simpeg.potential_fields.magnetics.Simulation3DDifferential.Jtvec#

Simulation3DDifferential.Jtvec(m, v, u=None)[source]#

Computing Jacobian^T multiplied by vector.

$$(\frac{\delta \mathbf{P}\mathbf{B}}{\delta \mathbf{m}}{)}^T={\left[{\mathbf{P}}_{deriv}\frac{\partial \mu }{\partial \mathbf{m}}[\text{diag}({\text{M}}_{{\mu }_0^{-1}}^f{\mathbf{B}}_0)\text{dMfMuI}-\text{diag}({\text{Div}}^T\mathbf{u})\text{dMfMuI}]\right]}^T-{[{\mathbf{P}}_{deriv}(\text{MfMui}{)}^{-1}{\text{Div}}^T\frac{\delta \mathbf{u}}{\delta \mathbf{m}}]}^T$$

where

$${\mathbf{P}}_{derv}=\frac{\partial \mathbf{P}}{\partial \mathbf{B}}$$

Note

Here we only want to compute

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