Modeling electromagnetics on cylindrical meshes with applications to steel-cased wells

\begin{split} \mathbf{C} \mathbf{e} + i\omega\mathbf{b} &= \mathbf{0} \\ \mathbf{C}^\top \mathbf{M}_{\boldsymbol{\mu}^{-1}}^f \mathbf{b} - \mathbf{M}_{\boldsymbol{\sigma}}^e \mathbf{e} &= \mathbf{s_e} \end{split}