Fast electromagnetic modeling of high-temperature superconductors: a reduced-order scheme for the T–A formulation

Abstract The T–A formulation, which couples the magnetic vector potential A and the current vector potential T , has become one of the dominant models for the electromagnetic modeling of high-temperature superconducting (HTS) structures. Due to the limitation of the mixed formulation, the discretization of the T–A formulation needs to be performed carefully to prevent spurious numerical oscillations. For this purpose, the second-order Lagrangian elements are employed for the magnetic vector potential A , and the linear elements for the current vector potential T . Nevertheless, the higher-order elements increase the degrees of freedom and restrict the computational efficiency. In this paper, a reduced-order T–A formulation is proposed based on mesh misalignment to eliminate the oscillation phenomenon and improve the computational efficiency. The mesh misalignment ensures that the electromagnetic energy is calculated at the consistent node without additional interpolation by the product of work-conjugate quantities (the magnetic vector potential A and the current density J ). In this way, the linear elements are applied for the magnetic vector potential A and the current vector potential T . Therefore, the spurious numerical oscillations disappear in the reduced-order T – A formulation. And the degrees of freedom are significantly reduced. The reduced-order T–A formulation could significantly improve the computational efficiency for electromagnetic modeling of large-scale superconducting systems, especially for the three-dimensional HTS structures.