A Lagrangian approach for solving an axisymmetric thermo-electromagnetic problem Application to time-varying geometry processes
<|reference_start|>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 var\'ies with time and undergoes large deformations; the motion will be a known data. The work will be a first step towards building a complete thermoelectromagnetic-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 inplane current; the source will be given in terms of currents or voltages defined at sorne 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.<|reference_end|>
@article{benítez2024a,
    title={A Lagrangian approach for solving an axisymmetric thermo-electromagnetic
  problem. Application to time-varying geometry processes},
    author={Marta Ben'itez, Alfredo Berm'udez, Pedro Font'an, Iv'an
  Mart'inez, Pilar Salgado},
    journal={arXiv preprint arXiv:2403.04377},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.04377},
    primaryClass={math.NA cs.NA}
}