{"id":"https://openalex.org/W4285392201","doi":"https://doi.org/10.3390/a15070245","title":"Efficient Local Refinement near Parametric Boundaries Using kd-Tree Data Structure and Algebraic Level Sets","display_name":"Efficient Local Refinement near Parametric Boundaries Using kd-Tree Data Structure and Algebraic Level Sets","publication_year":2022,"publication_date":"2022-07-13","ids":{"openalex":"https://openalex.org/W4285392201","doi":"https://doi.org/10.3390/a15070245"},"language":"en","primary_location":{"id":"doi:10.3390/a15070245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15070245","pdf_url":"https://www.mdpi.com/1999-4893/15/7/245/pdf?version=1657785513","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/15/7/245/pdf?version=1657785513","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101763602","display_name":"Tao Song","orcid":"https://orcid.org/0000-0003-0907-720X"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tao Song","raw_affiliation_strings":["School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012034156","display_name":"Huanyu Liao","orcid":"https://orcid.org/0000-0002-3004-056X"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Huanyu Liao","raw_affiliation_strings":["School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080314217","display_name":"Ganesh Subbarayan","orcid":"https://orcid.org/0000-0003-0462-1130"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ganesh Subbarayan","raw_affiliation_strings":["School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA"],"raw_orcid":"https://orcid.org/0000-0003-0462-1130","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA","institution_ids":["https://openalex.org/I219193219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080314217"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.2804,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.41810138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"15","issue":"7","first_page":"245","last_page":"245"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":1.0,"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/T10514","display_name":"Numerical methods in engineering","score":0.9771999716758728,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.9617999792098999,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6584196090698242},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5756940245628357},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5481432676315308},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.497196227312088},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.47305527329444885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4658084511756897},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.4462658762931824},{"id":"https://openalex.org/keywords/tree-structure","display_name":"Tree structure","score":0.4424588680267334},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.43835383653640747},{"id":"https://openalex.org/keywords/adaptive-quadrature","display_name":"Adaptive quadrature","score":0.4363689422607422},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.4326731264591217},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4293188452720642},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.4284765124320984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4241166114807129},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.35543814301490784},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.23958396911621094},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23127037286758423},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14079546928405762}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6584196090698242},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5756940245628357},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5481432676315308},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.497196227312088},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.47305527329444885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4658084511756897},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.4462658762931824},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.4424588680267334},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.43835383653640747},{"id":"https://openalex.org/C184599523","wikidata":"https://www.wikidata.org/wiki/Q4680758","display_name":"Adaptive quadrature","level":4,"score":0.4363689422607422},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.4326731264591217},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4293188452720642},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.4284765124320984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4241166114807129},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35543814301490784},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.23958396911621094},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23127037286758423},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14079546928405762},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a15070245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15070245","pdf_url":"https://www.mdpi.com/1999-4893/15/7/245/pdf?version=1657785513","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:a8e90e1bde58465ca6c97dfd90dbeb3e","is_oa":false,"landing_page_url":"https://doaj.org/article/a8e90e1bde58465ca6c97dfd90dbeb3e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 15, Iss 7, p 245 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/15/7/245/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a15070245","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms; Volume 15; Issue 7; Pages: 245","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a15070245","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a15070245","pdf_url":"https://www.mdpi.com/1999-4893/15/7/245/pdf?version=1657785513","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4285392201.pdf","grobid_xml":"https://content.openalex.org/works/W4285392201.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W90319264","https://openalex.org/W213642339","https://openalex.org/W1571317019","https://openalex.org/W1733539008","https://openalex.org/W1788335260","https://openalex.org/W1867526242","https://openalex.org/W1969130880","https://openalex.org/W1980220299","https://openalex.org/W1989151181","https://openalex.org/W1989512090","https://openalex.org/W1989594010","https://openalex.org/W1994910594","https://openalex.org/W1995404822","https://openalex.org/W2000425991","https://openalex.org/W2018060978","https://openalex.org/W2019341779","https://openalex.org/W2032325716","https://openalex.org/W2038233234","https://openalex.org/W2047732228","https://openalex.org/W2051125725","https://openalex.org/W2058306916","https://openalex.org/W2065189656","https://openalex.org/W2068085190","https://openalex.org/W2072418953","https://openalex.org/W2076814225","https://openalex.org/W2079304554","https://openalex.org/W2080811944","https://openalex.org/W2081893716","https://openalex.org/W2082931449","https://openalex.org/W2083824454","https://openalex.org/W2084843176","https://openalex.org/W2090657062","https://openalex.org/W2093643056","https://openalex.org/W2110186881","https://openalex.org/W2129372062","https://openalex.org/W2134158653","https://openalex.org/W2145535304","https://openalex.org/W2155315557","https://openalex.org/W2170882539","https://openalex.org/W2275397232","https://openalex.org/W2537829093","https://openalex.org/W3014190875","https://openalex.org/W3130261140","https://openalex.org/W4205649593","https://openalex.org/W4242246215","https://openalex.org/W4249019869"],"related_works":["https://openalex.org/W2032097736","https://openalex.org/W1990999456","https://openalex.org/W1544783803","https://openalex.org/W2929787118","https://openalex.org/W3037461666","https://openalex.org/W1909296238","https://openalex.org/W2014524345","https://openalex.org/W4378009103","https://openalex.org/W2162905854","https://openalex.org/W2809114818"],"abstract_inverted_index":{"In":[0,63],"analysis":[1],"of":[2,37,104,140,203],"problems":[3],"with":[4,71,151,183],"parametric":[5,105],"spline":[6],"boundaries":[7,43,51,86,214],"that":[8],"are":[9],"immersed":[10,42],"or":[11],"inserted":[12,29,50,85,124,173,215],"into":[13],"an":[14],"underlying":[15,21,34,56],"domain,":[16,57],"the":[17,20,28,32,41,45,49,55,60,84,94,123,137,145,152,166,172,178,184,185,199,204],"discretization":[18,35],"on":[19,165],"domain":[22],"usually":[23],"does":[24],"not":[25],"conform":[26],"to":[27,111,122,132,144],"boundaries.":[30,95],"While":[31],"fixed":[33],"is":[36,78,130],"great":[38],"convenience":[39],"as":[40,58,87,89,117,119,142],"evolve,":[44],"field":[46],"approximations":[47],"near":[48,83,93,212],"require":[52],"refinement":[53,76,82,129,162,180,207],"in":[54],"do":[59],"quadrature":[61,92,211],"cells.":[62],"this":[64],"paper,":[65],"a":[66,72,158,160],"kd-tree":[67,127,153,186],"data":[68,154,187],"structure":[69,188],"together":[70],"sign-based":[73],"and/or":[74],"distance-based":[75],"strategy":[77,181,208],"proposed":[79],"for":[80,90,136],"local":[81,128,179,206],"well":[88,118],"adaptive":[91,210],"The":[96,126],"developed":[97,205],"algorithms":[98],"construct":[99],"and":[100,168,201],"utilize":[101],"implicit":[102],"forms":[103],"Non-Uniform":[106],"Rational":[107],"B-Spline":[108],"(NURBS)":[109],"surfaces":[110],"algebraically":[112],"(and":[113],"non-iteratively)":[114],"estimate":[115],"distance":[116,170],"sign":[120],"relative":[121],"boundary.":[125,174],"demonstrated":[131],"produce":[133],"fewer":[134],"sub-cells":[135],"same":[138],"accuracy":[139,200],"solution":[141],"compared":[143],"classical":[146],"quad/oct":[147],"tree-based":[148],"subdivision.":[149],"Consistent":[150],"structure,":[155],"we":[156],"describe":[157],"new":[159],"priori":[161],"algorithm":[163],"based":[164],"signed":[167],"unsigned":[169],"from":[171],"We":[175,196],"first":[176],"demonstrate":[177,198],"coupled":[182],"by":[189],"constructing":[190],"Truncated":[191],"Hierarchical":[192],"B-spline":[193],"(THB-spline)":[194],"\u201cmeshes\u201d.":[195],"next":[197],"efficiency":[202],"through":[209],"NURBS":[213,219],"within":[216],"volumetric":[217],"three-dimensional":[218],"discretizations.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}
