SimPEG.electromagnetics.time_domain.Simulation3DElectricField

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

Bases: BaseTDEMSimulation

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

Starting with

$$\mathrm{\nabla }\times \mathbf{e}+\frac{\partial \mathbf{b}}{\partial t}={\mathbf{s}}_{\mathbf{m}}\mathrm{\nabla }\times {\mu }^{-1}\mathbf{b}-\sigma \mathbf{e}={\mathbf{s}}_{\mathbf{e}}$$

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

$$\frac{\partial \mathbf{b}}{\partial t}=-\mathrm{\nabla }\times \mathbf{e}+{\mathbf{s}}_{\mathbf{m}}$$

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

$$\frac{\partial }{\partial t}(\mathrm{\nabla }\times {\mu }^{-1}\mathbf{b}-\sigma \mathbf{e})=\frac{\partial {\mathbf{s}}_{\mathbf{e}}}{\partial t}\mathrm{\nabla }\times {\mu }^{-1}\frac{\partial \mathbf{b}}{\partial t}-\sigma \frac{\partial \mathbf{e}}{\partial t}=\frac{\partial {\mathbf{s}}_{\mathbf{e}}}{\partial t}$$

which gives us

$$\mathrm{\nabla }\times {\mu }^{-1}\mathrm{\nabla }\times \mathbf{e}+\sigma \frac{\partial \mathbf{e}}{\partial t}=\mathrm{\nabla }\times {\mu }^{-1}{\mathbf{s}}_{\mathbf{m}}+\frac{\partial {\mathbf{s}}_{\mathbf{e}}}{\partial t}$$

Methods

Fields_Derivs	alias of FieldsDerivativesEB
Jtvec(m, v[, f])	Jvec computes the adjoint of the sensitivity times a vector
fieldsPair	alias of Fields3DElectricField
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