Magnetic Linear Inverse Problem


I am working on Reconstruction of current distribution from Magnetic field measurements.
By using Biot&Svart’s law, we can obtain a linear inverse problem of the form: d = Gm, where d is the Magnetic field measurements and m the Current distribution. So here, I have no sources, only receivers.
I would like to use SimPEG to solve this problem (even if it’s not directly related to geophysics) because of the nice mesh generator, easiness to add constraints, …

Thus, I am trying to find a Current Distribution on the edges of the mesh (2D or 3D), I struggle to find a nice way to do it, since every problems I see are modelled/solved on cells and not edges. (Am I wrong ?)
For example :

  • The regularization.Tikhonov() class requires a mesh object (to work on cells and not edges).
  • I cannot find a nice way to build a model on edges (model_builder from SimPEG.utils is good to build model on cells)

Is my way of sovling this problem wrong ?

I am quite new to all of this, so this is maybe some stupid questions…

Thank you very much