# Gridap.jl field-circuit coupling for magnetostatics

Hi all,

I am trying to solve a field-circuit coupled problem using the Gridap.jl package.
I want to simulate the current distribution inside a high-voltage cable, as well as the associated magnetic field.

This means I have two equations I would like to solve simultaneously:

1. A second order differential equation for the magnetic potential in terms of an imposed current density. This equation includes a term for eddy currents (time-harmonic assumption).
\nabla\cdot(\nu \nabla A_z) - j\omega\sigma A_z = -J_z
2. A circuit equation which imposes a certain current I_{coil} on the cable.
\iint_{coil} J_z d\Omega = I_{coil}

I have successfully solved this problem using a home-brew FEM implementation, which manually constructs the linear system with a loop over the elements (see this Jupyter notebook, and solution figures for 3 different frequencies). The results from this code match quite well with those from COMSOL Multiphysics.

I am wondering how to solve this problem using Gridap.jl? The first equation is no problem, as this can be solved by just following the first tutorial. However, I am unable to find a suitable starting point for including equation 2 in the documentation, and would greatly appreciate if someone could point me in the right direction.