{"id":"https://openalex.org/W7077513525","doi":"https://doi.org/10.48550/arxiv.2508.16060","title":"Using the Immersed Penalized Boundary Method with Splines to Solve PDE's on Curved Domains in 3D","display_name":"Using the Immersed Penalized Boundary Method with Splines to Solve PDE's on Curved Domains in 3D","publication_year":2025,"publication_date":"2025-08-22","ids":{"openalex":"https://openalex.org/W7077513525","doi":"https://doi.org/10.48550/arxiv.2508.16060"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2508.16060","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.16060","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":null,"license_id":null,"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.2508.16060","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Greene, Aussie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Greene, Aussie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Schumaker, Larry L.","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schumaker, Larry L.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"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":true,"primary_topic":{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.6507999897003174,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.6507999897003174,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T13067","display_name":"Geological Modeling and Analysis","score":0.025100000202655792,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14311","display_name":"Electrical and Electromagnetic Research","score":0.020400000736117363,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/spline","display_name":"Spline (mechanical)","score":0.6474999785423279},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5845000147819519},{"id":"https://openalex.org/keywords/thin-plate-spline","display_name":"Thin plate spline","score":0.47769999504089355},{"id":"https://openalex.org/keywords/m-spline","display_name":"M-spline","score":0.4399000108242035},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4235000014305115},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.392300009727478},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.383899986743927},{"id":"https://openalex.org/keywords/bivariate-analysis","display_name":"Bivariate analysis","score":0.3603000044822693}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7245000004768372},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.6474999785423279},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5845000147819519},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.510200023651123},{"id":"https://openalex.org/C93132110","wikidata":"https://www.wikidata.org/wiki/Q7784288","display_name":"Thin plate spline","level":4,"score":0.47769999504089355},{"id":"https://openalex.org/C199765470","wikidata":"https://www.wikidata.org/wiki/Q6712116","display_name":"M-spline","level":5,"score":0.4399000108242035},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4235000014305115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41760000586509705},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.392300009727478},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C64341305","wikidata":"https://www.wikidata.org/wiki/Q4919225","display_name":"Bivariate analysis","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C107457265","wikidata":"https://www.wikidata.org/wiki/Q7546460","display_name":"Smoothing spline","level":4,"score":0.3447999954223633},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30720001459121704},{"id":"https://openalex.org/C78383375","wikidata":"https://www.wikidata.org/wiki/Q4951620","display_name":"Box spline","level":4,"score":0.304500013589859},{"id":"https://openalex.org/C205224112","wikidata":"https://www.wikidata.org/wiki/Q4426180","display_name":"Perfect spline","level":5,"score":0.29789999127388},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29600000381469727},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28600001335144043},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C2187777","wikidata":"https://www.wikidata.org/wiki/Q1071743","display_name":"Parametric surface","level":3,"score":0.25839999318122864},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2549000084400177},{"id":"https://openalex.org/C121704545","wikidata":"https://www.wikidata.org/wiki/Q11425899","display_name":"Immersed boundary method","level":3,"score":0.2522999942302704}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2508.16060","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.16060","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2508.16060","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.16060","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Second-order":[0],"elliptic":[1,51],"boundary-value":[2,120],"problems":[3,121],"defined":[4],"on":[5,53,122],"curved":[6,56,123],"domains":[7,54,124],"in":[8,14,46,125],"2D":[9],"and":[10,34],"3D":[11],"arise":[12],"frequently":[13],"practice.":[15],"A":[16],"lot":[17],"of":[18,31,75,78,103],"work":[19],"has":[20],"gone":[21],"into":[22],"developing":[23],"numerical":[24],"methods":[25,37,80,113],"for":[26],"solving":[27],"such":[28],"problems.":[29],"One":[30],"the":[32,39,76,87],"newest":[33],"most":[35],"promising":[36],"is":[38,106],"$\\textit{immersed":[40],"penalized":[41,61],"boundary":[42,62],"method}$":[43],"(IPBM)":[44],"introduced":[45],"[Schumaker,":[47,90],"L.":[48,91],"L.,":[49],"Solving":[50],"PDE's":[52],"with":[55,58,81,114],"boundaries":[57],"an":[59],"immersed":[60],"method,":[63],"J.":[64],"Sci.":[65],"Comp.":[66],"${\\bf":[67],"80(3)}$":[68],"(2019),":[69],"1369--1394].":[70],"For":[71],"a":[72],"comprehensive":[73],"discussion":[74],"use":[77,111],"these":[79],"various":[82],"bivariate":[83],"spline":[84,116],"spaces,":[85],"see":[86],"recent":[88],"book":[89],"L.:":[92],"$\\textit{Spline":[93],"Functions:":[94],"More":[95],"Computational":[96],"Methods}$,":[97],"SIAM":[98],"(Philadelphia),":[99],"2024].":[100],"The":[101],"purpose":[102],"this":[104],"paper":[105],"to":[107,110,118],"show":[108],"how":[109],"IPBM":[112],"trivariate":[115],"spaces":[117],"solve":[119],"3D.":[126]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}