RT Journal Article
T1 Numerical Solution of an Axisymmetric Eddy Current Model with Current and Voltage Excitations
A1 Bermúdez de Castro López-Varela, Alfredo
A1 López-Rodríguez, Bibiana
A1 Pena, Francisco José
A1 Rodríguez, Rodolfo
A1 Salgado Rodríguez, María del Pilar
A1 Venegas, Pablo
K1 Axisymmetric problem
K1 Eddy-current model
K1 Finite elements
K1 Error estimates
AB The aim of this paper is to study the numerical approximation of an axisymmetric time-harmonic eddy current problem involving an in-plane current. The analysis of the problem restricts to the conductor. The source of the problem is given in terms of boundary data currents and/or voltage drops defined in the so-called electric ports, which are parts of the boundary connected to exterior sources. This leads to an elliptic problem written in terms of the magnetic field with nonlocal boundary conditions. First, we prove the existence and uniqueness of the solution for a weak formulation written in terms of Sobolev spaces with appropriate weights. We show that the magnetic field is not the most appropriate variable to impose the boundary conditions when Lagrangian finite elements are used to discretize the problem. We propose an alternative weak formulation of the problem which allows us to avoid this drawback. We compute the numerical solution of the problem by using Lagrangian finite elements ad hoc modified on the vicinity of the symmetry axis. We provide a convergence result under rather general conditions. Moreover, we prove quasi-optimal order error estimates under additional regularity assumptions. Finally, we report numerical results which allow us to confirm the theoretical estimates and to assess the performance of the proposed method in a physical application which is the motivation of this paper: the computation of the current density distribution in a steel cylindrical bar submitted to electric-upsetting.
PB Springer Link
SN 0885-7474
YR 2022
FD 2022
LK http://hdl.handle.net/10347/32400
UL http://hdl.handle.net/10347/32400
LA eng
NO Bermúdez, López-Rodríguez, Pena, Rodríguez, Salgado, & Venegas. (2022). Numerical Solution of an Axisymmetric Eddy Current Model with Current and Voltage Excitations. Journal of Scientific Computing, 91(1). https://doi.org/10.1007/S10915-022-01780-4
NO This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10915-022-01780-4
NO R. Rodríguez was partially supported by CONICYT-Chile through project AFB170001. P. Venegas was partially supported by FONDECYT-Chile project 1211030 and by Centro de Modelamiento Matemático (CMM), FB210005, BASAL funds for centers of excellence from ANID-Chile. B. López-Rodríguez was partially supported by Universidad Nacional de Colombia through Hermes project 52759.
DS Minerva
RD 25 abr 2026