{"id":"https://openalex.org/W2088179604","doi":"https://doi.org/10.1137/09075946x","title":"A New Level Set Method for Motion in Normal Direction Based on a Semi-Implicit Forward-Backward Diffusion Approach","display_name":"A New Level Set Method for Motion in Normal Direction Based on a Semi-Implicit Forward-Backward Diffusion Approach","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2088179604","doi":"https://doi.org/10.1137/09075946x","mag":"2088179604"},"language":"en","primary_location":{"id":"doi:10.1137/09075946x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09075946x","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/A5012615158","display_name":"Karol Mikula","orcid":"https://orcid.org/0000-0002-5360-8779"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Karol Mikula","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039193717","display_name":"Mario Ohlberger","orcid":"https://orcid.org/0000-0002-6260-3574"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mario Ohlberger","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6702,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.73157475,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","issue":"3","first_page":"1527","last_page":"1544"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9977999925613403,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.996399998664856,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7562084794044495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7366361618041992},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.6461482048034668},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5780755877494812},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5647811889648438},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4801082909107208},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4749588966369629},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.44117966294288635},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.4341958463191986},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4279100298881531},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42358285188674927},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.40727102756500244},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15382370352745056}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7562084794044495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7366361618041992},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.6461482048034668},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5780755877494812},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5647811889648438},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4801082909107208},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4749588966369629},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.44117966294288635},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.4341958463191986},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4279100298881531},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42358285188674927},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40727102756500244},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15382370352745056},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/09075946x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09075946x","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1238092070","https://openalex.org/W1549748890","https://openalex.org/W1974509213","https://openalex.org/W1979810525","https://openalex.org/W1991113069","https://openalex.org/W1994214710","https://openalex.org/W2001241964","https://openalex.org/W2008777025","https://openalex.org/W2022444670","https://openalex.org/W2043034481","https://openalex.org/W2093834886","https://openalex.org/W2106141466","https://openalex.org/W2169859810","https://openalex.org/W2998023265"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W2231544277","https://openalex.org/W4388482258","https://openalex.org/W2337838060","https://openalex.org/W2011648757","https://openalex.org/W2803286947"],"abstract_inverted_index":{"We":[0,37],"introduce":[1],"a":[2,16,22,39,69],"new":[3],"level":[4],"set":[5],"method":[6,88],"for":[7,99],"motion":[8],"in":[9,18,53],"normal":[10],"direction.":[11],"It":[12],"is":[13,30,62,75,89,95,120],"based":[14],"on":[15,91,129],"formulation":[17],"the":[19,33,46,51,58,73,125],"form":[20],"of":[21,50,72,108],"second":[23,96],"order":[24,97],"forward-backward":[25],"diffusion":[26,48,60,67,85],"equation.":[27],"The":[28,87],"equation":[29],"discretized":[31],"by":[32],"finite":[34],"volume":[35],"method.":[36],"propose":[38],"semi-implicit":[40],"time":[41,109],"discretization":[42],"taking":[43],"into":[44],"account":[45],"forward":[47,66],"part":[49,61],"solution":[52,74],"an":[54,105],"implicit":[55],"way,":[56],"while":[57,77],"backward":[59,84],"treated":[63],"explicitly.":[64],"When":[65],"dominates,":[68],"straightforward":[70],"reconstruction":[71],"used,":[76],"larger":[78],"(smoothing)":[79],"stencils":[80],"are":[81,127],"used":[82],"when":[83],"dominates.":[86],"precise":[90],"coarse":[92],"grids":[93],"and":[94,110,115],"accurate":[98],"smooth":[100],"solutions.":[101],"Numerical":[102,122],"experiments":[103],"show":[104],"optimal":[106],"coupling":[107],"space":[111],"steps":[112],"with":[113,124],"$\\tau=h$,":[114],"no":[116],"stronger":[117],"CFL":[118],"condition":[119],"required.":[121],"tests":[123],"scheme":[126],"discussed":[128],"representative":[130],"examples.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
