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:

$${\mathbf{A}}_k=\mathbf{C}{\mathbf{M}}_{\mathbf{e}\sigma }^{\mathbf{-}\mathbf{1}}{\mathbf{C}}^{\mathbf{T}}{\mathbf{M}}_{\mathbf{f}\frac{\mathbf{1}}{\mu }}+\frac{1}{\mathrm{\Delta }{t}_k}\mathbf{I}$$

where

• $\mathrm{\Delta }{t}_k$ is the step length

• $\mathbf{I}$ is the identity matrix

• $\mathbf{C}$ is the discrete curl operator

• ${\mathbf{M}}_{\mathbf{e}\sigma }$ is the conductivity inner-product matrix on edges

• ${\mathbf{M}}_{\mathbf{f}\frac{\mathbf{1}}{\mu }}$ 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.