simpeg.electromagnetics.time_domain.Simulation3DMagneticFluxDensity.getRHS#

Simulation3DMagneticFluxDensity.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:

$${\mathbf{q}}_k=\mathbf{C}{\mathbf{M}}_{\mathbf{e}\sigma }^{\mathbf{-}\mathbf{1}}{\mathbf{s}}_{\mathbf{e},k}-\frac{1}{\mathrm{\Delta }{t}_k}[{\mathbf{s}}_{\mathbf{m},k}-{\mathbf{s}}_{\mathbf{m},k-1}]$$

where

• $\mathrm{\Delta }{t}_k$ is the step length

• $\mathbf{C}$ is the discrete curl operator

• ${\mathbf{s}}_{\mathbf{m}}$ and ${\mathbf{s}}_{\mathbf{e}}$ are the integrated magnetic and electric source terms, respectively

• ${\mathbf{M}}_{\mathbf{e}\sigma }$ is the inner-product matrix for conductivities projected to edges

See the Notes section of the doc strings for Simulation3DMagneticFluxDensity for a full description of the formulation.

Parameters:

tIndint

The time index; between [0, n_steps].

Returns:

(n_faces, n_sources) numpy.ndarray

The right-hand sides.