{"id":"https://openalex.org/W1550050946","doi":"https://doi.org/10.1007/978-3-540-70942-8_9","title":"Multigrid\u2013Based Optimal Shape and Topology Design in Magnetostatics","display_name":"Multigrid\u2013Based Optimal Shape and Topology Design in Magnetostatics","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1550050946","doi":"https://doi.org/10.1007/978-3-540-70942-8_9","mag":"1550050946"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-70942-8_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-70942-8_9","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":"book-chapter","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/A5014635086","display_name":"Dalibor Luk\u00e1\u0161","orcid":"https://orcid.org/0000-0002-5818-4362"},"institutions":[{"id":"https://openalex.org/I142208455","display_name":"VSB - Technical University of Ostrava","ror":"https://ror.org/05x8mcb75","country_code":"CZ","type":"education","lineage":["https://openalex.org/I142208455"]}],"countries":["CZ"],"is_corresponding":true,"raw_author_name":"Dalibor Luk\u00e1\u0161","raw_affiliation_strings":["Department of Applied Mathematics, V\u0160B\u2013Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava\u2013Poruba, Czech Republic","Department of Applied Mathematics, V\u0160B Technical University of Ostrava, Ostrava-Poruba, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, V\u0160B\u2013Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava\u2013Poruba, Czech Republic","institution_ids":["https://openalex.org/I142208455"]},{"raw_affiliation_string":"Department of Applied Mathematics, V\u0160B Technical University of Ostrava, Ostrava-Poruba, Czech Republic","institution_ids":["https://openalex.org/I142208455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014635086"],"corresponding_institution_ids":["https://openalex.org/I142208455"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09370702,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"82","last_page":"90"},"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9980000257492065,"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/multigrid-method","display_name":"Multigrid method","score":0.8078278303146362},{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.7288902401924133},{"id":"https://openalex.org/keywords/shape-optimization","display_name":"Shape optimization","score":0.6560804843902588},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.6356671452522278},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6167266368865967},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5512406229972839},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.5428114533424377},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5289962887763977},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.48596513271331787},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.4680582880973816},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38485321402549744},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.3467877507209778},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27526307106018066},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.26035863161087036},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.25573140382766724},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22887155413627625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13938015699386597},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08759462833404541},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.07952779531478882}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8078278303146362},{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.7288902401924133},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.6560804843902588},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.6356671452522278},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6167266368865967},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5512406229972839},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.5428114533424377},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5289962887763977},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.48596513271331787},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.4680582880973816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38485321402549744},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.3467877507209778},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27526307106018066},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.26035863161087036},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.25573140382766724},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22887155413627625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13938015699386597},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08759462833404541},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.07952779531478882},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-540-70942-8_9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-70942-8_9","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1966781202","https://openalex.org/W1966886095","https://openalex.org/W2004291775","https://openalex.org/W2004943774","https://openalex.org/W2038253697","https://openalex.org/W2084078689","https://openalex.org/W2123443336","https://openalex.org/W2127981460","https://openalex.org/W4230055019"],"related_works":["https://openalex.org/W4389317411","https://openalex.org/W2336762304","https://openalex.org/W1492522302","https://openalex.org/W2120298265","https://openalex.org/W2096454229","https://openalex.org/W2042199958","https://openalex.org/W2103149966","https://openalex.org/W2039312875","https://openalex.org/W2177482563","https://openalex.org/W2016008514"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}