SimPEG.electromagnetics.frequency_domain.Simulation3DCurrentDensity.getADeriv_rho#

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

Product of the derivative of our system matrix with respect to the model and a vector

In this case, we assume that electrical conductivity, $\sigma$ is the physical property of interest (i.e. $\sigma$ = model.transform). Then we want

$$\frac{\mathbf{A}\mathbf{(}\sigma \mathbf{)}\mathbf{v}}{d\mathbf{m}}=\mathbf{C}{\mathbf{M}}_{{\mathbf{mu}}^{\mathbf{-}\mathbf{1}}}^{\mathbf{e}}{\mathbf{C}}^{\mathrm{\top }}\frac{d{\mathbf{M}}_{{\sigma }^{\mathbf{-}\mathbf{1}}}^{\mathbf{f}}\mathbf{v}}{d\mathbf{m}}$$

Parameters:

• freq (float) – frequency

• u (numpy.ndarray) – solution vector (nF,)

• v (numpy.ndarray) – vector to take prodct with (nP,) or (nD,) for adjoint

• adjoint (bool) – adjoint?

Return type:

numpy.ndarray

Returns:

derivative of the system matrix times a vector (nP,) or adjoint (nD,)