Mixed-dimensional elements in transient thermal analysis of gradient coils

This article proposes a numerical formulation for handling mixed- dimensional elements embedded in a standard three-dimensional (3d) mesh, avoiding thus the volume meshing of filaments and strips. The method is then applied to predict the temperature heating and cooling profile of gradient coils in magnetic resonance imaging. These coils are typically constructed from copper wires or tracks and embedded in an epoxy layer. It was found that the new method significantly reduces the computational time of steady-state and transient simulations, with speedups in the range of 3.5-5. The method proved to be accurate, with relative errors below 0.5% for steady-state simulations and 1.5% with respect to a complete 3d simulation.