simpeg.electromagnetics.frequency_domain.Simulation3DMagneticField.getRHSDeriv#

Simulation3DMagneticField.getRHSDeriv(freq, src, v, adjoint=False)[source]#

Derivative of the right-hand side times a vector for a given source and frequency.

The right-hand side for each source is constructed according to:

\[\mathbf{q} = \mathbf{C^T M_{f\rho} s_e} - i\omega \mathbf{s_m}\]

where

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

  • \(\mathbf{s_m}\) and \(\mathbf{s_e}\) are the integrated magnetic and electric source terms, respectively

  • \(\mathbf{M_{e\mu}}\) is the inner-product matrices for permeabilities projected to edges

  • \(\mathbf{M_{f\rho}}\) is the inner-product matrices for resistivities projected to faces

See the Notes section of the doc strings for Simulation3DMagneticField for a full description of the formulation.

Where \(\mathbf{m}\) are the set of model parameters and \(\mathbf{v}\) is a vector, this method returns

\[\frac{\partial \mathbf{q_k}}{\partial \mathbf{m}} \, \mathbf{v}\]

Or the adjoint operation

\[\frac{\partial \mathbf{q_k}}{\partial \mathbf{m}}^T \, \mathbf{v}\]
Parameters:
freqint

The frequency in Hz.

srcfrequency_domain.sources.BaseFDEMSrc

The FDEM source object.

vnumpy.ndarray

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

adjointbool

Whether to perform the adjoint operation.

Returns:
numpy.ndarray

Derivative of the right-hand sides times a vector. (n_edges,) for the standard operation. (n_param,) for the adjoint operation.