{"id":"https://openalex.org/W7214909579","doi":"https://doi.org/10.48550/arxiv.2609.36487","title":"TT-FDTD: Tensor Train Accelerated Three-Dimensional FDTD With Logarithmic Cost of Spatial Operators","display_name":"TT-FDTD: Tensor Train Accelerated Three-Dimensional FDTD With Logarithmic Cost of Spatial Operators","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214909579","doi":"https://doi.org/10.48550/arxiv.2609.36487"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36487","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36487","pdf_url":"https://arxiv.org/pdf/2609.36487","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.36487","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104198786","display_name":"Chris Nguy\u1ec5n","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nguyen, Chris","raw_affiliation_strings":["Department of Electrical and Computer Engineering , University of Manitoba , Winnipeg , MB R3T 5V6 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , University of Manitoba , Winnipeg , MB R3T 5V6 , Canada","institution_ids":["https://openalex.org/I46247651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018042203","display_name":"Vladimir Okhmatovski","orcid":"https://orcid.org/0000-0002-1688-3691","observed_orcids":["https://orcid.org/0000-0002-1688-3691"]},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Okhmatovski, Vladimir","raw_affiliation_strings":["Department of Electrical and Computer Engineering , University of Manitoba , Winnipeg , MB R3T 5V6 , Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , University of Manitoba , Winnipeg , MB R3T 5V6 , Canada","institution_ids":["https://openalex.org/I46247651"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I46247651"],"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9883000254631042,"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":0.9883000254631042,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.006800000090152025,"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/T12303","display_name":"Tensor decomposition and applications","score":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tensor-train","display_name":"tensor train","score":0.5799999833106995},{"id":"https://openalex.org/keywords/three-dimensional-fdtd","display_name":"three-dimensional FDTD","score":0.7369999885559082},{"id":"https://openalex.org/keywords/yee-grid","display_name":"Yee grid","score":0.7599999904632568},{"id":"https://openalex.org/keywords/gaussian-regularization","display_name":"Gaussian regularization","score":0.5559999942779541},{"id":"https://openalex.org/keywords/head-model","display_name":"human head model","score":0.7160000205039978},{"id":"https://openalex.org/keywords/dielectric-sphere","display_name":"dielectric sphere","score":0.8479999899864197},{"id":"https://openalex.org/keywords/tensor-contraction","display_name":"tensor contraction","score":0.45399999618530273}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8621000051498413},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6913999915122986},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5837000012397766},{"id":"https://openalex.org/C184880428","wikidata":"https://www.wikidata.org/wiki/Q1417308","display_name":"Finite-difference time-domain method","level":2,"score":0.5827999711036682},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5705999732017517},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5701000094413757},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5311999917030334},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.47530001401901245},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4262999892234802},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.424699991941452},{"id":"https://openalex.org/C133386390","wikidata":"https://www.wikidata.org/wiki/Q184996","display_name":"Dielectric","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.40230000019073486},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3749000132083893},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.34599998593330383},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.31049999594688416},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2849000096321106},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C41700454","wikidata":"https://www.wikidata.org/wiki/Q1852282","display_name":"Reflection coefficient","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.25690001249313354},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36487","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36487","pdf_url":"https://arxiv.org/pdf/2609.36487","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.36487","doi":"https://doi.org/10.48550/arxiv.2609.36487","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36487","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36487","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36487","pdf_url":"https://arxiv.org/pdf/2609.36487","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,"listed_in":[],"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214909579.pdf","grobid_xml":"https://content.openalex.org/works/W7214909579.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1963973528","https://openalex.org/W1993482030","https://openalex.org/W1995406764","https://openalex.org/W2013029478","https://openalex.org/W2024165284","https://openalex.org/W2807720599","https://openalex.org/W4360955172","https://openalex.org/W4387374077","https://openalex.org/W4408946467","https://openalex.org/W7134981490"],"related_works":["https://openalex.org/W7213563753","https://openalex.org/W4408946467","https://openalex.org/W7223411307","https://openalex.org/W4411950391","https://openalex.org/W7168403982","https://openalex.org/W7162218374","https://openalex.org/W7151374057","https://openalex.org/W2082052425","https://openalex.org/W4225938260","https://openalex.org/W7214252978"],"abstract_inverted_index":{"Quantized":[0],"tensor-train":[1],"(QTT)":[2],"compression":[3],"is":[4,44,60],"incorporated":[5],"into":[6],"a":[7,69],"full-vector":[8],"three-dimensional":[9,148],"scattered-field":[10],"finite-difference":[11,30],"time-domain":[12],"(FDTD)":[13],"formulation":[14,59],"on":[15,73,106],"uniform":[16],"Yee":[17],"grids.":[18],"All":[19],"six":[20],"electromagnetic-field":[21],"components,":[22],"material-dependent":[23],"update":[24],"coefficients,":[25],"equivalent-current":[26],"sources,":[27],"and":[28,55,68,92,131,143],"staggered":[29],"operators":[31],"are":[32],"represented":[33],"in":[34,111],"compatible":[35],"QTT":[36],"form.":[37],"Gaussian":[38],"regularization":[39],"of":[40,109,146],"voxelized":[41],"material":[42],"interfaces":[43],"used":[45],"to":[46,77],"reduce":[47],"the":[48,94,98,107,112,119,141],"coefficient":[49],"ranks":[50,91],"generated":[51],"by":[52],"abrupt":[53],"dielectric":[54,71],"conductivity":[56],"transitions.":[57],"The":[58,81],"evaluated":[61],"for":[62,150],"an":[63],"anatomically":[64],"heterogeneous":[65],"human-head":[66],"model":[67],"homogeneous":[70],"sphere":[72],"grids":[74],"containing":[75],"up":[76],"$512^3$":[78],"spatial":[79],"cells.":[80],"reported":[82],"results":[83,139],"show":[84],"that":[85,93],"interface":[86],"smoothing":[87],"substantially":[88],"reduces":[89,123],"material-coefficient":[90],"TT--FDTD":[95],"solution":[96],"reproduces":[97],"full-grid":[99],"transient":[100],"fields":[101],"with":[102,116],"pointwise":[103],"absolute":[104],"errors":[105],"order":[108],"$10^{-4}$":[110],"examined":[113],"slices.":[114],"Compared":[115],"conventional":[117],"FDTD,":[118],"tensor":[120,129],"representation":[121],"greatly":[122],"storage":[124],"at":[125],"fine":[126],"discretizations,":[127],"although":[128],"contractions":[130],"recompression":[132],"introduce":[133],"additional":[134],"per-step":[135],"computational":[136],"cost.":[137],"These":[138],"demonstrate":[140],"feasibility":[142],"memory--time":[144],"tradeoff":[145],"QTT-accelerated":[147],"FDTD":[149],"large":[151],"structured-grid":[152],"simulations.":[153]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
