{"id":"https://openalex.org/W7133353917","doi":"https://doi.org/10.48550/arxiv.2603.00880","title":"A natural language framework for non-conforming hybrid polytopal methods in Gridap.jl","display_name":"A natural language framework for non-conforming hybrid polytopal methods in Gridap.jl","publication_year":2026,"publication_date":"2026-03-01","ids":{"openalex":"https://openalex.org/W7133353917","doi":"https://doi.org/10.48550/arxiv.2603.00880"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.00880","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00880","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.00880","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113145418","display_name":"J. Manyer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Manyer, Jordi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058616433","display_name":"Jai Tushar","orcid":"https://orcid.org/0000-0002-5773-8466"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tushar, Jai","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5071818847","display_name":"Santiago Badia","orcid":"https://orcid.org/0000-0003-2391-4086"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Badia, Santiago","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113145418"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.8962000012397766,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.8962000012397766,"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/T11416","display_name":"Numerical methods for differential equations","score":0.018200000748038292,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.015300000086426735,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.510699987411499},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4781000018119812},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4717999994754791},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4397999942302704},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.4381999969482422},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4372999966144562},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40700000524520874},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.39660000801086426},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.3840999901294708}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5450000166893005},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5292999744415283},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.510699987411499},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4781000018119812},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4717999994754791},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.450300008058548},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4397999942302704},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.4381999969482422},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4372999966144562},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40700000524520874},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.3840999901294708},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37439998984336853},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3700000047683716},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3698999881744385},{"id":"https://openalex.org/C50897621","wikidata":"https://www.wikidata.org/wiki/Q2665508","display_name":"Hybrid system","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.32989999651908875},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.314300000667572},{"id":"https://openalex.org/C160191386","wikidata":"https://www.wikidata.org/wiki/Q868299","display_name":"Control flow","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.31299999356269836},{"id":"https://openalex.org/C131053463","wikidata":"https://www.wikidata.org/wiki/Q4680751","display_name":"Adaptive mesh refinement","level":2,"score":0.31139999628067017},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2980000078678131},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.29280000925064087},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.2775999903678894},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.27079999446868896},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.26190000772476196}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.00880","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00880","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.00880","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00880","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Hybrid":[0],"finite":[1,63],"element":[2,64],"methods":[3,34,59,106,130],"such":[4,58],"as":[5,16],"hybridizable":[6],"discontinuous":[7],"Galerkin,":[8],"hybrid":[9,41,105],"high-order":[10],"and":[11,47,95,115,140],"weak":[12],"Galerkin":[13],"have":[14],"emerged":[15],"powerful":[17],"techniques":[18],"for":[19,56,70,87,131],"solving":[20],"partial":[21],"differential":[22],"equations":[23],"on":[24,80,143],"general":[25],"polytopal":[26,71,129,144],"meshes.":[27,145],"Despite":[28],"their":[29],"diverse":[30],"mathematical":[31],"origins,":[32],"these":[33],"share":[35],"a":[36,53],"common":[37],"computational":[38,109],"structure":[39],"involving":[40],"discrete":[42],"spaces,":[43],"local":[44,85,92],"projection":[45],"operators":[46],"static":[48,97],"condensation.":[49,98],"This":[50],"work":[51],"presents":[52],"comprehensive":[54],"framework":[55,123],"implementing":[57],"within":[60],"the":[61,122,132],"Gridap":[62],"library.":[65],"We":[66,120],"introduce":[67],"new":[68],"abstractions":[69,100],"mesh":[72,82],"representation":[73],"using":[74],"graph-based":[75],"structures,":[76],"broken":[77],"polynomial":[78],"spaces":[79],"arbitrary":[81],"entities,":[83],"patch-based":[84],"assembly":[86],"cell-wise":[88],"linear":[89,135],"systems,":[90],"high-level":[91],"operator":[93],"construction":[94],"automated":[96],"These":[99],"enable":[101],"concise":[102],"implementations":[103,125],"of":[104,126],"while":[107],"maintaining":[108],"efficiency":[110],"through":[111,124],"Julia's":[112],"just-in-time":[113],"compilation":[114],"Gridap's":[116],"lazy":[117],"evaluation":[118],"strategies.":[119],"demonstrate":[121],"several":[127],"non-conforming":[128],"Poisson":[133],"problem,":[134],"elasticity,":[136],"incompressible":[137],"Stokes":[138],"flow":[139],"optimal":[141],"control":[142]},"counts_by_year":[],"updated_date":"2026-03-04T07:09:34.246503","created_date":"2026-03-04T00:00:00"}