A Nodal Finite Element Method for a Thermally Coupled Eddy-Current Problem with Moving Conductors (Communications in Computational Physics, 2021)
This paper aims to design and analyze a solution method for a time-dependent, nonlinear and thermally coupled eddy-current problem with a movingconductor on hyper-velocity. We transform the problem into an equivalent coupledsystem 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 isdecoupled and implicitly solved by a time step-length iteration method and the Picarditeration. We numerically and theoretically prove that the finite element approximations have the optimal error estimates and both the two iteration methods possess thelinear convergence. For the proposed method, numerical stability and accuracy of theapproximations can be held even for coarser mesh partitions and larger time steps.We also construct a preconditioner for the discrete operator defined by the linearizedbilinear form and show that this preconditioner is uniformly effective. Numerical experiments are done to confirm the theoretical results and illustrate that the proposedmethod 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.