simpeg.electromagnetics.time_domain.Simulation3DCurrentDensity.getRHS#
- Simulation3DCurrentDensity.getRHS(tInd)[source]#
Right-hand sides for the given time index.
This method returns the right-hand sides for the time index provided. The right-hand side for each source is constructed according to:
\[\mathbf{q}_k = - \frac{1}{\Delta t_k} \big [ \mathbf{s}_{\mathbf{e},k} + \mathbf{s}_{\mathbf{e},k-1} \big ] \; - \; \frac{1}{\Delta t_k} \mathbf{C M_{e\mu}^{-1}} \big [ \mathbf{s}_{\mathbf{m},k} + \mathbf{s}_{\mathbf{m},k-1} \big ]\]where
\(\Delta t_k\) is the step length
\(\mathbf{C}\) 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 matrix for permeabilities projected to edges
See the Notes section of the doc strings for
Simulation3DCurrentDensityfor a full description of the formulation.- Parameters:
- tInd
int The time index; between
[0, n_steps].
- tInd
- Returns:
- (
n_faces,n_sources)numpy.ndarray The right-hand sides.
- (