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
\[\frac{\mathbf{A(\sigma)} \mathbf{v}}{d \mathbf{m}} = \mathbf{C} \mathbf{M^e_{mu^{-1}}} \mathbf{C^{\top}} \frac{d \mathbf{M^f_{\sigma^{-1}}}\mathbf{v} }{d \mathbf{m}}\]- 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:
- Returns:
derivative of the system matrix times a vector (nP,) or adjoint (nD,)