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:
\[\mathbf{A_{dc}}\boldsymbol{\phi_0} = \mathbf{q_{dc}}\]where \(\mathbf{A_{dc}}\) is the DC resistivity system matrix, \(\boldsymbol{\phi_0}\) is the discrete solution for the electric potentials at the initial time, and \(\mathbf{q_{dc}}\) is the galvanic source term. For a vector \(\mathbf{v}\), this method assumes the discrete solution is fixed and returns
\[\frac{\partial (\mathbf{A_{dc}}\boldsymbol{\phi_0})}{\partial \mathbf{m}} \, \mathbf{v}\]Or the adjoint operation
\[\frac{\partial (\mathbf{A_{dc}}\boldsymbol{\phi_0})}{\partial \mathbf{m}}^T \, \mathbf{v}\]- Parameters:
- u(n_cells,)
numpy.ndarray The solution for the fields for the current model; i.e. electric potentials at cell centers.
- v
numpy.ndarray The vector. (n_param,) for the standard operation. (n_cells,) for the adjoint operation.
- adjointbool
Whether to perform the adjoint operation.
- u(n_cells,)
- Returns:
numpy.ndarrayDerivative of the DC resistivity system matrix times a vector. (n_cells,) for the standard operation. (n_param,) for the adjoint operation.