{"id":"https://openalex.org/W7162582576","doi":"https://doi.org/10.48550/arxiv.2605.26623","title":"An Unconditionally Linearly Convergent ADMM Approach for the Allen-Cahn Equation with Flory-Huggins Potential","display_name":"An Unconditionally Linearly Convergent ADMM Approach for the Allen-Cahn Equation with Flory-Huggins Potential","publication_year":2026,"publication_date":"2026-05-26","ids":{"openalex":"https://openalex.org/W7162582576","doi":"https://doi.org/10.48550/arxiv.2605.26623"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.26623","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26623","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.26623","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137119326","display_name":"Peng Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Peng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104301276","display_name":"Shengtong Liang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liang, Shengtong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032760958","display_name":"Tiao Lu","orcid":"https://orcid.org/0000-0003-3404-9331"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Tiao","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":null,"has_fulltext":false,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9848999977111816,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11471","display_name":"Block Copolymer Self-Assembly","score":0.008100000210106373,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.671500027179718},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6341000199317932},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5892999768257141},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5257999897003174},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.46380001306533813},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.45809999108314514},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.3978999853134155},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.38519999384880066}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.671500027179718},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6341000199317932},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5892999768257141},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5803999900817871},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5570999979972839},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5257999897003174},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.46380001306533813},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.45809999108314514},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.3978999853134155},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.38519999384880066},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3813999891281128},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C89397928","wikidata":"https://www.wikidata.org/wiki/Q1630320","display_name":"Unconditional convergence","level":5,"score":0.33169999718666077},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.328900009393692},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30140000581741333},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2777999937534332},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.2736999988555908},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.259799987077713}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.26623","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26623","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.26623","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.26623","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.6178721785545349,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,33,123],"Allen-Cahn":[1,38],"equation":[2,39,146],"with":[3],"Flory-Huggins":[4,63],"potential":[5],"is":[6,40,107],"a":[7,24,89,158,172],"fundamental":[8],"and":[9,53,77,131,215],"crucial":[10],"model":[11],"in":[12,27,61,211],"phase":[13,18],"field":[14],"simulation":[15,35,86],"for":[16,110,143,179],"describing":[17],"separation":[19,194],"phenomena,":[20],"which":[21,82],"serves":[22],"as":[23,128],"core":[25],"tool":[26],"diverse":[28],"branches":[29],"of":[30,36,41,56,119,160,175],"natural":[31],"sciences.":[32],"numerical":[34,85,197],"the":[37,50,54,62,84,115,137,144,164,176,180,187],"great":[42],"importance":[43],"but":[44],"poses":[45],"significant":[46],"challenges":[47],"due":[48],"to":[49,73,87],"strong":[51],"nonlinearity":[52],"presence":[55],"logarithmic":[57],"singularities":[58],"at":[59,97],"$u=0,1$":[60],"potential.":[64],"In":[65],"this":[66,75],"paper,":[67],"we":[68],"consider":[69],"convex":[70],"splitting":[71],"schemes":[72],"%preserve":[74],"bound":[76,129],"guarantee":[78],"unconditional":[79,161],"unique":[80],"solvability,":[81],"reduces":[83],"solving":[88],"singular":[90],"nonlinear":[91],"system":[92],"arising":[93],"from":[94,189],"spatial":[95],"discretization":[96],"each":[98],"time":[99],"step.":[100],"We":[101],"propose":[102],"an":[103],"iterative":[104],"solver":[105,188],"that":[106],"specifically":[108],"designed":[109],"such":[111,127],"systems":[112],"based":[113],"on":[114],"alternating":[116],"direction":[117],"method":[118],"multipliers":[120],"(ADMM)":[121],"approach.":[122],"scheme":[124],"possesses":[125],"properties":[126],"preserving":[130],"discrete":[132],"energy":[133],"stability.":[134],"Building":[135],"upon":[136],"recent":[138],"unconditionally":[139],"convergent":[140],"ADMM":[141,182,202],"framework":[142],"Cahn-Hilliard":[145],"(Li":[147],"et":[148],"al.,":[149],"2026),":[150],"our":[151,200],"key":[152],"theoretical":[153,206],"contributions":[154],"are":[155,208],"twofold:":[156],"(a)":[157],"proof":[159],"convergence":[162,178],"when":[163],"multiplier":[165],"update":[166],"step":[167],"size":[168],"$\u03b1\\in":[169],"(0,\\frac{\\sqrt{5}+1}{2})$;":[170],"(b)":[171],"rigorous":[173],"establishment":[174],"linear":[177],"embedded":[181],"solver.":[183],"This":[184],"effectively":[185],"liberates":[186],"time-step":[190],"constraints":[191],"or":[192],"strict":[193],"conditions.":[195],"Comprehensive":[196],"experiments":[198],"validate":[199],"proposed":[201],"framework,":[203],"where":[204],"its":[205],"predictions":[207],"fully":[209],"substantiated":[210],"practice,":[212],"showcasing":[213],"efficiency":[214],"robustness.":[216]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-28T00:00:00"}
