{"id":"https://openalex.org/W2061500928","doi":"https://doi.org/10.1137/090757502","title":"A Gauge Invariant Discretization on Simplicial Grids of the Schr\u00f6dinger Eigenvalue Problem in an Electromagnetic Field","display_name":"A Gauge Invariant Discretization on Simplicial Grids of the Schr\u00f6dinger Eigenvalue Problem in an Electromagnetic Field","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2061500928","doi":"https://doi.org/10.1137/090757502","mag":"2061500928"},"language":"en","primary_location":{"id":"doi:10.1137/090757502","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090757502","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10852/10462","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006596455","display_name":"Snorre H. Christiansen","orcid":"https://orcid.org/0000-0001-7618-9514"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Snorre H. Christiansen","raw_affiliation_strings":["snorrec@math.uio.no and toregha@gmail.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"snorrec@math.uio.no and toregha@gmail.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021363105","display_name":"Tore Gunnar Halvorsen","orcid":null},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Tore G. Halvorsen","raw_affiliation_strings":["University of Oslo#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oslo#TAB#","institution_ids":["https://openalex.org/I184942183"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7617,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84318794,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"49","issue":"1","first_page":"331","last_page":"345"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994999766349792,"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/mathematics","display_name":"Mathematics","score":0.7828152179718018},{"id":"https://openalex.org/keywords/electromagnetic-field","display_name":"Electromagnetic field","score":0.6276920437812805},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6015338897705078},{"id":"https://openalex.org/keywords/polygon-mesh","display_name":"Polygon mesh","score":0.5026326179504395},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.48589009046554565},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4847569167613983},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47293949127197266},{"id":"https://openalex.org/keywords/gauge-theory","display_name":"Gauge theory","score":0.43848860263824463},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4218595027923584},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3605028986930847},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.25863802433013916},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22569185495376587},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17705756425857544},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13863134384155273}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7828152179718018},{"id":"https://openalex.org/C28843909","wikidata":"https://www.wikidata.org/wiki/Q177625","display_name":"Electromagnetic field","level":2,"score":0.6276920437812805},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6015338897705078},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.5026326179504395},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.48589009046554565},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4847569167613983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47293949127197266},{"id":"https://openalex.org/C181830111","wikidata":"https://www.wikidata.org/wiki/Q214850","display_name":"Gauge theory","level":2,"score":0.43848860263824463},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4218595027923584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3605028986930847},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.25863802433013916},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22569185495376587},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17705756425857544},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13863134384155273}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090757502","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090757502","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:www.duo.uio.no:10852/10462","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/10462","pdf_url":null,"source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"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:www.duo.uio.no:10852/10462","is_oa":true,"landing_page_url":"http://hdl.handle.net/10852/10462","pdf_url":null,"source":{"id":"https://openalex.org/S4306401717","display_name":"Duo Research Archive (University of Oslo)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I184942183","host_organization_name":"University of Oslo","host_organization_lineage":["https://openalex.org/I184942183"],"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"},"sustainable_development_goals":[{"score":0.8199999928474426,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1492326914","https://openalex.org/W1522382323","https://openalex.org/W1582734821","https://openalex.org/W1969038938","https://openalex.org/W1975069663","https://openalex.org/W1978455689","https://openalex.org/W2003116365","https://openalex.org/W2005005412","https://openalex.org/W2017976561","https://openalex.org/W2034029678","https://openalex.org/W2037807380","https://openalex.org/W2062618977","https://openalex.org/W2066037896","https://openalex.org/W2077376884","https://openalex.org/W2138486270","https://openalex.org/W2172949211","https://openalex.org/W2475086119","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2166142625","https://openalex.org/W2376950174","https://openalex.org/W1999976185","https://openalex.org/W2143829464","https://openalex.org/W2791967325","https://openalex.org/W4299794286","https://openalex.org/W1978496658","https://openalex.org/W2965585506","https://openalex.org/W2556186148","https://openalex.org/W282462167"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2,13,72,91,107,118],"method":[3,28,60],"to":[4],"compute":[5],"approximate":[6],"eigenpairs":[7],"of":[8,19,43,58,66,98,101,112,126],"the":[9,17,27,39,44,54,59,64,77,83,95,99,102],"Schr\u00f6dinger":[10],"operator":[11],"on":[12],"bounded":[14],"domain":[15],"in":[16,53,63],"presence":[18],"an":[20],"electromagnetic":[21,93,122],"field.":[22],"Formulated":[23],"for":[24,48,90,106,117],"simplicial":[25],"meshes,":[26],"combines":[29],"techniques":[30],"from":[31],"lattice":[32],"gauge":[33,41],"theory":[34],"and":[35,81,116],"finite":[36,120],"elements,":[37],"retaining":[38],"discrete":[40,84],"invariance":[42],"former":[45],"but":[46],"allowing":[47],"noncongruent":[49],"space":[50],"elements":[51],"as":[52],"latter.":[55],"The":[56],"error":[57],"is":[61,97,111,125],"studied":[62],"framework":[65],"Strang's":[67],"variational":[68],"crimes,":[69],"comparing":[70],"with":[71],"standard":[73],"Galerkin":[74],"approach.":[75],"When":[76],"meshes":[78],"are":[79],"quasi-uniform":[80],"satisfy":[82],"maximum":[85],"principle,":[86],"we":[87],"prove":[88],"that":[89],"smooth":[92],"field":[94,123],"crime":[96],"order":[100,113,127],"mesh":[103],"width":[104],"h,":[105],"Coulomb":[108],"potential":[109],"it":[110,124],"$h|\\log":[114],"h|$,":[115],"general":[119],"energy":[121],"$h^{1/2}$.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
