A Finite-Element Variable Time-Stepping Algorithm for Solving the Electromagnetic Diffusion Equation

This paper presents a new methodology for applying the Backward Differentiation Formula (BDF) and the Theta algorithm for the variable time-stepping finite-element discretization. The developed BDF-Theta formulation was implemented for solving the Electromagnetic Diffusion equation. An initial-guess prediction algorithm was adopted for convergence acceleration. An algorithm for the selection of the order and time-step size is also included. A minimum time step criterion is adopted. The proposed methodology was validated against an analytical solution and good results were obtained. The adaptive time-step (BDF) requires less computation time than using the fixed time-step implicit Euler.