# SimPEG.electromagnetics.time_domain.Simulation3DElectricField#

class SimPEG.electromagnetics.time_domain.Simulation3DElectricField(mesh, survey=None, dt_threshold=1e-08, **kwargs)[source]#

Solve the EB-formulation of Maxwell’s equations for the electric field, e.

Starting with

$\nabla \times \mathbf{e} + \frac{\partial \mathbf{b}}{\partial t} = \mathbf{s_m} \ \nabla \times \mu^{-1} \mathbf{b} - \sigma \mathbf{e} = \mathbf{s_e}$

we eliminate $$\frac{\partial b}{\partial t}$$ using

$\frac{\partial \mathbf{b}}{\partial t} = - \nabla \times \mathbf{e} + \mathbf{s_m}$

taking the time-derivative of Ampere’s law, we see

$\frac{\partial}{\partial t}\left( \nabla \times \mu^{-1} \mathbf{b} - \sigma \mathbf{e} \right) = \frac{\partial \mathbf{s_e}}{\partial t} \ \nabla \times \mu^{-1} \frac{\partial \mathbf{b}}{\partial t} - \sigma \frac{\partial\mathbf{e}}{\partial t} = \frac{\partial \mathbf{s_e}}{\partial t}$

which gives us

$\nabla \times \mu^{-1} \nabla \times \mathbf{e} + \sigma \frac{\partial\mathbf{e}}{\partial t} = \nabla \times \mu^{-1} \mathbf{s_m} + \frac{\partial \mathbf{s_e}}{\partial t}$

Methods

 Fields_Derivs Jtvec(m, v[, f]) Jvec computes the adjoint of the sensitivity times a vector fieldsPair getAdiag(tInd) Diagonal of the system matrix at a given time index getAdiagDeriv(tInd, u, v[, adjoint]) Deriv of ADiag with respect to electrical conductivity getAsubdiag(tInd) Matrix below the diagonal getAsubdiagDeriv(tInd, u, v[, adjoint]) Derivative of the matrix below the diagonal with respect to electrical conductivity getRHS(tInd) right hand side
 getAdc getAdcDeriv getRHSDeriv

## Galleries and Tutorials using SimPEG.electromagnetics.time_domain.Simulation3DElectricField#

Time-domain CSEM for a resistive cube in a deep marine setting

Time-domain CSEM for a resistive cube in a deep marine setting

EM: TDEM: 1D: Inversion

EM: TDEM: 1D: Inversion

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions

Heagy et al., 2017 1D RESOLVE and SkyTEM Bookpurnong Inversions