simpeg.electromagnetics.time_domain.Simulation3DElectricField.getAdiag#

Simulation3DElectricField.getAdiag(tInd)[source]#

Diagonal system matrix for the time-step index provided.

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

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

where

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

• $\mathbf{C}$ 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 Simulation3DElectricField for a full description of the formulation.

Parameters:

tIndint

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

Returns:

(n_edges, n_edges) sp.sparse.csr_matrix

The diagonal system matrix.