simpeg.electromagnetics.time_domain.Simulation3DCurrentDensity.getAdcDeriv#

Simulation3DCurrentDensity.getAdcDeriv(u, v, adjoint=False)[source]#

Derivative operation for the DC resistivity system matrix times a vector.

The discrete solution to the 3D DC resistivity problem is expressed as:

$${\mathbf{A}}_{\mathbf{dc}}{\mathit{\varphi }}_{\mathbf{0}}={\mathbf{q}}_{\mathbf{dc}}$$

where ${\mathbf{A}}_{\mathbf{dc}}$ is the DC resistivity system matrix, ${\mathit{\varphi }}_{\mathbf{0}}$ is the discrete solution for the electric potentials at the initial time, and ${\mathbf{q}}_{\mathbf{dc}}$ is the galvanic source term. For a vector $\mathbf{v}$, this method assumes the discrete solution is fixed and returns

$$\frac{\partial ({\mathbf{A}}_{\mathbf{dc}}{\mathit{\varphi }}_{\mathbf{0}})}{\partial \mathbf{m}}\mathbf{v}$$

Or the adjoint operation

$${\frac{\partial ({\mathbf{A}}_{\mathbf{dc}}{\mathit{\varphi }}_{\mathbf{0}})}{\partial \mathbf{m}}}^T\mathbf{v}$$

Parameters:

u(n_cells,) numpy.ndarray

The solution for the fields for the current model; i.e. electric potentials at cell centers.

vnumpy.ndarray

The vector. (n_param,) for the standard operation. (n_cells,) for the adjoint operation.

adjointbool

Whether to perform the adjoint operation.

Returns:

numpy.ndarray

Derivative of the DC resistivity system matrix times a vector. (n_cells,) for the standard operation. (n_param,) for the adjoint operation.