SimPEG.electromagnetics.time_domain.Simulation3DCurrentDensity.Jtvec#

Simulation3DCurrentDensity.Jtvec(m, v, f=None)[source]#

Jvec computes the adjoint of the sensitivity times a vector

$${\mathbf{J}}^{\mathrm{\top }}\mathbf{v}=({\frac{d\mathbf{u}}{d\mathbf{m}}}^{\mathrm{\top }}{\frac{d\mathbf{F}}{d\mathbf{u}}}^{\mathrm{\top }}+{\frac{\partial \mathbf{F}}{\partial \mathbf{m}}}^{\mathrm{\top }}){\frac{d\mathbf{P}}{d\mathbf{F}}}^{\mathrm{\top }}\mathbf{v}$$

where

$${\frac{d\mathbf{u}}{d\mathbf{m}}}^{\mathrm{\top }}{\mathbf{A}}^{\mathrm{\top }}+{\frac{d\mathbf{A}(\mathbf{u})}{d\mathbf{m}}}^{\mathrm{\top }}={\frac{d\mathbf{RHS}}{d\mathbf{m}}}^{\mathrm{\top }}$$