{"id":"https://openalex.org/W1910188845","doi":"https://doi.org/10.1007/978-3-662-05105-4_6","title":"Identifying Vector Field Singularities Using a Discrete Hodge Decomposition","display_name":"Identifying Vector Field Singularities Using a Discrete Hodge Decomposition","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1910188845","doi":"https://doi.org/10.1007/978-3-662-05105-4_6","mag":"1910188845"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-662-05105-4_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-05105-4_6","pdf_url":null,"source":{"id":"https://openalex.org/S4210191043","display_name":"Mathematics and visualization","issn_l":"1612-3786","issn":["1612-3786","2197-666X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Visualization","raw_type":"book-chapter"},"type":"book-chapter","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/A5027138169","display_name":"Konrad Polthier","orcid":"https://orcid.org/0000-0001-9663-3037"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Konrad Polthier","raw_affiliation_strings":["Institut f\u00fcr Mathematik, MA 8\u20133, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","Institute of Mathematics, Technical University Berlin, MA 8-3, 10623, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, MA 8\u20133, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 136, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Institute of Mathematics, Technical University Berlin, MA 8-3, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078579348","display_name":"Eike Preu\u00df","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Eike Preu\u00df","raw_affiliation_strings":["Institute of Mathematics, Technical University Berlin, MA 8-3, 10623, Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Technical University Berlin, MA 8-3, 10623, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027138169"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":null,"apc_paid":null,"fwci":20.882,"has_fulltext":false,"cited_by_count":171,"citation_normalized_percentile":{"value":0.99604863,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"113","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9976000189781189,"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":0.9976000189781189,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9799000024795532,"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":0.9706000089645386,"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/vector-field","display_name":"Vector field","score":0.7389050126075745},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6620491743087769},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6439957618713379},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.58991938829422},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5285590887069702},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4571388363838196},{"id":"https://openalex.org/keywords/scalar-field","display_name":"Scalar field","score":0.44106751680374146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4399054944515228},{"id":"https://openalex.org/keywords/vector-potential","display_name":"Vector potential","score":0.41862913966178894},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39101845026016235},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2872259020805359},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21691539883613586},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1658916473388672},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.1342906653881073}],"concepts":[{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.7389050126075745},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6620491743087769},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6439957618713379},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.58991938829422},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5285590887069702},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4571388363838196},{"id":"https://openalex.org/C110521144","wikidata":"https://www.wikidata.org/wiki/Q193460","display_name":"Scalar field","level":2,"score":0.44106751680374146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4399054944515228},{"id":"https://openalex.org/C2027888","wikidata":"https://www.wikidata.org/wiki/Q521126","display_name":"Vector potential","level":3,"score":0.41862913966178894},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39101845026016235},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2872259020805359},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21691539883613586},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1658916473388672},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.1342906653881073},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-662-05105-4_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-05105-4_6","pdf_url":null,"source":{"id":"https://openalex.org/S4210191043","display_name":"Mathematics and visualization","issn_l":"1612-3786","issn":["1612-3786","2197-666X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Visualization","raw_type":"book-chapter"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.15.4339","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.4339","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-sfb288.math.tu-berlin.de/~konrad/articles/hodge/hodge_final.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W8289804","https://openalex.org/W121374037","https://openalex.org/W151364726","https://openalex.org/W1491242074","https://openalex.org/W1492326914","https://openalex.org/W1522382323","https://openalex.org/W1587541211","https://openalex.org/W1974956622","https://openalex.org/W1999616998","https://openalex.org/W2002243081","https://openalex.org/W2005780385","https://openalex.org/W2041523977","https://openalex.org/W2092284067","https://openalex.org/W2101731201","https://openalex.org/W2125638038","https://openalex.org/W2129302988","https://openalex.org/W2136524923","https://openalex.org/W2142917543","https://openalex.org/W2150797568","https://openalex.org/W2155221979","https://openalex.org/W2161414603","https://openalex.org/W2171904101","https://openalex.org/W2965892125","https://openalex.org/W4206477975","https://openalex.org/W4230460931","https://openalex.org/W4241226388","https://openalex.org/W6629429686","https://openalex.org/W6651729414","https://openalex.org/W6685430937"],"related_works":["https://openalex.org/W3136192696","https://openalex.org/W3088363171","https://openalex.org/W2893311157","https://openalex.org/W2062275258","https://openalex.org/W2201760101","https://openalex.org/W4289750301","https://openalex.org/W2990084823","https://openalex.org/W2025438663","https://openalex.org/W2478780871","https://openalex.org/W2001646560"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":11}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}