{"id":"https://openalex.org/W1899086482","doi":"https://doi.org/10.1137/140999323","title":"A Space-Time Discontinuous Galerkin Trefftz Method for Time Dependent Maxwell's Equations","display_name":"A Space-Time Discontinuous Galerkin Trefftz Method for Time Dependent Maxwell's Equations","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1899086482","doi":"https://doi.org/10.1137/140999323","mag":"1899086482"},"language":"en","primary_location":{"id":"doi:10.1137/140999323","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140999323","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/A5069912765","display_name":"Herbert Egger","orcid":"https://orcid.org/0000-0003-3769-8791"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Herbert Egger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085357800","display_name":"Fritz Kretzschmar","orcid":"https://orcid.org/0000-0001-9415-0330"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fritz Kretzschmar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035666788","display_name":"Sascha Schnepp","orcid":"https://orcid.org/0000-0002-5352-4911"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sascha M. Schnepp","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003067454","display_name":"Thomas Weiland","orcid":"https://orcid.org/0000-0002-5501-1220"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Weiland","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2092,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.88688856,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"37","issue":"5","first_page":"B689","last_page":"B711"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9997000098228455,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9988999962806702,"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":0.8434406518936157},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7132102251052856},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.7089592814445496},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6526918411254883},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.5322123765945435},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5153307318687439},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49073708057403564},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48953256011009216},{"id":"https://openalex.org/keywords/degree-of-a-polynomial","display_name":"Degree of a polynomial","score":0.4823867380619049},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.4716491103172302},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.44944998621940613},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4392697513103485},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4110379219055176},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08666932582855225}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8434406518936157},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7132102251052856},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.7089592814445496},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6526918411254883},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5322123765945435},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5153307318687439},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49073708057403564},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48953256011009216},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.4823867380619049},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.4716491103172302},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.44944998621940613},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4392697513103485},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4110379219055176},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08666932582855225},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140999323","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140999323","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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7400000095367432}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1834059481","https://openalex.org/W2002985909","https://openalex.org/W2010605025","https://openalex.org/W2017607754","https://openalex.org/W2028199013","https://openalex.org/W2043140788","https://openalex.org/W2047555787","https://openalex.org/W2067527388","https://openalex.org/W2072522548","https://openalex.org/W2075828491","https://openalex.org/W2077458918","https://openalex.org/W2083855576","https://openalex.org/W2087110602","https://openalex.org/W2087592144","https://openalex.org/W2097794974","https://openalex.org/W2113022278","https://openalex.org/W2114019248","https://openalex.org/W2114085803","https://openalex.org/W2115449366","https://openalex.org/W2116225395","https://openalex.org/W2142063750","https://openalex.org/W2144778114","https://openalex.org/W2145800927","https://openalex.org/W2146479689","https://openalex.org/W2167486655"],"related_works":["https://openalex.org/W2167521757","https://openalex.org/W1528754490","https://openalex.org/W69679081","https://openalex.org/W2162026849","https://openalex.org/W154187677","https://openalex.org/W2394687667","https://openalex.org/W2013813162","https://openalex.org/W2885311694","https://openalex.org/W4289702954","https://openalex.org/W2106524561"],"abstract_inverted_index":{"We":[0,97],"consider":[1,80],"the":[2,41,46,71,84,94,106,126,132,135,150,153,166,180,189,196,203],"discretization":[3],"of":[4,53,86,102,118,125,134,165,168,191,193,202],"electromagnetic":[5],"wave":[6],"propagation":[7],"problems":[8],"by":[9],"a":[10,55,103,185],"discontinuous":[11,27,137,169],"Galerkin":[12,28,138,170],"method":[13,19,52,157,204],"based":[14,172],"on":[15,74,93,173],"Trefftz":[16,81,108,127,139],"polynomials.":[17],"This":[18],"fits":[20],"into":[21],"an":[22,60,99],"abstract":[23,154],"framework":[24],"for":[25,30,105,198],"space-time":[26,76],"methods":[29,171],"which":[31],"we":[32,78,129],"can":[33,130],"prove":[34],"consistency,":[35],"stability,":[36,142],"and":[37,112,115,143,195,205],"energy":[38,144],"dissipation":[39,145],"without":[40],"need":[42],"to":[43],"completely":[44],"specify":[45],"approximation":[47,73,176],"spaces":[48,109],"in":[49,59,110,159,188,211],"detail.":[50],"Any":[51],"such":[54],"general":[56],"form":[57],"results":[58,151],"implicit":[61],"time":[62,182],"stepping":[63],"scheme":[64],"with":[65],"some":[66,117],"basic":[67,120],"stability":[68],"properties.":[69,121],"For":[70],"local":[72,107,123],"every":[75],"element,":[77],"then":[79,146],"polynomials,":[82,128],"i.e.,":[83],"subspace":[85],"polynomials":[87],"that":[88],"satisfy":[89],"Maxwell's":[90],"equations":[91],"exactly":[92],"respective":[95],"element.":[96],"present":[98],"explicit":[100],"construction":[101],"basis":[104],"two":[111],"three":[113],"dimensions":[114],"summarize":[116],"their":[119],"Using":[122],"properties":[124],"establish":[131],"well-posedness":[133],"resulting":[136],"method.":[140],"Consistency,":[141],"follow":[147],"immediately":[148],"from":[149],"about":[152],"framework.":[155],"The":[156,200],"proposed":[158],"this":[160],"paper":[161],"therefore":[162],"shares":[163],"many":[164],"advantages":[167],"full":[174],"polynomial":[175],"spaces,":[177],"while":[178],"at":[179],"same":[181],"it":[183],"yields":[184],"substantial":[186],"reduction":[187],"number":[190],"degrees":[192],"freedom":[194],"cost":[197],"assembling.":[199],"viability":[201],"its":[206],"spectral":[207],"convergence":[208],"are":[209],"demonstrated":[210],"numerical":[212],"tests.":[213]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
