simpeg.electromagnetics.frequency_domain.Simulation3DMagneticFluxDensity.getA#

Simulation3DMagneticFluxDensity.getA(freq)[source]#

System matrix for the frequency provided.

This method returns the system matrix for the frequency provided:

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

where

• $\mathbf{I}$ is the identity matrix

• $\mathbf{C}$ is the curl operator

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

• ${\mathbf{M}}_{\mathbf{f}\frac{\mathbf{1}}{\mu }}$ is the inner-product matrix for inverse permeabilities projected to faces

See the Notes section of the doc strings for Simulation3DMagneticFluxDensity 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.