simpeg.electromagnetics.static.spectral_induced_polarization.Simulation3DCellCentered.getA#

Simulation3DCellCentered.getA(resistivity=None)[source]#

Return the system matrix.

This method generates and returns the system matrix for the cell-centered DC resistivity problem. The system matrix is given by:

\[\mathbf{A} = \mathbf{M_c D M_{f\rho} (G - B) M_c}\]

where

  • \(\mathbf{D}\) is the divergence operator (faces to cell centers)

  • \(\mathbf{B}\) is a matrix that implements boundary conditions

  • \(\mathbf{M_c}\) is the cell inner-product matrix

  • \(\mathbf{M_{f\rho}}\) is the inner-product matrix for resistivities projected to faces

Parameters:
resistivity(n_cells,) numpy.ndarray

Electrical resistivities defined at cell centers

Returns:
(n_cells, n_cells) sp.sparse.csr_matrix

The system matrix.