Marta Benítez, Alfredo Bermúdez, Pedro Fontán, Iván Martínez, Pilar Salgado
{"title":"解决轴对称热电磁问题的拉格朗日方法。时变几何过程的应用","authors":"Marta Benítez, Alfredo Bermúdez, Pedro Fontán, Iván Martínez, Pilar Salgado","doi":"10.1007/s10444-024-10121-y","DOIUrl":null,"url":null,"abstract":"<div><p>The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry varies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermo-electromagnetic-mechanical model suitable for simulating electrically assisted forming processes, which is the main motivation of the work. The electromagnetic model will be obtained from the time-harmonic eddy current problem with an in-plane current; the source will be given in terms of currents or voltages defined at some parts of the boundary. Finite element methods based on a Lagrangian weak formulation will be used for the numerical solution. This approach will avoid the need to compute and remesh the thermo-electromagnetic domain along the time. The numerical tools will be implemented in FEniCS and validated by using a suitable test also solved in Eulerian coordinates.</p></div>","PeriodicalId":50869,"journal":{"name":"Advances in Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10444-024-10121-y.pdf","citationCount":"0","resultStr":"{\"title\":\"A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes\",\"authors\":\"Marta Benítez, Alfredo Bermúdez, Pedro Fontán, Iván Martínez, Pilar Salgado\",\"doi\":\"10.1007/s10444-024-10121-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry varies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermo-electromagnetic-mechanical model suitable for simulating electrically assisted forming processes, which is the main motivation of the work. The electromagnetic model will be obtained from the time-harmonic eddy current problem with an in-plane current; the source will be given in terms of currents or voltages defined at some parts of the boundary. Finite element methods based on a Lagrangian weak formulation will be used for the numerical solution. This approach will avoid the need to compute and remesh the thermo-electromagnetic domain along the time. The numerical tools will be implemented in FEniCS and validated by using a suitable test also solved in Eulerian coordinates.</p></div>\",\"PeriodicalId\":50869,\"journal\":{\"name\":\"Advances in Computational Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10444-024-10121-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Computational Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10444-024-10121-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10444-024-10121-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem. Application to time-varying geometry processes
The aim of this work is to introduce a thermo-electromagnetic model for calculating the temperature and the power dissipated in cylindrical pieces whose geometry varies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermo-electromagnetic-mechanical model suitable for simulating electrically assisted forming processes, which is the main motivation of the work. The electromagnetic model will be obtained from the time-harmonic eddy current problem with an in-plane current; the source will be given in terms of currents or voltages defined at some parts of the boundary. Finite element methods based on a Lagrangian weak formulation will be used for the numerical solution. This approach will avoid the need to compute and remesh the thermo-electromagnetic domain along the time. The numerical tools will be implemented in FEniCS and validated by using a suitable test also solved in Eulerian coordinates.
期刊介绍:
Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis.
This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.