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 - <p style="text-align: justify;">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.</p>