simpeg.electromagnetics.frequency_domain.Simulation3DElectricField.getRHSDeriv#
- Simulation3DElectricField.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:
\[\mathbf{q} = -i \omega \mathbf{s_e} - i \omega \mathbf{C^T M_{f\frac{1}{\mu}} s_m }\]where
\(\mathbf{C}\) is the discrete curl operator
\(\mathbf{s_m}\) and \(\mathbf{s_e}\) are the integrated magnetic and electric source terms, respectively
\(\mathbf{M_{f\frac{1}{\mu}}}\) is the inner-product matrices for inverse permeabilities projected to faces
See the Notes section of the doc strings for
Simulation3DElectricFieldfor 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:
- freq
int The frequency in Hz.
- src
frequency_domain.sources.BaseFDEMSrc The FDEM source object.
- v
numpy.ndarray The vector. (n_param,) for the standard operation. (n_edges,) for the adjoint operation.
- adjointbool
Whether to perform the adjoint operation.
- freq
- Returns:
numpy.ndarrayDerivative of the right-hand sides times a vector. (n_edges,) for the standard operation. (n_param,) for the adjoint operation.