The growing field of superconducting technology is witnessing remarkable advancements driven by the global energy transition. These advancements bear significance, offering promising avenues for optimizing the design and performance of superconducting systems modeled by homogenized technique and/or thin strip approximation, including electrical machines, fusion energy generation, fault current limiters, superconducting cables, and superconducting maglev trains. This article introduces a thin strip homogenizing approximation and a versatile constraint methodology tailored for analyzing series, parallel, or series-parallel connections within superconducting devices. Leveraging the J-A formulation, comprehensive modeling of coils, stacks, thin strips, racetracks, and double crossed loops (DCLs) is undertaken to validate the proposed methodologies. Through meticulous investigations, encompassing analyses of magnetic flux density, current density distribution, current profiles, and losses, the efficacy and applicability of the proposed techniques are demonstrated.

The J-A formulation has been proposed as a way to model the electromagnetic behavior of superconducting devices in finite element simulations. It is based on the current density, J, and the magnetic vector potential, A. It has been found that, to ensure better stability of simulations results, the shape functions of J should be discontinuous Lagrange of constant order, whereas for A second order continuous Lagrange functions should be used. However, applying second order shape functions increase the computational complexity of the simulation, both of degrees of freedom and computation time. In this paper, an approach to solve this issue is proposed. The finite element domain is divided into two parts, superconducting and non-superconducting. For the superconducting parts, the shape function of A is second order continuous Lagrange to ensure numerical stability. For the non-superconducting parts, a first order continuous Lagrange is used for A. To couple the two types of domains, Dirichlet Boundary Conditions are used. Three case scenarios are investigated and their results are compared to those of the common J-A formulation. Full agreement is obtained.