source":{"id":"https://openalex.org/S185367456","display_name":"ACM Transactions on Graphics","issn_l":"0730-0301","issn":["0730-0301","1557-7368"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Graphics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1644141869","https://openalex.org/W1672666614","https://openalex.org/W1964035419","https://openalex.org/W1981382127","https://openalex.org/W1992906507","https://openalex.org/W1994078971","https://openalex.org/W1997844094","https://openalex.org/W2008073424","https://openalex.org/W2018451527","https://openalex.org/W2024395588","https://openalex.org/W2044391901","https://openalex.org/W2049790739","https://openalex.org/W2053776542","https://openalex.org/W2054622952","https://openalex.org/W2055795991","https://openalex.org/W2065962703","https://openalex.org/W2066429811","https://openalex.org/W2076017704","https://openalex.org/W2080948710","https://openalex.org/W2082922739","https://openalex.org/W2083206954","https://openalex.org/W2084161481","https://openalex.org/W2086410114","https://openalex.org/W2087568854","https://openalex.org/W2091657244","https://openalex.org/W2096320147","https://openalex.org/W2098476371","https://openalex.org/W2099452464","https://openalex.org/W2119984419","https://openalex.org/W2126195192","https://openalex.org/W2135353663","https://openalex.org/W2160993863","https://openalex.org/W2166478562","https://openalex.org/W2170854520","https://openalex.org/W2237109911","https://openalex.org/W2295821368","https://openalex.org/W4206677916","https://openalex.org/W4242728694"],"related_works":["https://openalex.org/W2573021234","https://openalex.org/W2106610492","https://openalex.org/W66408621","https://openalex.org/W2493281735","https://openalex.org/W2004285327","https://openalex.org/W2020385488","https://openalex.org/W4391952019","https://openalex.org/W1604758548","https://openalex.org/W105006890","https://openalex.org/W2804126825"],"abstract_inverted_index":{"Solving":[0],"the":[1,6,25,41,116,121,138],"N":[2],"-body":[3],"problem,":[4],"i.e.":[5],"Poisson":[7,189,200],"problem":[8,192],"with":[9,87,96,107,125,177],"point":[10],"sources,":[11],"is":[12,70],"a":[13,63,81,88,93,97,108,126,134,154,165,188,198],"common":[14],"task":[15],"in":[16,78],"graphics":[17],"and":[18,50,73,153],"simulation.":[19],"The":[20],"naive":[21],"direct":[22],"summation":[23],"of":[24,123],"kernel":[26],"function":[27],"over":[28],"all":[29],"particles":[30],"scales":[31],"quadratically,":[32],"rendering":[33],"it":[34],"too":[35,54],"slow":[36],"for":[37,157,187],"large":[38],"problems,":[39],"while":[40,101],"optimal":[42],"Fast":[43],"Multipole":[44],"Method":[45],"has":[46],"drastic":[47],"implementation":[48],"complexity":[49],"can":[51,171],"sometimes":[52],"carry":[53],"high":[55],"an":[56],"overhead":[57],"to":[58,75,112,137,143,193],"be":[59],"practical.":[60],"We":[61,83,119],"present":[62],"new":[64,109,127,155],"Particle-Particle":[65],"Particle-Mesh":[66],"(PPPM)":[67],"algorithm":[68],"which":[69,132],"fast,":[71],"accurate,":[72],"easy":[74],"implement":[76],"even":[77],"parallel":[79],"on":[80,92,148],"GPU.":[82],"capture":[84],"long-range":[85],"interactions":[86,103],"fast":[89],"multigrid":[90],"solver":[91,186],"background":[94,117],"grid":[95],"novel":[98],"boundary":[99,161],"condition,":[100],"short-range":[102],"are":[104],"calculated":[105],"directly":[106],"error":[110,114],"compensation":[111],"avoid":[113],"from":[115,160],"grid.":[118],"demonstrate":[120],"power":[122],"PPPM":[124,170,185],"vortex":[128,135,158],"particle":[129],"smoke":[130],"solver,":[131],"features":[133],"segment-approach":[136],"stretching":[139],"term,":[140],"potential":[141,196],"flow":[142],"enforce":[144],"no-stick":[145],"solid":[146,151],"boundaries":[147],"arbitrary":[149],"moving":[150],"boundaries,":[152],"mechanism":[156],"shedding":[159],"layers.":[162],"Comparison":[163],"against":[164],"simpler":[166],"Vortex-in-Cell":[167],"approach":[168],"shows":[169],"produce":[172],"significantly":[173],"more":[174],"detailed":[175],"results":[176],"less":[178],"computation.":[179],"In":[180],"addition,":[181],"we":[182],"use":[183],"our":[184],"surface":[190],"reconstruction":[191],"show":[194],"its":[195],"as":[197],"general-purpose":[199],"solver.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}