SimPEG.potential_fields.magnetics.Simulation3DDifferential.Jtvec

Simulation3DDifferential.Jtvec(m, v, u=None)

Computing Jacobian^T multiplied by vector.

\[ \begin{align}\begin{aligned}(\frac{\delta \mathbf{P}\mathbf{B}} {\delta \mathbf{m}})^{T} = \left[ \mathbf{P}_{deriv}\frac{\partial \mathbf{\mu} } {\partial \mathbf{m} } \left[ \diag(\M^f_{\mu_{0}^{-1} } \mathbf{B}_0) \dMfMuI \ - \diag (\Div^T\mathbf{u})\dMfMuI \right ]\right]^{T}\\ - \left[\mathbf{P}_{deriv}(\MfMui)^{-1}\Div^T\frac{\delta\mathbf{u}}{\delta \mathbf{m}} \right]^{T}\end{aligned}\end{align} \]

where

\[\mathbf{P}_{derv} = \frac{\partial \mathbf{P}}{\partial\mathbf{B}}\]

Note

Here we only want to compute

\[\mathbf{J}^{T}\mathbf{v} = (\frac{\delta \mathbf{P}\mathbf{B}} {\delta \mathbf{m}})^{T} \mathbf{v}\]