Volume 29, Issue 3
A Nodal Finite Element Method for a Thermally Coupled Eddy-Current Problem with Moving Conductors

Zezhong Wang & Qiya Hu

Commun. Comput. Phys., 29 (2021), pp. 767-801.

Published online: 2021-01

Preview Purchase PDF 8 3188
Export citation
  • Abstract

This paper aims to design and analyze a solution method for a time-dependent, nonlinear and thermally coupled eddy-current problem with a moving conductor on hyper-velocity. We transform the problem into an equivalent coupled system and use the nodal finite element discretization (in space) and the implicit Euler method (in time) for the coupled system. The resulting discrete coupled system is decoupled and implicitly solved by a time step-length iteration method and the Picard iteration. We numerically and theoretically prove that the finite element approximations have the optimal error estimates and both the two iteration methods possess the linear convergence. For the proposed method, numerical stability and accuracy of the approximations can be held even for coarser mesh partitions and larger time steps. We also construct a preconditioner for the discrete operator defined by the linearized bilinear form and show that this preconditioner is uniformly effective. Numerical experiments are done to confirm the theoretical results and illustrate that the proposed method is well behaved in large-scale numerical simulations.

  • Keywords

Thermally coupled eddy-current problem, finite element method, time step-length iteration, Picard iteration, optimal error estimates, preconditioner.

  • AMS Subject Headings

65N30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-29-767, author = {Wang , Zezhong and Hu , Qiya}, title = {A Nodal Finite Element Method for a Thermally Coupled Eddy-Current Problem with Moving Conductors}, journal = {Communications in Computational Physics}, year = {2021}, volume = {29}, number = {3}, pages = {767--801}, abstract = {

This paper aims to design and analyze a solution method for a time-dependent, nonlinear and thermally coupled eddy-current problem with a moving conductor on hyper-velocity. We transform the problem into an equivalent coupled system and use the nodal finite element discretization (in space) and the implicit Euler method (in time) for the coupled system. The resulting discrete coupled system is decoupled and implicitly solved by a time step-length iteration method and the Picard iteration. We numerically and theoretically prove that the finite element approximations have the optimal error estimates and both the two iteration methods possess the linear convergence. For the proposed method, numerical stability and accuracy of the approximations can be held even for coarser mesh partitions and larger time steps. We also construct a preconditioner for the discrete operator defined by the linearized bilinear form and show that this preconditioner is uniformly effective. Numerical experiments are done to confirm the theoretical results and illustrate that the proposed method is well behaved in large-scale numerical simulations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0024}, url = {http://global-sci.org/intro/article_detail/cicp/18566.html} }
TY - JOUR T1 - A Nodal Finite Element Method for a Thermally Coupled Eddy-Current Problem with Moving Conductors AU - Wang , Zezhong AU - Hu , Qiya JO - Communications in Computational Physics VL - 3 SP - 767 EP - 801 PY - 2021 DA - 2021/01 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2020-0024 UR - https://global-sci.org/intro/article_detail/cicp/18566.html KW - Thermally coupled eddy-current problem, finite element method, time step-length iteration, Picard iteration, optimal error estimates, preconditioner. AB -

This paper aims to design and analyze a solution method for a time-dependent, nonlinear and thermally coupled eddy-current problem with a moving conductor on hyper-velocity. We transform the problem into an equivalent coupled system and use the nodal finite element discretization (in space) and the implicit Euler method (in time) for the coupled system. The resulting discrete coupled system is decoupled and implicitly solved by a time step-length iteration method and the Picard iteration. We numerically and theoretically prove that the finite element approximations have the optimal error estimates and both the two iteration methods possess the linear convergence. For the proposed method, numerical stability and accuracy of the approximations can be held even for coarser mesh partitions and larger time steps. We also construct a preconditioner for the discrete operator defined by the linearized bilinear form and show that this preconditioner is uniformly effective. Numerical experiments are done to confirm the theoretical results and illustrate that the proposed method is well behaved in large-scale numerical simulations.

Zezhong Wang & Qiya Hu. (2021). A Nodal Finite Element Method for a Thermally Coupled Eddy-Current Problem with Moving Conductors. Communications in Computational Physics. 29 (3). 767-801. doi:10.4208/cicp.OA-2020-0024
Copy to clipboard
The citation has been copied to your clipboard