The major advantage of reduced magnetic vector potential formulations (RMVPs) is that complicated coil structures do not need to be resolved by a computational mesh. Instead, they are modeled by thin wires, whose source field is included into the simulation model along Biot-Savart's law. Such an approach has already been successfully employed in ROXIE for the simulation of superconducting Large Hadron Collider magnets at CERN. This work presents an updated RMVP approach, which significantly outperforms the original method. The updated formulation is postulated, implemented, verified, compared to the original formulation, and applied for the simulation of a quadrupole magnet. The promising results of this work encourage further investigation towards an updated simulation framework for next-generation accelerator magnets.