simpeg.electromagnetics.time_domain.Simulation3DElectricField.getAdc#
- Simulation3DElectricField.getAdc()[source]#
The system matrix for the DC resistivity problem.
The solution to the DC resistivity problem is necessary at the initial time for galvanic sources whose currents are non-zero at the initial time. 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. This method returns the system matrix for the nodal formulation, i.e.:
\[\mathbf{A_{dc}} = \mathbf{G^T \, M_{e\sigma} \, G}\]where \(\mathbf{G}\) is the nodal gradient operator with imposed boundary conditions, and \(\mathbf{M_{e\sigma}}\) is the inner product matrix for conductivities projected to edges.
The electric fields at the initial time \(\mathbf{e_0}\) are obtained by applying the nodal gradient operator. I.e.:
\[\mathbf{e_0} = \mathbf{G} \, \boldsymbol{\phi_0}\]See the Notes section of the doc strings for
resistivity.Simulation3DNodalfor a full description of the nodal DC resistivity formulation.- Returns:
- (
n_nodes,n_nodes)sp.sparse.csr_matrix The system matrix for the DC resistivity problem.
- (