{"id":"https://openalex.org/W7164546967","doi":"https://doi.org/10.48550/arxiv.2606.13549","title":"A general-purpose global regularization method for 3D volume integral operators","display_name":"A general-purpose global regularization method for 3D volume integral operators","publication_year":2026,"publication_date":"2026-06-11","ids":{"openalex":"https://openalex.org/W7164546967","doi":"https://doi.org/10.48550/arxiv.2606.13549"},"language":"en","primary_location":{"id":"pmh:oai:HAL:hal-05654535v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05654535","pdf_url":"https://hal.science/hal-05654535v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-05654535v1/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138539299","display_name":"Thomas G. Anderson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anderson, Thomas G.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014740141","display_name":"Marc Bonnet","orcid":"https://orcid.org/0000-0001-8834-3777"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bonnet, Marc","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017462848","display_name":"Luiz M. Faria","orcid":"https://orcid.org/0000-0002-8090-934X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Faria, Luiz M.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138486051","display_name":"Carlos P\u00e9rez-Arancibia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P\u00e9rez-Arancibia, Carlos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.4578000009059906,"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"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.4578000009059906,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.22920000553131104,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.06260000169277191,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5605999827384949},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5372999906539917},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5329999923706055},{"id":"https://openalex.org/keywords/fourier-integral-operator","display_name":"Fourier integral operator","score":0.5224000215530396},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5149999856948853},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.44279998540878296},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42260000109672546},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.40860000252723694},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.39500001072883606},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.39259999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8339999914169312},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5605999827384949},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5572999715805054},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5372999906539917},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5329999923706055},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.5224000215530396},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5149999856948853},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4596000015735626},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.44279998540878296},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42260000109672546},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.40860000252723694},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.39500001072883606},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.39259999990463257},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.38929998874664307},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.38850000500679016},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.3880000114440918},{"id":"https://openalex.org/C94950523","wikidata":"https://www.wikidata.org/wiki/Q7524241","display_name":"Singular integral operators of convolution type","level":5,"score":0.3801000118255615},{"id":"https://openalex.org/C129683796","wikidata":"https://www.wikidata.org/wiki/Q430450","display_name":"Microlocal analysis","level":4,"score":0.3783999979496002},{"id":"https://openalex.org/C2992640183","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral operators","level":4,"score":0.35830000042915344},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.35030001401901245},{"id":"https://openalex.org/C51577431","wikidata":"https://www.wikidata.org/wiki/Q1788036","display_name":"Volume integral","level":3,"score":0.33709999918937683},{"id":"https://openalex.org/C167528306","wikidata":"https://www.wikidata.org/wiki/Q5508776","display_name":"Function representation","level":3,"score":0.3359000086784363},{"id":"https://openalex.org/C134466208","wikidata":"https://www.wikidata.org/wiki/Q1520657","display_name":"Weight function","level":2,"score":0.3357999920845032},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C43994743","wikidata":"https://www.wikidata.org/wiki/Q516776","display_name":"Measurable function","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C113285462","wikidata":"https://www.wikidata.org/wiki/Q856103","display_name":"Methods of contour integration","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C189987565","wikidata":"https://www.wikidata.org/wiki/Q7333166","display_name":"Riesz potential","level":2,"score":0.2567000091075897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:hal-05654535v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05654535","pdf_url":"https://hal.science/hal-05654535v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2606.13549","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.13549","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":"pmh:oai:HAL:hal-05654535v1","is_oa":true,"landing_page_url":"https://hal.science/hal-05654535","pdf_url":"https://hal.science/hal-05654535v1/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7164546967.pdf","grobid_xml":"https://content.openalex.org/works/W7164546967.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Singular":[0],"volume":[1,41,86,95],"integral":[2,87],"operators":[3,9,33,88],"associated":[4],"with":[5,135,142],"constant-coefficient":[6],"partial":[7],"differential":[8],"extend":[10],"the":[11,28,52,102,106,111,114,124,127],"applicability":[12],"of":[13,47,55,81,91,105,145],"potential":[14],"theory":[15],"to":[16,36,60,66,76,126],"inhomogeneous":[17],"problems,":[18],"for":[19],"example":[20],"arising":[21],"from":[22],"nonlinearities":[23],"or":[24],"variable":[25],"coefficients.":[26],"Typically":[27],"PDE":[29],"kernels":[30,57],"in":[31,44,110,118],"these":[32],"give":[34,58],"rise":[35,59],"singularities":[37],"at":[38],"all":[39],"$\\mathcal{O}(1/h^3)$":[40],"discretization/evaluation":[42],"points":[43],"a":[45,78,92],"mesh":[46],"characteristic":[48],"size":[49],"$h$,":[50],"while":[51],"slowly-decaying":[53],"nature":[54],"such":[56],"long-range":[61],"interactions":[62],"that":[63,113],"require":[64],"coupling":[65],"fast":[67],"summation":[68],"algorithms.":[69],"The":[70,98],"presented":[71],"method":[72],"uses":[73],"Green's":[74,128],"identities":[75],"regularize":[77],"wide":[79],"variety":[80],"both":[82],"scalar-valued":[83],"and":[84],"vector-valued":[85],"by":[89],"use":[90],"certain":[93],"regularizing":[94,103],"density":[96],"interpolant.":[97],"analysis":[99],"shows":[100],"how":[101],"effect":[104],"interpolant":[107],"is":[108],"global":[109],"sense":[112],"interpolation":[115],"quality":[116],"increases":[117],"an":[119],"exactly":[120],"compensatory":[121],"fashion":[122],"as":[123],"distance":[125],"function":[129],"singularity":[130],"decreases.":[131],"High-order":[132],"convergence":[133],"estimates":[134],"tabulated":[136],"simplex":[137],"quadratures":[138],"are":[139],"established,":[140],"including":[141],"exact":[143],"representation":[144],"curved":[146],"domains.":[147]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2026-06-13T00:00:00"}
