simpeg.electromagnetics.time_domain.Simulation3DMagneticFluxDensity.getAdiag#

Simulation3DMagneticFluxDensity.getAdiag(tInd)[source]#

Diagonal system matrix for the given time-step index.

This method returns the diagonal system matrix for the time-step index provided:

\[\mathbf{A}_k = \mathbf{C M_{e\sigma}^{-1} C^T M_{f\frac{1}{\mu}}} + \frac{1}{\Delta t_k} \mathbf{I}\]

where

  • \(\Delta t_k\) is the step length

  • \(\mathbf{I}\) is the identity matrix

  • \(\mathbf{C}\) is the discrete curl operator

  • \(\mathbf{M_{e \sigma}}\) is the conductivity inner-product matrix on edges

  • \(\mathbf{M_{f\frac{1}{\mu}}}\) is the inverse permeability inner-product matrix on faces

See the Notes section of the doc strings for Simulation3DMagneticFluxDensity for a full description of the formulation.

Parameters:
tIndint

The time-step index; between [0, n_steps-1].

Returns:
(n_faces, n_faces) sp.sparse.csr_matrix

The diagonal system matrix.