{"id":"https://openalex.org/W1965505816","doi":"https://doi.org/10.1137/110860380","title":"The Method of Fundamental Solutions Applied to Some Inverse Eigenproblems","display_name":"The Method of Fundamental Solutions Applied to Some Inverse Eigenproblems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1965505816","doi":"https://doi.org/10.1137/110860380","mag":"1965505816"},"language":"en","primary_location":{"id":"doi:10.1137/110860380","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110860380","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039250293","display_name":"Carlos J.S. Alves","orcid":"https://orcid.org/0000-0002-3834-500X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlos J. S. Alves","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5064795422","display_name":"Pedro R. S. Antunes","orcid":"https://orcid.org/0000-0003-1969-1860"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pedro R. S. Antunes","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":4.4315,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.92862577,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"35","issue":"3","first_page":"A1689","last_page":"A1708"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9936000108718872,"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/T10514","display_name":"Numerical methods in engineering","score":0.9921000003814697,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8111890554428101},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.737972617149353},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6266923546791077},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.5724128484725952},{"id":"https://openalex.org/keywords/normal-mode","display_name":"Normal mode","score":0.5675839185714722},{"id":"https://openalex.org/keywords/shape-optimization","display_name":"Shape optimization","score":0.5442694425582886},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5278881788253784},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5017104148864746},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4929158687591553},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.46775221824645996},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4584912359714508},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4008602201938629},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3972422182559967},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3478163480758667},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1750040054321289},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13499605655670166},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12750810384750366},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.11133918166160583}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8111890554428101},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.737972617149353},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6266923546791077},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.5724128484725952},{"id":"https://openalex.org/C32758168","wikidata":"https://www.wikidata.org/wiki/Q900488","display_name":"Normal mode","level":3,"score":0.5675839185714722},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.5442694425582886},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5278881788253784},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5017104148864746},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4929158687591553},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.46775221824645996},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4584912359714508},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4008602201938629},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3972422182559967},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3478163480758667},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1750040054321289},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13499605655670166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12750810384750366},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.11133918166160583},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110860380","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110860380","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5299999713897705}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1499071767","https://openalex.org/W1499165040","https://openalex.org/W1510221418","https://openalex.org/W1514699173","https://openalex.org/W1578221370","https://openalex.org/W1608492828","https://openalex.org/W1680579736","https://openalex.org/W1970136394","https://openalex.org/W1981156623","https://openalex.org/W1984477344","https://openalex.org/W1991897805","https://openalex.org/W1992570613","https://openalex.org/W1998006824","https://openalex.org/W2000523938","https://openalex.org/W2001030631","https://openalex.org/W2006920249","https://openalex.org/W2012123976","https://openalex.org/W2015557869","https://openalex.org/W2021974250","https://openalex.org/W2028078738","https://openalex.org/W2031688153","https://openalex.org/W2032144610","https://openalex.org/W2046224300","https://openalex.org/W2047734849","https://openalex.org/W2050210602","https://openalex.org/W2052222585","https://openalex.org/W2061953601","https://openalex.org/W2074576683","https://openalex.org/W2082914631","https://openalex.org/W2092234892","https://openalex.org/W2106226212","https://openalex.org/W2111470998","https://openalex.org/W2120497877","https://openalex.org/W2124253405","https://openalex.org/W2126022791","https://openalex.org/W2145948434","https://openalex.org/W2165369994","https://openalex.org/W2468662436","https://openalex.org/W2592983627","https://openalex.org/W2963848200","https://openalex.org/W3145733612","https://openalex.org/W4254817357"],"related_works":["https://openalex.org/W2349952486","https://openalex.org/W1489260687","https://openalex.org/W2775700832","https://openalex.org/W3204670144","https://openalex.org/W2163101548","https://openalex.org/W1988934358","https://openalex.org/W2587222766","https://openalex.org/W4389574038","https://openalex.org/W4387718369","https://openalex.org/W2046055439"],"abstract_inverted_index":{"In":[0],"this":[1],"work":[2],"we":[3,77,90],"address":[4,79],"the":[5,8,43,46,50,59,68,75,86,92],"application":[6],"of":[7,10,37,45,71,103],"method":[9],"fundamental":[11],"solution":[12],"(MFS)":[13],"as":[14],"a":[15,35,99,115,122],"forward":[16],"solver":[17],"in":[18,23,67,82],"some":[19,112],"shape":[20,44,72,83],"optimization":[21],"problems":[22],"two-":[24],"and":[25],"three-dimensional":[26],"domains.":[27],"It":[28],"is":[29,53],"well":[30,55],"known":[31],"(Kac's":[32],"problem)":[33],"that":[34,97,106,110,120],"set":[36,102],"eigenvalues":[38],"does":[39],"not":[40,54],"determine":[41],"uniquely":[42],"domain.":[47],"Moreover,":[48],"even":[49],"existence":[51],"problem":[52,70],"defined":[56],"due":[57],"to":[58,94],"Ashbaugh--Benguria":[60],"inequality.":[61],"Although":[62],"these":[63],"results":[64],"constitute":[65],"counterexamples":[66],"general":[69],"determination":[73,84],"from":[74],"eigenfrequencies,":[76],"can":[78],"simpler":[80],"questions":[81],"using":[85],"MFS.":[87],"For":[88],"instance,":[89],"apply":[91],"MFS":[93],"build":[95],"domains":[96],"include":[98],"specific":[100],"finite":[101],"eigenvalues,":[104],"or":[105],"have":[107],"an":[108,118],"eigenmode":[109,119],"verifies":[111],"prescribed":[113],"conditions---as":[114],"particular":[116],"case,":[117],"defines":[121],"certain":[123],"nodal":[124],"line.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}