{"id":"https://openalex.org/W4415107970","doi":"https://doi.org/10.48550/arxiv.2506.13078","title":"High-Order Quadrature for Implicitly Defined Surfaces and Regions","display_name":"High-Order Quadrature for Implicitly Defined Surfaces and Regions","publication_year":2025,"publication_date":"2025-06-16","ids":{"openalex":"https://openalex.org/W4415107970","doi":"https://doi.org/10.48550/arxiv.2506.13078"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2506.13078","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2506.13078","pdf_url":"https://arxiv.org/pdf/2506.13078","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2506.13078","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Zhao, Zibo","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhao, Zibo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Shi, Zuoqiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shi, Zuoqiang","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":true,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9937000274658203,"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":0.9937000274658203,"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":0.9689000248908997,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.95169997215271,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.723800003528595},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.6995000243186951},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6855000257492065},{"id":"https://openalex.org/keywords/clenshaw\u2013curtis-quadrature","display_name":"Clenshaw\u2013Curtis quadrature","score":0.6531999707221985},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.6309999823570251},{"id":"https://openalex.org/keywords/tanh-sinh-quadrature","display_name":"Tanh-sinh quadrature","score":0.6208000183105469},{"id":"https://openalex.org/keywords/gauss\u2013hermite-quadrature","display_name":"Gauss\u2013Hermite quadrature","score":0.5728999972343445},{"id":"https://openalex.org/keywords/gauss\u2013laguerre-quadrature","display_name":"Gauss\u2013Laguerre quadrature","score":0.5123000144958496}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7820000052452087},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.723800003528595},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.6995000243186951},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6855000257492065},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.6531999707221985},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.6309999823570251},{"id":"https://openalex.org/C162046254","wikidata":"https://www.wikidata.org/wiki/Q7683194","display_name":"Tanh-sinh quadrature","level":5,"score":0.6208000183105469},{"id":"https://openalex.org/C167590341","wikidata":"https://www.wikidata.org/wiki/Q5527850","display_name":"Gauss\u2013Hermite quadrature","level":5,"score":0.5728999972343445},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5526000261306763},{"id":"https://openalex.org/C6866599","wikidata":"https://www.wikidata.org/wiki/Q4218412","display_name":"Gauss\u2013Laguerre quadrature","level":5,"score":0.5123000144958496},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45579999685287476},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4514000117778778},{"id":"https://openalex.org/C54691486","wikidata":"https://www.wikidata.org/wiki/Q5527851","display_name":"Gauss\u2013Jacobi quadrature","level":5,"score":0.44760000705718994},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4287000000476837},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.42340001463890076},{"id":"https://openalex.org/C184599523","wikidata":"https://www.wikidata.org/wiki/Q4680758","display_name":"Adaptive quadrature","level":4,"score":0.39899998903274536},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3847000002861023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3499999940395355},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3474999964237213},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3190999925136566},{"id":"https://openalex.org/C194777461","wikidata":"https://www.wikidata.org/wiki/Q1085860","display_name":"Root-finding algorithm","level":3,"score":0.2793999910354614},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2718999981880188},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2506.13078","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2506.13078","pdf_url":"https://arxiv.org/pdf/2506.13078","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2506.13078","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.13078","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:arXiv.org:2506.13078","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2506.13078","pdf_url":"https://arxiv.org/pdf/2506.13078","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2485535630","display_name":null,"funder_award_id":"92370125","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415107970.pdf","grobid_xml":"https://content.openalex.org/works/W4415107970.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,107],"propose":[1],"a":[2,26,49],"high-order":[3,109],"quadrature":[4,87,97],"method":[5,24],"for":[6,111],"integrating":[7],"over":[8],"curves,":[9],"surfaces,":[10],"and":[11,51,59,81,95,102,114,119,125],"enclosed":[12],"regions":[13],"defined":[14],"implicitly":[15],"as":[16],"zero":[17],"level":[18,57],"sets":[19],"of":[20],"smooth":[21],"functions.":[22],"The":[23,37,92],"combines":[25],"mesh":[27,38,42,126],"adjustment":[28,39],"procedure":[29],"with":[30],"local":[31],"change-of-variables":[32],"parametrizations":[33],"on":[34,88,131],"cut":[35,65],"elements.":[36],"moves":[40],"background":[41],"vertices":[43],"away":[44],"from":[45],"the":[46,56,60,67,136],"interface,":[47],"ensuring":[48],"simple":[50],"nondegenerate":[52],"intersection":[53],"pattern":[54],"between":[55],"set":[58],"simplicial":[61],"mesh.":[62],"On":[63],"each":[64],"element,":[66],"interface":[68],"is":[69],"parametrized":[70],"by":[71],"solving":[72],"one-dimensional":[73],"nonlinear":[74],"equations":[75],"along":[76],"prescribed":[77],"rays,":[78],"reducing":[79],"surface":[80,96],"region":[82,115],"integration":[83],"to":[84],"standard":[85],"Gauss--Legendre":[86],"fixed":[89],"reference":[90],"domains.":[91],"resulting":[93],"curve":[94],"rules":[98],"are":[99],"local,":[100],"nonrecursive,":[101],"have":[103],"strictly":[104],"positive":[105],"weights.":[106],"prove":[108],"accuracy":[110],"curve,":[112],"surface,":[113],"integrals":[116],"in":[117],"two":[118],"three":[120],"dimensions":[121],"under":[122],"natural":[123],"smoothness":[124],"consistency":[127],"assumptions.":[128],"Numerical":[129],"experiments":[130],"representative":[132],"implicit":[133],"geometries":[134],"confirm":[135],"predicted":[137],"convergence":[138],"rates.":[139]},"counts_by_year":[],"updated_date":"2026-08-14T07:06:38.338062","created_date":"2025-10-13T00:00:00"}