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:

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

where

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

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

  • \(\mathbf{M_{e\sigma}}\) is the inner-product matrix for conductivities projected to edges

  • \(\mathbf{M_{f\frac{1}{\mu}}}\) 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.