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

Return type

numpy.ndarray

Returns

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