{"id":"https://openalex.org/W7155165519","doi":"https://doi.org/10.48550/arxiv.2604.18886","title":"Matrix-Free Multigrid with Algebraically Consistent Coarsening on Adaptive Octrees","display_name":"Matrix-Free Multigrid with Algebraically Consistent Coarsening on Adaptive Octrees","publication_year":2026,"publication_date":"2026-04-20","ids":{"openalex":"https://openalex.org/W7155165519","doi":"https://doi.org/10.48550/arxiv.2604.18886"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.18886","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.18886","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2604.18886","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109793933","display_name":"M.Y. Wang","orcid":"https://orcid.org/0000-0001-5757-3510"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Mengdi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134331231","display_name":"Yuchen Sun","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sun, Yuchen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5134350798","display_name":"Bo Zhu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhu, Bo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.7045000195503235,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.7045000195503235,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.08879999816417694,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.03819999843835831,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/multigrid-method","display_name":"Multigrid method","score":0.8949000239372253},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.7178999781608582},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.6689000129699707},{"id":"https://openalex.org/keywords/octree","display_name":"Octree","score":0.6439999938011169},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5127999782562256},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5120000243186951},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.4876999855041504},{"id":"https://openalex.org/keywords/adaptive-mesh-refinement","display_name":"Adaptive mesh refinement","score":0.4323999881744385}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8949000239372253},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7178999781608582},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.6689000129699707},{"id":"https://openalex.org/C141297171","wikidata":"https://www.wikidata.org/wiki/Q1143237","display_name":"Octree","level":2,"score":0.6439999938011169},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5807999968528748},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5127999782562256},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5120000243186951},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49729999899864197},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.4876999855041504},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4876999855041504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43869999051094055},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.43799999356269836},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.37070000171661377},{"id":"https://openalex.org/C96716743","wikidata":"https://www.wikidata.org/wiki/Q827688","display_name":"Poisson's equation","level":2,"score":0.3682999908924103},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.3499000072479248},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33500000834465027},{"id":"https://openalex.org/C31388003","wikidata":"https://www.wikidata.org/wiki/Q7624548","display_name":"Strong consistency","level":3,"score":0.3118000030517578},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2996000051498413},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.28139999508857727},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2745000123977661},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.266400009393692}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.18886","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.18886","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2604.18886","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.18886","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,38,58,90],"matrix-free":[3,50,60],"GPU":[4],"multigrid":[5],"preconditioner":[6],"with":[7,19,77],"algebraically":[8],"consistent":[9],"coarsening":[10,26],"for":[11,63],"solving":[12],"Poisson":[13,109],"equations":[14],"on":[15,66,82,107,118],"adaptive":[16],"octree":[17],"grids":[18],"irregular":[20],"domains.":[21],"Within":[22],"uniform-resolution":[23],"regions,":[24],"the":[25,28,48,96],"satisfies":[27],"Galerkin":[29],"principle.":[30],"At":[31],"T-junctions":[32],"between":[33],"refinement":[34],"levels,":[35],"we":[36],"propose":[37],"flux-consistent":[39],"coarse-grid":[40],"correction":[41],"that":[42],"restores":[43],"cross-level":[44],"consistency":[45],"while":[46],"preserving":[47],"compact":[49,59],"representation.":[51],"The":[52],"coarse":[53],"operators":[54],"are":[55],"stored":[56],"in":[57,86,122],"form":[61],"suitable":[62],"parallel":[64],"execution":[65],"GPUs.":[67],"Numerical":[68],"experiments":[69],"demonstrate":[70],"second-order":[71],"accuracy,":[72],"grid-independent":[73],"convergence":[74],"when":[75],"used":[76],"PCG,":[78],"and":[79,111],"robust":[80],"performance":[81],"cut-cell":[83],"problems":[84,121],"arising":[85],"fluid":[87,123],"simulation.":[88,124],"On":[89],"single":[91],"NVIDIA":[92],"RTX":[93],"4090":[94],"GPU,":[95],"solver":[97],"achieves":[98],"full-solve":[99],"throughputs":[100],"above":[101,112],"200":[102],"million":[103,114],"cells":[104,115],"per":[105,116],"second":[106,117],"analytical":[108],"tests":[110],"70":[113],"pressure":[119],"projection":[120]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-04-23T00:00:00"}