{"id":"https://openalex.org/W4412471469","doi":"https://doi.org/10.1515/jnma-2024-0149","title":"Benchmarking numerical algorithms for harmonic maps into the sphere","display_name":"Benchmarking numerical algorithms for harmonic maps into the sphere","publication_year":2025,"publication_date":"2025-07-16","ids":{"openalex":"https://openalex.org/W4412471469","doi":"https://doi.org/10.1515/jnma-2024-0149"},"language":"en","primary_location":{"id":"doi:10.1515/jnma-2024-0149","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2024-0149","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1515/jnma-2024-0149","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017359935","display_name":"S\u00f6ren Bartels","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"S\u00f6ren Bartels","raw_affiliation_strings":["Department of Applied Mathematics , University of Freiburg , Freiburg im Breisgau , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Freiburg , Freiburg im Breisgau , Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061305648","display_name":"Klaus B\u00f6hnlein","orcid":null},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus B\u00f6hnlein","raw_affiliation_strings":["Institute of Numerical Mathematics , 9169 Technische Universit\u00e4t Dresden , Dresden , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Numerical Mathematics , 9169 Technische Universit\u00e4t Dresden , Dresden , Germany","institution_ids":["https://openalex.org/I78650965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042846615","display_name":"Christian Palus","orcid":null},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Palus","raw_affiliation_strings":["Department of Applied Mathematics , University of Freiburg , Freiburg im Breisgau , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , University of Freiburg , Freiburg im Breisgau , Germany","institution_ids":["https://openalex.org/I161046081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082524584","display_name":"Oliver Sander","orcid":"https://orcid.org/0000-0003-1093-6374"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Oliver Sander","raw_affiliation_strings":["Institute of Numerical Mathematics , 9169 Technische Universit\u00e4t Dresden , Dresden , Germany"],"raw_orcid":"https://orcid.org/0000-0003-1093-6374","affiliations":[{"raw_affiliation_string":"Institute of Numerical Mathematics , 9169 Technische Universit\u00e4t Dresden , Dresden , Germany","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8854,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78167723,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"34","issue":"1","first_page":"61","last_page":"89"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9958000183105469,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9958000183105469,"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/T11737","display_name":"Advanced Materials and Mechanics","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.991100013256073,"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/benchmarking","display_name":"Benchmarking","score":0.8300155401229858},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6891101002693176},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6005899310112},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3388044238090515}],"concepts":[{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.8300155401229858},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6891101002693176},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6005899310112},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3388044238090515},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1515/jnma-2024-0149","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2024-0149","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:freidok.uni-freiburg.de:269282","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/269282","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Numerical Mathematics. - (2025) , ISSN: 1569-3953","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1515/jnma-2024-0149","is_oa":true,"landing_page_url":"https://doi.org/10.1515/jnma-2024-0149","pdf_url":null,"source":{"id":"https://openalex.org/S60483245","display_name":"Journal of Numerical Mathematics","issn_l":"1569-3953","issn":["1569-3953","1570-2820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Numerical Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W147998453","https://openalex.org/W418503264","https://openalex.org/W569093612","https://openalex.org/W972019084","https://openalex.org/W1488292173","https://openalex.org/W1561385072","https://openalex.org/W1569061876","https://openalex.org/W1593038947","https://openalex.org/W1755177043","https://openalex.org/W1972289266","https://openalex.org/W1982223847","https://openalex.org/W2010532103","https://openalex.org/W2011530793","https://openalex.org/W2019658175","https://openalex.org/W2019798593","https://openalex.org/W2032008511","https://openalex.org/W2035427049","https://openalex.org/W2047453954","https://openalex.org/W2084889427","https://openalex.org/W2087755793","https://openalex.org/W2117496726","https://openalex.org/W2124673822","https://openalex.org/W2129261057","https://openalex.org/W2139329469","https://openalex.org/W2152394501","https://openalex.org/W2153963232","https://openalex.org/W2155258047","https://openalex.org/W2224750552","https://openalex.org/W2232537544","https://openalex.org/W2269438076","https://openalex.org/W2429937204","https://openalex.org/W2577603277","https://openalex.org/W2963277021","https://openalex.org/W2964029910","https://openalex.org/W2996234610","https://openalex.org/W3014793339","https://openalex.org/W3022249670","https://openalex.org/W3043048973","https://openalex.org/W3100717425","https://openalex.org/W3105714921","https://openalex.org/W3112401890","https://openalex.org/W3153530743","https://openalex.org/W3195424214","https://openalex.org/W4205293427","https://openalex.org/W4206004254","https://openalex.org/W4252383231","https://openalex.org/W4300417572","https://openalex.org/W4360869595","https://openalex.org/W4384560417","https://openalex.org/W4386322654","https://openalex.org/W4403128498","https://openalex.org/W6703547763","https://openalex.org/W6725096261","https://openalex.org/W6740982285"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4238897586","https://openalex.org/W435179959","https://openalex.org/W2619091065","https://openalex.org/W2059640416","https://openalex.org/W1490753184","https://openalex.org/W2284465472","https://openalex.org/W2291782699","https://openalex.org/W1993948687","https://openalex.org/W2000169967"],"abstract_inverted_index":{"Abstract":[0],"We":[1,97],"numerically":[2],"benchmark":[3],"methods":[4],"for":[5,111],"computing":[6],"harmonic":[7,17],"maps":[8,18],"into":[9],"the":[10,22,36,40,45,48,57,61,64,93,101,104,114,121,124,133,141],"unit":[11],"sphere,":[12],"with":[13,19,74],"particular":[14],"focus":[15],"on":[16,31],"singularities.":[20],"For":[21,60],"discretization":[23,116],"we":[24,68],"compare":[25,69],"two":[26],"different":[27],"approaches,":[28],"both":[29,107],"based":[30],"Lagrange":[32,46],"finite":[33],"elements.":[34],"While":[35],"first":[37],"method":[38,127],"enforces":[39],"unit-length":[41],"constraint":[42,58],"only":[43],"at":[44],"nodes,":[47],"other":[49],"one":[50],"adds":[51],"a":[52,70,75],"pointwise":[53],"projection":[54],"to":[55,86,89,140],"fulfill":[56],"everywhere.":[59],"solution":[62],"of":[63,92,135],"resulting":[65],"algebraic":[66],"problems":[67],"nonconforming":[71,102,115],"gradient":[72],"flow":[73],"Riemannian":[76],"trust-region":[77,126],"method.":[78],"Both":[79],"are":[80],"energy-decreasing":[81],"and":[82,103],"can":[83],"be":[84],"shown":[85],"converge":[87],"globally":[88],"stationary":[90],"points":[91],"discretized":[94],"Dirichlet":[95],"energy.":[96],"observe":[98],"that":[99],"while":[100],"conforming":[105],"discretizations":[106],"show":[108],"similar":[109],"behavior":[110],"smooth":[112],"problems,":[113],"handles":[117],"singularities":[118],"better.":[119],"On":[120],"solver":[122],"side,":[123],"second-order":[125],"converges":[128],"after":[129],"few":[130],"steps,":[131],"whereas":[132],"number":[134],"gradient-flow":[136],"steps":[137],"increases":[138],"proportionally":[139],"inverse":[142],"grid":[143],"element":[144],"diameter.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}