{"id":"https://openalex.org/W4320730833","doi":"https://doi.org/10.1515/cmam-2022-0159","title":"Fractional Laplacian \u2013 Quadrature Rules for Singular Double Integrals in 3D","display_name":"Fractional Laplacian \u2013 Quadrature Rules for Singular Double Integrals in 3D","publication_year":2023,"publication_date":"2023-02-14","ids":{"openalex":"https://openalex.org/W4320730833","doi":"https://doi.org/10.1515/cmam-2022-0159"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2022-0159","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0159","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066404254","display_name":"Bernd Feist","orcid":null},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Bernd Feist","raw_affiliation_strings":["Mathematisches Institut , Universit\u00e4t Bayreuth , 95447 Bayreuth , Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut , Universit\u00e4t Bayreuth , 95447 Bayreuth , Germany","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064337181","display_name":"Mario Bebendorf","orcid":null},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mario Bebendorf","raw_affiliation_strings":["Mathematisches Institut , Universit\u00e4t Bayreuth , 95447 Bayreuth , Germany"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut , Universit\u00e4t Bayreuth , 95447 Bayreuth , Germany","institution_ids":["https://openalex.org/I54009628"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066404254"],"corresponding_institution_ids":["https://openalex.org/I54009628"],"apc_list":null,"apc_paid":null,"fwci":0.519,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.54642025,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"23","issue":"3","first_page":"623","last_page":"645"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998999834060669,"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":0.9998999834060669,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9990000128746033,"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/mathematics","display_name":"Mathematics","score":0.7305910587310791},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6800199151039124},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.6583998799324036},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.6428185701370239},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5930339694023132},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.513582706451416},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.49669963121414185},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4643939137458801},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.4487150013446808},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.43831345438957214},{"id":"https://openalex.org/keywords/fractional-laplacian","display_name":"Fractional Laplacian","score":0.43723323941230774},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43674802780151367},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.4259454309940338},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.41272085905075073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3971374034881592},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13252133131027222},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.11751621961593628},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.10867127776145935},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07526898384094238}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7305910587310791},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6800199151039124},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.6583998799324036},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.6428185701370239},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5930339694023132},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.513582706451416},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.49669963121414185},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4643939137458801},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.4487150013446808},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.43831345438957214},{"id":"https://openalex.org/C2775913539","wikidata":"https://www.wikidata.org/wiki/Q30694381","display_name":"Fractional Laplacian","level":2,"score":0.43723323941230774},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43674802780151367},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.4259454309940338},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.41272085905075073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3971374034881592},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13252133131027222},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.11751621961593628},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.10867127776145935},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07526898384094238},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2022-0159","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0159","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1972152164","https://openalex.org/W1973352373","https://openalex.org/W2006455026","https://openalex.org/W2009985306","https://openalex.org/W2064361774","https://openalex.org/W2081212234","https://openalex.org/W2127570421","https://openalex.org/W2140620666","https://openalex.org/W2395085125","https://openalex.org/W2464615737","https://openalex.org/W2477251619","https://openalex.org/W2486821353","https://openalex.org/W2532859297","https://openalex.org/W2744610720","https://openalex.org/W2749611175","https://openalex.org/W2797636543","https://openalex.org/W3123275897","https://openalex.org/W3200506295","https://openalex.org/W4292079583"],"related_works":["https://openalex.org/W4387847482","https://openalex.org/W2012929093","https://openalex.org/W4377005030","https://openalex.org/W4205354206","https://openalex.org/W2990351226","https://openalex.org/W3109298388","https://openalex.org/W2085681042","https://openalex.org/W2317230014","https://openalex.org/W1996418117","https://openalex.org/W2168497266"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,40,58,97],"article,":[3],"quadrature":[4],"rules":[5,24],"for":[6,14,36],"the":[7,11,15,28,45,48,71,83,89],"efficient":[8],"computation":[9],"of":[10,47,73,82,86],"stiffness":[12],"matrix":[13],"fractional":[16,49],"Laplacian":[17,50],"in":[18,51,96,108],"three":[19,52,109],"dimensions":[20,110],"are":[21,25,61,81],"presented.":[22],"These":[23],"based":[26],"on":[27,70],"Duffy":[29,59],"transformation,":[30],"which":[31,80],"is":[32,42],"a":[33],"common":[34],"tool":[35],"singularity":[37],"removal.":[38],"Here,":[39],"transformation":[41,60],"adapted":[43,102],"to":[44,76,103],"needs":[46],"dimensions.":[53],"The":[54,93],"integrals":[55,63,107],"resulting":[56],"from":[57],"regular":[62],"over":[64],"less-dimensional":[65],"domains.":[66],"We":[67],"present":[68],"bounds":[69],"number":[72],"Gauss":[74],"points":[75],"guarantee":[77],"error":[78],"estimates":[79],"same":[84],"order":[85],"magnitude":[87],"as":[88],"finite":[90],"element":[91],"error.":[92],"methods":[94],"presented":[95],"article":[98],"can":[99],"easily":[100],"be":[101],"other":[104],"singular":[105],"double":[106],"with":[111],"algebraic":[112],"singularities.":[113]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}