simpeg.electromagnetics.frequency_domain.Simulation3DCurrentDensity.getADeriv_mu#

Simulation3DCurrentDensity.getADeriv_mu(freq, u, v, adjoint=False)[source]#

Permeability derivative operation for the system matrix times a vector.

The system matrix at each frequency is given by:

A=CMeμ1CTMfρ+iωI

where

  • Mfρ is the inner-product matrix for resistivities projected to faces

  • Meμ 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.

Where mμ are the set of model parameters defining the permeability, v is a vector and j is the discrete current density solution, this method assumes the discrete solution is fixed and returns

(Aj)mμv

Or the adjoint operation

(Aj)mμTv
Parameters:
freqfloat

The frequency in Hz.

u(n_faces,) numpy.ndarray

The solution for the fields for the current model at the specified frequency.

vnumpy.ndarray

The vector. (n_param,) for the standard operation. (n_faces,) for the adjoint operation.

adjointbool

Whether to perform the adjoint operation.

Returns:
numpy.ndarray

Derivative of system matrix times a vector. (n_faces,) for the standard operation. (n_param,) for the adjoint operation.