{"id":"https://openalex.org/W4399399602","doi":"https://doi.org/10.48550/arxiv.2406.00878","title":"A New Parallel-in-time Direct Inverse Method for Nonlinear Differential\n Equations","display_name":"A New Parallel-in-time Direct Inverse Method for Nonlinear Differential\n Equations","publication_year":2024,"publication_date":"2024-06-02","ids":{"openalex":"https://openalex.org/W4399399602","doi":"https://doi.org/10.48550/arxiv.2406.00878"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2406.00878","pdf_url":"https://arxiv.org/pdf/2406.00878","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"type":"preprint","type_crossref":"posted-content","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2406.00878","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067996940","display_name":"Nail K. Yamaleev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yamaleev, Nail K.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5099038226","display_name":"Subhash Paudel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paudel, Subhash","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":77},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9955,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9955,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9924,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9877,"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":[],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.67962736},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6614122},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4284569},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42434537},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41622952},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2135056},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07851237},{"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":[{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2406.00878","pdf_url":"https://arxiv.org/pdf/2406.00878","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2406.00878","pdf_url":"https://arxiv.org/pdf/2406.00878","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3002753104","https://openalex.org/W2748952813","https://openalex.org/W2600246793","https://openalex.org/W2142036596","https://openalex.org/W2077600819","https://openalex.org/W2072657027","https://openalex.org/W2061531152","https://openalex.org/W2007980826","https://openalex.org/W1979597421"],"abstract_inverted_index":{"We":[0],"present":[1],"a":[2,115,121,153],"new":[3,197],"approach":[4],"to":[5,120,182,206],"parallelization":[6],"of":[7,14,41,63,76,123,139,156,158,162,172,184,204],"the":[8,15,24,39,45,50,64,81,87,96,140,159,163,169,185,196,202,213],"first-order":[9],"backward":[10],"difference":[11],"discretization":[12,143],"(BDF1)":[13],"time":[16,32,92,130,190],"derivative":[17,33],"in":[18,69,80,114,177],"partial":[19,216],"differential":[20,146,217],"equations,":[21],"such":[22],"as":[23],"nonlinear":[25,77,145,215],"heat":[26],"and":[27,52,66,222],"viscous":[28,53],"Burgers":[29],"equations.":[30,147],"The":[31,73,148],"term":[34],"is":[35,84,106,179],"discretized":[36],"by":[37,57,86],"using":[38],"method":[40,89,151,161],"lines":[42],"based":[43],"on":[44,208],"implicit":[46,141],"BDF1":[47,97,142,165,199],"scheme,":[48,166],"while":[49],"inviscid":[51],"terms":[54],"are":[55],"approximated":[56],"conventional":[58],"2nd-order":[59,67],"3-point":[60],"central":[61],"discretizations":[62],"1st-":[65],"derivatives":[68],"each":[70,103,129,174,189],"spatial":[71],"direction.":[72],"global":[74],"system":[75,101],"discrete":[78],"equations":[79,126,218],"space-time":[82],"domain":[83],"solved":[85],"Newton":[88,104,160],"for":[90,134,144,212],"all":[91],"levels":[93],"simultaneously.":[94],"For":[95],"discretization,":[98],"this":[99],"all-at-once":[100],"at":[102,188],"iteration":[105],"block":[107,175],"bidiagonal,":[108],"which":[109],"can":[110],"be":[111],"inverted":[112],"directly":[113],"blockwise":[116],"manner,":[117],"thus":[118],"leading":[119],"set":[122],"fully":[124],"decoupled":[125],"associated":[127],"with":[128,219],"level.":[131],"This":[132],"allows":[133],"an":[135],"efficient":[136],"parallel-in-time":[137,150,198],"implementation":[138],"proposed":[149],"preserves":[152],"quadratic":[154],"rate":[155],"convergence":[157],"sequential":[164,186],"so":[167],"that":[168,183,195],"computational":[170],"cost":[171],"solving":[173],"matrix":[176],"parallel":[178],"nearly":[180],"identical":[181],"counterpart":[187],"step.":[191],"Numerical":[192],"results":[193],"show":[194],"scheme":[200],"provides":[201],"speedup":[203],"up":[205],"28":[207],"32":[209],"computing":[210],"cores":[211],"2-D":[214],"both":[220],"smooth":[221],"discontinuous":[223],"solutions.":[224]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4399399602","counts_by_year":[],"updated_date":"2025-04-19T04:50:53.823705","created_date":"2024-06-07"}