{"id":"https://openalex.org/W2898360446","doi":"https://doi.org/10.1007/s10915-018-0859-7","title":"Numerical Simulation and Error Estimation of the Time-Dependent Allen\u2013Cahn Equation on Surfaces with Radial Basis Functions","display_name":"Numerical Simulation and Error Estimation of the Time-Dependent Allen\u2013Cahn Equation on Surfaces with Radial Basis Functions","publication_year":2018,"publication_date":"2018-10-26","ids":{"openalex":"https://openalex.org/W2898360446","doi":"https://doi.org/10.1007/s10915-018-0859-7","mag":"2898360446"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-018-0859-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0859-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of 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/A5090517671","display_name":"V. Mohammadi","orcid":"https://orcid.org/0000-0002-2457-3167"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Vahid Mohammadi","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran","institution_ids":["https://openalex.org/I158248296"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061434040","display_name":"Davoud Mirzaei","orcid":"https://orcid.org/0000-0002-0166-4760"},"institutions":[{"id":"https://openalex.org/I39268498","display_name":"University of Isfahan","ror":"https://ror.org/05h9t7759","country_code":"IR","type":"education","lineage":["https://openalex.org/I39268498"]},{"id":"https://openalex.org/I4210146419","display_name":"Institute for Research in Fundamental Sciences","ror":"https://ror.org/04xreqs31","country_code":"IR","type":"facility","lineage":["https://openalex.org/I4210146419"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Davoud Mirzaei","raw_affiliation_strings":["Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran","School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran","institution_ids":["https://openalex.org/I39268498"]},{"raw_affiliation_string":"School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, 19395-5746, Iran","institution_ids":["https://openalex.org/I4210146419"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044309986","display_name":"Mehdi Dehghan","orcid":"https://orcid.org/0000-0002-2573-9755"},"institutions":[{"id":"https://openalex.org/I158248296","display_name":"Amirkabir University of Technology","ror":"https://ror.org/04gzbav43","country_code":"IR","type":"education","lineage":["https://openalex.org/I158248296"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mehdi Dehghan","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran, 15914, Iran","institution_ids":["https://openalex.org/I158248296"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044309986"],"corresponding_institution_ids":["https://openalex.org/I158248296"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":1.226,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.77959156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"79","issue":"1","first_page":"493","last_page":"516"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9991999864578247,"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":0.9991999864578247,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9958000183105469,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9940000176429749,"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":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8043073415756226},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.688491702079773},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6207529306411743},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.6002222299575806},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5774008631706238},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.5410922169685364},{"id":"https://openalex.org/keywords/allen\u2013cahn-equation","display_name":"Allen\u2013Cahn equation","score":0.5410261750221252},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.524610161781311},{"id":"https://openalex.org/keywords/torus","display_name":"Torus","score":0.5035714507102966},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.49703696370124817},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.43134722113609314},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4276866316795349},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41183534264564514},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.34781333804130554}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8043073415756226},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.688491702079773},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6207529306411743},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.6002222299575806},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5774008631706238},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.5410922169685364},{"id":"https://openalex.org/C2777166216","wikidata":"https://www.wikidata.org/wiki/Q4732089","display_name":"Allen\u2013Cahn equation","level":2,"score":0.5410261750221252},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.524610161781311},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.5035714507102966},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.49703696370124817},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.43134722113609314},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4276866316795349},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41183534264564514},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34781333804130554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-018-0859-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-018-0859-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of 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":51,"referenced_works":["https://openalex.org/W19451620","https://openalex.org/W50490584","https://openalex.org/W971523040","https://openalex.org/W1486164486","https://openalex.org/W1525717382","https://openalex.org/W1580929281","https://openalex.org/W1846478001","https://openalex.org/W1973878509","https://openalex.org/W1988473367","https://openalex.org/W1995274909","https://openalex.org/W2009262561","https://openalex.org/W2011290221","https://openalex.org/W2012220122","https://openalex.org/W2017142556","https://openalex.org/W2025043986","https://openalex.org/W2040314635","https://openalex.org/W2041001120","https://openalex.org/W2041099140","https://openalex.org/W2042396553","https://openalex.org/W2043546299","https://openalex.org/W2052177822","https://openalex.org/W2059176502","https://openalex.org/W2062360755","https://openalex.org/W2066036475","https://openalex.org/W2069452363","https://openalex.org/W2069887143","https://openalex.org/W2070330278","https://openalex.org/W2071121523","https://openalex.org/W2076699062","https://openalex.org/W2076776678","https://openalex.org/W2090739984","https://openalex.org/W2094108357","https://openalex.org/W2097973750","https://openalex.org/W2102596289","https://openalex.org/W2108707014","https://openalex.org/W2111231572","https://openalex.org/W2113751265","https://openalex.org/W2126858039","https://openalex.org/W2126928268","https://openalex.org/W2139101145","https://openalex.org/W2166050051","https://openalex.org/W2167410947","https://openalex.org/W2342769790","https://openalex.org/W2481312347","https://openalex.org/W2571181132","https://openalex.org/W2611363983","https://openalex.org/W2614651524","https://openalex.org/W2756899824","https://openalex.org/W2784974683","https://openalex.org/W2964094877","https://openalex.org/W3200227310"],"related_works":["https://openalex.org/W2787174914","https://openalex.org/W4302407027","https://openalex.org/W4299978068","https://openalex.org/W2164189677","https://openalex.org/W2964308048","https://openalex.org/W4388722486","https://openalex.org/W2950745223","https://openalex.org/W1727769347","https://openalex.org/W2441614350","https://openalex.org/W603561220"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":3}],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2025-10-10T00:00:00"}
