An Alternating Explicit-Implicit Time-Domain Difference Method Based on the Volume Integral Formulation for Electromagnetic Simulations of High-Temperature Superconductors

The electromagnetic simulation of large-scale high-temperature superconducting (HTS) applications is a pressing focus in current research. The key challenge lies in reducing computational costs. In this paper, starting from a time-domain analysis perspective, an alternating explicit-implicit time-domain difference method is proposed. The goal is to minimize the computational effort required to handle nonlinear terms in the J − ϕ volume integral formulation at large time steps, while maintaining numerical stability. The principle of this method is to insert an unconditionally stable implicit time-domain difference scheme to counteract the error amplification effects of the explicit method when nonlinear terms are inactive. This paper demonstrates that the proposed method significantly reduces computational costs under applied magnetic field and transport current conditions compared to traditional approaches. Furthermore, an error estimation criterion is introduced to determine whether the nonlinear terms need to be evaluated at each time step. This improved version further reduces the computational cost.