{"id":"https://openalex.org/W2101251393","doi":"https://doi.org/10.1137/110849018","title":"On the Efficiency and Accuracy of Interpolation Methods for Spectral Codes","display_name":"On the Efficiency and Accuracy of Interpolation Methods for Spectral Codes","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2101251393","doi":"https://doi.org/10.1137/110849018","mag":"2101251393"},"language":"en","primary_location":{"id":"doi:10.1137/110849018","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110849018","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.tue.nl/en/publications/fa05f590-35bc-44ce-af80-d7a07317423f","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051869021","display_name":"M. A. T. van Hinsberg","orcid":null},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"M. A. T. van Hinsberg","raw_affiliation_strings":["Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Eindhoven University of Technology, P.O. Box 513, 5600MB Eindhoven, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108646076","display_name":"J. H. M. Thije Boonkkamp","orcid":null},"institutions":[{"id":"https://openalex.org/I4210090500","display_name":"Office of Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22","country_code":"US","type":"government","lineage":["https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210090500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. H. M. Thije Boonkkamp","raw_affiliation_strings":["Scientific Computing"],"affiliations":[{"raw_affiliation_string":"Scientific Computing","institution_ids":["https://openalex.org/I4210090500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061447676","display_name":"Federico Toschi","orcid":"https://orcid.org/0000-0001-5935-2332"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Toschi","raw_affiliation_strings":["Fluids and Flows"],"affiliations":[{"raw_affiliation_string":"Fluids and Flows","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005309801","display_name":"H. J. H. Clercx","orcid":"https://orcid.org/0000-0001-8769-0435"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. J. H. Clercx","raw_affiliation_strings":["Fluids and Flows"],"affiliations":[{"raw_affiliation_string":"Fluids and Flows","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5051869021"],"corresponding_institution_ids":["https://openalex.org/I83019370"],"apc_list":null,"apc_paid":null,"fwci":1.0535,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.77729478,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"34","issue":"4","first_page":"B479","last_page":"B498"},"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":0.9941999912261963,"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":0.9941999912261963,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9922999739646912,"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":0.9868000149726868,"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/mathematics","display_name":"Mathematics","score":0.7659875750541687},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.63132643699646},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4477241635322571},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4355664551258087},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.4134688377380371},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32452070713043213},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18922525644302368},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16992729902267456},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09580191969871521}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7659875750541687},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.63132643699646},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4477241635322571},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4355664551258087},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4134688377380371},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32452070713043213},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18922525644302368},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16992729902267456},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09580191969871521},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":8,"locations":[{"id":"doi:10.1137/110849018","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110849018","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.tue.nl:openaire/fa05f590-35bc-44ce-af80-d7a07317423f","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/fa05f590-35bc-44ce-af80-d7a07317423f","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hinsberg, van, M A T, Thije Boonkkamp, ten, J H M, Toschi, F & Clercx, H J H 2012, 'On the efficiency and accuracy of interpolation methods for spectral codes', SIAM Journal on Scientific Computing, vol. 34, no. 4, pp. B479-B498. https://doi.org/10.1137/110849018","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:ris.utwente.nl:openaire/a1ca6660-2233-4f62-a35a-497d0032756b","is_oa":false,"landing_page_url":"https://research.utwente.nl/en/publications/a1ca6660-2233-4f62-a35a-497d0032756b","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"van Hinsberg, M A T, ten Thije Boonkkamp, J H M, Toschi, F & Clercx, H J H 2012, 'On the efficiency and accuracy of interpolation methods for spectral codes', SIAM journal on scientific computing, vol. 34, no. 4, pp. B479-B498. https://doi.org/10.1137/110849018","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:tue:oai:pure.tue.nl:publications/fa05f590-35bc-44ce-af80-d7a07317423f","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/fa05f590-35bc-44ce-af80-d7a07317423f","pdf_url":"https://research.tue.nl/nl/publications/fa05f590-35bc-44ce-af80-d7a07317423f","source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 34(4), B479 - B498. Society for Industrial and Applied Mathematics (SIAM)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/0204b8a5-a4c6-469d-ace5-d652c89485da","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/0204b8a5-a4c6-469d-ace5-d652c89485da","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Hinsberg, van , M A T , Thije Boonkkamp, ten , J H M , Toschi , F & Clercx , H J H 2011 , On the efficiency and accuracy of interpolation methods for spectral codes . CASA-report , vol. 1150 , Technische Universiteit Eindhoven , Eindhoven .","raw_type":"book"},{"id":"pmh:tue:oai:library.tue.nl:719199","is_oa":false,"landing_page_url":"http://repository.tue.nl/719199","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"},{"id":"pmh:tue:oai:library.tue.nl:734452","is_oa":false,"landing_page_url":"http://repository.tue.nl/734452","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, 34(4), B479","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:tue:oai:pure.tue.nl:publications/0204b8a5-a4c6-469d-ace5-d652c89485da","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/0204b8a5-a4c6-469d-ace5-d652c89485da","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/report"}],"best_oa_location":{"id":"pmh:oai:pure.tue.nl:openaire/fa05f590-35bc-44ce-af80-d7a07317423f","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/fa05f590-35bc-44ce-af80-d7a07317423f","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hinsberg, van, M A T, Thije Boonkkamp, ten, J H M, Toschi, F & Clercx, H J H 2012, 'On the efficiency and accuracy of interpolation methods for spectral codes', SIAM Journal on Scientific Computing, vol. 34, no. 4, pp. B479-B498. https://doi.org/10.1137/110849018","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6009445997","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G629491556","display_name":null,"funder_award_id":"(NWO)","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1964937505","https://openalex.org/W1973159757","https://openalex.org/W1973573835","https://openalex.org/W2007745549","https://openalex.org/W2013224421","https://openalex.org/W2024165284","https://openalex.org/W2024251976","https://openalex.org/W2043397824","https://openalex.org/W2044665398","https://openalex.org/W2059407301","https://openalex.org/W2070981356","https://openalex.org/W2085743661","https://openalex.org/W2086002623","https://openalex.org/W2099557614","https://openalex.org/W2113524221","https://openalex.org/W2118448675","https://openalex.org/W2123403678","https://openalex.org/W2141328758","https://openalex.org/W2144240453","https://openalex.org/W2153845440","https://openalex.org/W2171756828"],"related_works":["https://openalex.org/W2165589608","https://openalex.org/W3093557575","https://openalex.org/W2367652182","https://openalex.org/W2037074416","https://openalex.org/W2101207231","https://openalex.org/W2741873457","https://openalex.org/W1519931592","https://openalex.org/W2319983895","https://openalex.org/W2142192217","https://openalex.org/W4388093525"],"abstract_inverted_index":{"In":[0,44],"this":[1,19,45],"paper":[2],"a":[3,10,64,130],"general":[4],"theory":[5,20,32],"for":[6,26,99,109,116],"interpolation":[7,24,38,69,78,112,122],"methods":[8,70,136],"on":[9],"rectangular":[11],"grid":[12],"is":[13,29,71,96,106],"introduced.":[14],"By":[15],"the":[16,34,37,68,76,88,93,118,121],"use":[17],"of":[18,36,51,54,58,67,90,92,127],"an":[21],"efficient":[22],"B-spline-based":[23,77],"method":[25,39,79],"spectral":[27,42],"codes":[28],"presented.":[30],"The":[31],"links":[33],"order":[35,50,53,89],"with":[40],"its":[41],"properties.":[43],"way":[46],"many":[47],"properties":[48],"like":[49],"continuity,":[52],"convergence,":[55],"and":[56],"magnitude":[57],"errors":[59],"can":[60],"be":[61],"explained.":[62],"Furthermore,":[63],"fast":[65],"implementation":[66],"given.":[72],"We":[73],"show":[74],"that":[75,126],"has":[80],"several":[81],"advantages":[82],"compared":[83],"to":[84],"other":[85,100,135],"methods.":[86,101],"First,":[87],"continuity":[91],"interpolated":[94],"field":[95],"higher":[97],"than":[98],"Second,":[102],"only":[103],"one":[104],"FFT":[105],"needed,":[107],"whereas,":[108],"example,":[110],"Hermite":[111,128],"needs":[113],"multiple":[114],"FFTs":[115],"computing":[117],"derivatives.":[119],"Third,":[120],"error":[123],"almost":[124],"matches":[125],"interpolation,":[129],"property":[131],"not":[132],"reached":[133],"by":[134],"investigated.":[137]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}