{"id":"https://openalex.org/W2962941456","doi":"https://doi.org/10.1007/s10444-020-09804-z","title":"An integral equation\u2013based numerical method for the forced heat equation on complex domains","display_name":"An integral equation\u2013based numerical method for the forced heat equation on complex domains","publication_year":2020,"publication_date":"2020-08-20","ids":{"openalex":"https://openalex.org/W2962941456","doi":"https://doi.org/10.1007/s10444-020-09804-z","mag":"2962941456"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-020-09804-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-020-09804-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-020-09804-z.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10444-020-09804-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090405412","display_name":"Fredrik Fryklund","orcid":"https://orcid.org/0000-0002-0434-2580"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Fredrik Fryklund","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden;"],"raw_orcid":"https://orcid.org/0000-0002-0434-2580","affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden;","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110620538","display_name":"Mary Catherine A. Kropinski","orcid":null},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mary Catherine A. Kropinski","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University, Burnaby, Canada","Department of Mathematics , Simon Fraser University , Burnaby, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, Burnaby, Canada","institution_ids":["https://openalex.org/I18014758"]},{"raw_affiliation_string":"Department of Mathematics , Simon Fraser University , Burnaby, Canada","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091831807","display_name":"Anna\u2010Karin Tornberg","orcid":"https://orcid.org/0000-0002-4290-1670"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Anna-Karin Tornberg","raw_affiliation_strings":["Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden;","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090405412"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.3904,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.47826852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"46","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.996399998664856,"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/helmholtz-equation","display_name":"Helmholtz equation","score":0.7011428475379944},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6958656907081604},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.6561564207077026},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.6195366978645325},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.5815277695655823},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5691717863082886},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5432741045951843},{"id":"https://openalex.org/keywords/electric-field-integral-equation","display_name":"Electric-field integral equation","score":0.5122184157371521},{"id":"https://openalex.org/keywords/summation-equation","display_name":"Summation equation","score":0.48550915718078613},{"id":"https://openalex.org/keywords/integro-differential-equation","display_name":"Integro-differential equation","score":0.4794518053531647},{"id":"https://openalex.org/keywords/volume-integral","display_name":"Volume integral","score":0.444794625043869},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.43405666947364807},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3967673182487488},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3451242446899414},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3216443359851837},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.16670191287994385},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08160477876663208}],"concepts":[{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.7011428475379944},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6958656907081604},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.6561564207077026},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.6195366978645325},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.5815277695655823},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5691717863082886},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5432741045951843},{"id":"https://openalex.org/C3537527","wikidata":"https://www.wikidata.org/wiki/Q5357276","display_name":"Electric-field integral equation","level":3,"score":0.5122184157371521},{"id":"https://openalex.org/C143591791","wikidata":"https://www.wikidata.org/wiki/Q7637218","display_name":"Summation equation","level":3,"score":0.48550915718078613},{"id":"https://openalex.org/C70985411","wikidata":"https://www.wikidata.org/wiki/Q2380676","display_name":"Integro-differential equation","level":4,"score":0.4794518053531647},{"id":"https://openalex.org/C51577431","wikidata":"https://www.wikidata.org/wiki/Q1788036","display_name":"Volume integral","level":3,"score":0.444794625043869},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43405666947364807},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3967673182487488},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3451242446899414},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3216443359851837},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.16670191287994385},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08160477876663208},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10444-020-09804-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-020-09804-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-020-09804-z.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1907.08537","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.08537","pdf_url":"https://arxiv.org/pdf/1907.08537","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2962941456","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1907.08537","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1907.08537","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1907.08537","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/s10444-020-09804-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10444-020-09804-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10444-020-09804-z.pdf","source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7702831438","display_name":"A fast intergal equation based numerical method for soluble surfactants in droplet microfluidics.","funder_award_id":"2015-04998","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320316588","display_name":"G\u00f6ran Gustafssons Stiftelser","ror":"https://ror.org/05s5h0e62"},{"id":"https://openalex.org/F4320321908","display_name":"G\u00f6ran Gustafssons Stiftelse f\u00f6r Naturvetenskaplig och Medicinsk Forskning","ror":"https://ror.org/05s5h0e62"},{"id":"https://openalex.org/F4320322509","display_name":"Kungliga Tekniska H\u00f6gskolan","ror":"https://ror.org/026vcq606"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2962941456.pdf","grobid_xml":"https://content.openalex.org/works/W2962941456.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W19451620","https://openalex.org/W1490180844","https://openalex.org/W1752975871","https://openalex.org/W1965790396","https://openalex.org/W1970212587","https://openalex.org/W1970213140","https://openalex.org/W1978291408","https://openalex.org/W1980928855","https://openalex.org/W1981474196","https://openalex.org/W1983713460","https://openalex.org/W1984741461","https://openalex.org/W1991574341","https://openalex.org/W1991962363","https://openalex.org/W1991971072","https://openalex.org/W2004797340","https://openalex.org/W2014016024","https://openalex.org/W2014208709","https://openalex.org/W2027206648","https://openalex.org/W2057754884","https://openalex.org/W2061776468","https://openalex.org/W2077852061","https://openalex.org/W2077852080","https://openalex.org/W2079447210","https://openalex.org/W2080219236","https://openalex.org/W2084831289","https://openalex.org/W2116209321","https://openalex.org/W2117648842","https://openalex.org/W2128506199","https://openalex.org/W2133543883","https://openalex.org/W2139494815","https://openalex.org/W2147169375","https://openalex.org/W2160651214","https://openalex.org/W2169437869","https://openalex.org/W2170668759","https://openalex.org/W2335216145","https://openalex.org/W2481312347","https://openalex.org/W2527940355","https://openalex.org/W2556291925","https://openalex.org/W2625275472","https://openalex.org/W2779258471","https://openalex.org/W2783855936","https://openalex.org/W2810875921","https://openalex.org/W2896338797","https://openalex.org/W2900913246","https://openalex.org/W2951151167","https://openalex.org/W3007937599"],"related_works":["https://openalex.org/W1966825323","https://openalex.org/W1992017546","https://openalex.org/W1973530788","https://openalex.org/W1970343910","https://openalex.org/W1975018682","https://openalex.org/W2157244071","https://openalex.org/W2048569222","https://openalex.org/W1553518710","https://openalex.org/W3088401801","https://openalex.org/W2114693086","https://openalex.org/W2061664938","https://openalex.org/W3184797601","https://openalex.org/W2514193682","https://openalex.org/W2293872238","https://openalex.org/W3816367","https://openalex.org/W2035514006","https://openalex.org/W165112632","https://openalex.org/W2009174503","https://openalex.org/W2962994565","https://openalex.org/W2276117703"],"abstract_inverted_index":{"Abstract":[0],"Integral":[1],"equation\u2013based":[2],"numerical":[3],"methods":[4],"are":[5,123],"directly":[6],"applicable":[7],"to":[8,16,35,133,154],"homogeneous":[9,84],"elliptic":[10],"PDEs":[11],"and":[12,22,92,149,158],"offer":[13],"the":[14,36,44,70,97,107,126,143,163,167],"ability":[15],"solve":[17,57],"these":[18],"with":[19,39,65,87],"high":[20],"accuracy":[21],"speed":[23],"on":[24,69],"complex":[25],"domains.":[26],"In":[27,115],"this":[28,116,129],"paper,":[29],"such":[30],"a":[31,58,66,83,88,93,103,112,131,136,140,150],"method":[32,91,132,153],"is":[33,47,78,99,147],"extended":[34],"heat":[37,45],"equation":[38,46,77,170],"inhomogeneous":[40,108],"source":[41,109],"terms.":[42],"First,":[43],"discretised":[48],"in":[49,52,162],"time,":[50],"then":[51,79],"each":[53],"time":[54,71,173],"step":[55,72,174],"we":[56,118],"sequence":[59],"of":[60,128,139,166],"so-called":[61],"modified":[62,75,168],"Helmholtz":[63,76,169],"equations":[64],"parameter":[67],"depending":[68],"size.":[73],"The":[74],"split":[80],"into":[81],"two:":[82],"part":[85],"solved":[86],"boundary":[89],"integral":[90,164],"particular":[94],"part,":[95],"where":[96,145],"solution":[98],"obtained":[100],"by":[101],"evaluating":[102],"volume":[104],"potential":[105],"over":[106,111],"term":[110],"simple":[113],"domain.":[114],"work,":[117],"introduce":[119],"two":[120],"components":[121],"which":[122],"critical":[124],"for":[125,171],"success":[127],"approach:":[130],"efficiently":[134],"compute":[135],"high-regularity":[137],"extension":[138],"function":[141],"outside":[142],"domain":[144],"it":[146],"defined,":[148],"special":[151],"quadrature":[152],"accurately":[155],"evaluate":[156],"singular":[157,160],"nearly":[159],"integrals":[161],"formulation":[165],"all":[172],"sizes.":[175]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
