simpeg.electromagnetics.frequency_domain.Simulation3DCurrentDensity.getA#

Simulation3DCurrentDensity.getA(freq)[source]#

System matrix for the frequency provided.

This method returns the system matrix for the frequency provided. The system matrix at each frequency is given by:

$$\mathbf{A}=\mathbf{C}{\mathbf{M}}_{\mathbf{e}\mu }^{\mathbf{-}\mathbf{1}}{\mathbf{C}}^{\mathbf{T}}{\mathbf{M}}_{\mathbf{f}\rho }+i\omega \mathbf{I}$$

where

• ${\mathbf{M}}_{\mathbf{f}\rho }$ is the inner-product matrix for resistivities projected to faces

• ${\mathbf{M}}_{\mathbf{e}\mu }$ is the inner-product matrix for permeabilities projected to edges

See the Notes section of the doc strings for Simulation3DCurrentDensity for a full description of the formulation.

Parameters:

freqfloat

The frequency in Hz.

Returns:

(n_faces, n_faces) sp.sparse.csr_matrix

The system matrix.