{"id":"https://openalex.org/W3170202143","doi":"https://doi.org/10.1007/978-3-030-77980-1_14","title":"A Three-Level Linearized Time Integration Scheme for Tumor Simulations with Cahn-Hilliard Equations","display_name":"A Three-Level Linearized Time Integration Scheme for Tumor Simulations with Cahn-Hilliard Equations","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3170202143","doi":"https://doi.org/10.1007/978-3-030-77980-1_14","mag":"3170202143"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-77980-1_14","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-77980-1_14","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5027877891","display_name":"Maciej Sm\u00f3\u0142ka","orcid":"https://orcid.org/0000-0002-3386-0555"},"institutions":[{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Maciej Smo\u0142ka","raw_affiliation_strings":["Institute of Computer Science, AGH University of Science and Technology, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-3386-0555","affiliations":[{"raw_affiliation_string":"Institute of Computer Science, AGH University of Science and Technology, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I4210087266","https://openalex.org/I686019"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011728048","display_name":"Maciej Wo\u017aniak","orcid":"https://orcid.org/0000-0002-5576-5671"},"institutions":[{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Maciej Wo\u017aniak","raw_affiliation_strings":["Institute of Computer Science, AGH University of Science and Technology, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-5576-5671","affiliations":[{"raw_affiliation_string":"Institute of Computer Science, AGH University of Science and Technology, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I4210087266","https://openalex.org/I686019"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047093707","display_name":"Robert Schaefer","orcid":"https://orcid.org/0000-0002-1669-2086"},"institutions":[{"id":"https://openalex.org/I4210087266","display_name":"Institute of Computer Science","ror":"https://ror.org/003fvp964","country_code":"PL","type":"facility","lineage":["https://openalex.org/I4210087266","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I686019","display_name":"AGH University of Krakow","ror":"https://ror.org/00bas1c41","country_code":"PL","type":"education","lineage":["https://openalex.org/I686019"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Robert Schaefer","raw_affiliation_strings":["Institute of Computer Science, AGH University of Science and Technology, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-1669-2086","affiliations":[{"raw_affiliation_string":"Institute of Computer Science, AGH University of Science and Technology, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I4210087266","https://openalex.org/I686019"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"173","last_page":"185"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9987000226974487,"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":0.9980999827384949,"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/cahn\u2013hilliard-equation","display_name":"Cahn\u2013Hilliard equation","score":0.8081503510475159},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7465190291404724},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.6205093264579773},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5651559829711914},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5548268556594849},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5106409192085266},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.49511995911598206},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.49039268493652344},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4402908682823181},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34831473231315613},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3296529948711395},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.20110777020454407},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1352802813053131}],"concepts":[{"id":"https://openalex.org/C24822716","wikidata":"https://www.wikidata.org/wiki/Q5017440","display_name":"Cahn\u2013Hilliard equation","level":3,"score":0.8081503510475159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7465190291404724},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6205093264579773},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5651559829711914},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5548268556594849},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5106409192085266},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49511995911598206},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.49039268493652344},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4402908682823181},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34831473231315613},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3296529948711395},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.20110777020454407},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1352802813053131},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-77980-1_14","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-77980-1_14","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W642107583","https://openalex.org/W1525717382","https://openalex.org/W1569090332","https://openalex.org/W1970009422","https://openalex.org/W1973166496","https://openalex.org/W1986775347","https://openalex.org/W1989512090","https://openalex.org/W2008209583","https://openalex.org/W2013424510","https://openalex.org/W2070299075","https://openalex.org/W2070571481","https://openalex.org/W2119682008","https://openalex.org/W2152275551","https://openalex.org/W2172014636","https://openalex.org/W2473882128","https://openalex.org/W2484659885","https://openalex.org/W2622825241","https://openalex.org/W2888888500","https://openalex.org/W2972859406","https://openalex.org/W2998678370","https://openalex.org/W4237713727","https://openalex.org/W4239704419"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W4301247218","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4298023222","https://openalex.org/W62102365"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
