{"id":"https://openalex.org/W7202388015","doi":"https://doi.org/10.1111/cgf.70491","title":"Surface Multigrid via Global Parametric Domain Simplification","display_name":"Surface Multigrid via Global Parametric Domain Simplification","publication_year":2026,"publication_date":"2026-08-13","ids":{"openalex":"https://openalex.org/W7202388015","doi":"https://doi.org/10.1111/cgf.70491"},"language":"en","primary_location":{"id":"doi:10.1111/cgf.70491","is_oa":false,"landing_page_url":"https://doi.org/10.1111/cgf.70491","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","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/A5147091632","display_name":"Anyu Zhao","orcid":"https://orcid.org/0009-0007-0831-6279"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]},{"id":"https://openalex.org/I2802974365","display_name":"Shanghai Innovative Research Center of Traditional Chinese Medicine","ror":"https://ror.org/01gnagj68","country_code":"CN","type":"facility","lineage":["https://openalex.org/I2802974365"]},{"id":"https://openalex.org/I4210150385","display_name":"Innovation Team (China)","ror":"https://ror.org/04ttbbx73","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210150385"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Anyu Zhao","raw_affiliation_strings":["Shanghai Innovation Institute  China","University of Science and Technology of China  China"],"raw_orcid":"https://orcid.org/0009-0007-0831-6279","affiliations":[{"raw_affiliation_string":"Shanghai Innovation Institute  China","institution_ids":["https://openalex.org/I2802974365","https://openalex.org/I4210150385"]},{"raw_affiliation_string":"University of Science and Technology of China  China","institution_ids":["https://openalex.org/I126520041","https://openalex.org/I150229711"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059433215","display_name":"Qing Fang","orcid":"https://orcid.org/0000-0001-7934-6060"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qing Fang","raw_affiliation_strings":["University of Science and Technology of China  China"],"raw_orcid":"https://orcid.org/0000-0001-7934-6060","affiliations":[{"raw_affiliation_string":"University of Science and Technology of China  China","institution_ids":["https://openalex.org/I126520041","https://openalex.org/I150229711"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100635702","display_name":"Ligang Liu","orcid":"https://orcid.org/0000-0003-4352-1431"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]},{"id":"https://openalex.org/I150229711","display_name":"University of Electronic Science and Technology of China","ror":"https://ror.org/04qr3zq92","country_code":"CN","type":"education","lineage":["https://openalex.org/I150229711"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ligang Liu","raw_affiliation_strings":["University of Science and Technology of China  China"],"raw_orcid":"https://orcid.org/0000-0003-4352-1431","affiliations":[{"raw_affiliation_string":"University of Science and Technology of China  China","institution_ids":["https://openalex.org/I126520041","https://openalex.org/I150229711"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5059433215"],"corresponding_institution_ids":["https://openalex.org/I126520041","https://openalex.org/I150229711"],"apc_list":{"value":3710,"currency":"USD","value_usd":3710},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.88069221,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.3504999876022339,"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/T10719","display_name":"3D Shape Modeling and Analysis","score":0.3504999876022339,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.21870000660419464,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.08489999920129776,"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/multigrid-method","display_name":"Multigrid method","score":0.9243000149726868},{"id":"https://openalex.org/keywords/parametric-surface","display_name":"Parametric surface","score":0.6712999939918518},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.5752999782562256},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.569100022315979},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.5138999819755554},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.4927999973297119},{"id":"https://openalex.org/keywords/prolongation","display_name":"Prolongation","score":0.48350000381469727},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4702000021934509},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4528999924659729}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.9243000149726868},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.6712999939918518},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5752999782562256},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.569100022315979},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5393000245094299},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5138999819755554},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.4927999973297119},{"id":"https://openalex.org/C2777672339","wikidata":"https://www.wikidata.org/wiki/Q7249641","display_name":"Prolongation","level":2,"score":0.48350000381469727},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4702000021934509},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4528999924659729},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4505000114440918},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4465999901294708},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43709999322891235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4090000092983246},{"id":"https://openalex.org/C20885615","wikidata":"https://www.wikidata.org/wiki/Q825595","display_name":"Surface reconstruction","level":3,"score":0.3935999870300293},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.367000013589859},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.35899999737739563},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.3450999855995178},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3328000009059906},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C99636146","wikidata":"https://www.wikidata.org/wiki/Q35889","display_name":"Parametric equation","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C29123130","wikidata":"https://www.wikidata.org/wiki/Q874709","display_name":"Computational geometry","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.2896000146865845},{"id":"https://openalex.org/C30707913","wikidata":"https://www.wikidata.org/wiki/Q1545397","display_name":"Minimal surface","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C2781310163","wikidata":"https://www.wikidata.org/wiki/Q6664315","display_name":"Local coordinates","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C199686383","wikidata":"https://www.wikidata.org/wiki/Q1529124","display_name":"Subdivision surface","level":3,"score":0.26589998602867126},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25369998812675476},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.2515999972820282},{"id":"https://openalex.org/C108882727","wikidata":"https://www.wikidata.org/wiki/Q2991685","display_name":"Solid modeling","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/cgf.70491","is_oa":false,"landing_page_url":"https://doi.org/10.1111/cgf.70491","pdf_url":null,"source":{"id":"https://openalex.org/S67831204","display_name":"Computer Graphics Forum","issn_l":"0167-7055","issn":["0167-7055","1467-8659"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computer Graphics Forum","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","score":0.6708366274833679,"id":"https://metadata.un.org/sdg/14"}],"awards":[{"id":"https://openalex.org/G1223194511","display_name":null,"funder_award_id":"2408085QF197","funder_id":"https://openalex.org/F4320334897","funder_display_name":"Natural Science Foundation of Anhui Province"},{"id":"https://openalex.org/G2514321366","display_name":null,"funder_award_id":"62502484","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3361998035","display_name":null,"funder_award_id":"62025207","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6226405349","display_name":null,"funder_award_id":"WK0010000095","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334897","display_name":"Natural Science Foundation of Anhui Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1626653188","https://openalex.org/W1974956622","https://openalex.org/W1990120195","https://openalex.org/W2000214666","https://openalex.org/W2027783854","https://openalex.org/W2044464362","https://openalex.org/W2079804759","https://openalex.org/W2101165370","https://openalex.org/W2128233236","https://openalex.org/W2132044017","https://openalex.org/W2143897237","https://openalex.org/W2151317657","https://openalex.org/W2171603394","https://openalex.org/W2235901111","https://openalex.org/W2293404936","https://openalex.org/W2504261469","https://openalex.org/W2607599593","https://openalex.org/W2946285945","https://openalex.org/W3158117306","https://openalex.org/W4200093672","https://openalex.org/W4230055019","https://openalex.org/W4384111662","https://openalex.org/W4385272066","https://openalex.org/W4389335116"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,81],"present":[2],"ParaMG,":[3],"a":[4,22,57,65,90],"surface":[5,29,110],"multigrid":[6,11,30,111],"method":[7],"that":[8,48,56],"restores":[9],"classical":[10],"structure":[12],"on":[13,33],"curved":[14],"surfaces":[15],"by":[16],"expressing":[17],"all":[18],"hierarchy":[19,84],"levels":[20],"in":[21,86,105,117],"single":[23],"globally":[24],"consistent":[25],"planar":[26,78],"domain.":[27],"Existing":[28],"methods":[31,112],"rely":[32],"composed":[34],"local":[35,46],"parameterizations":[36],"or":[37],"3D":[38],"projections":[39],"for":[40],"cross\u2010level":[41],"transfer,":[42],"requiring":[43],"repeated":[44],"per\u2010level":[45],"approximations":[47],"can":[49],"degrade":[50],"convergence.":[51],"Our":[52],"key":[53],"insight":[54],"is":[55],"global":[58],"conformal":[59],"parameterization":[60],"with":[61,69,98,119],"cone":[62],"singularities":[63],"provides":[64],"shared":[66],"coordinate":[67],"system":[68],"low,":[70],"controllable":[71],"distortion,":[72],"where":[73],"prolongation":[74,96],"reduces":[75],"to":[76],"exact":[77],"barycentric":[79],"interpolation.":[80],"construct":[82],"the":[83],"directly":[85],"this":[87],"domain":[88],"using":[89],"seam\u2010aware":[91],"simplification":[92],"strategy,":[93],"yielding":[94],"sparse":[95],"matrices":[97],"three":[99],"entries":[100],"per":[101],"row.":[102],"ParaMG":[103],"converges":[104],"fewer":[106],"V\u2010cycles":[107],"than":[108],"prior":[109],"and":[113,128],"delivers":[114],"substantial":[115],"speedups":[116],"applications":[118],"changing":[120],"linear":[121],"systems,":[122],"including":[123],"geometric":[124],"flows,":[125],"thin\u2010shell":[126],"simulation,":[127],"polycube":[129],"deformation.":[130]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2026-08-14T00:00:00"}