simpeg.electromagnetics.static.resistivity.Simulation3DHierarchicalNodal.getA#

Simulation3DHierarchicalNodal.getA(resistivity=None)[source]#

Return the system matrix.

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

\[\mathbf{A} = \mathbf{(G^T - B) M_{e\sigma} G}\]

where

  • \(\mathbf{G}\) is the nodal gradient operator

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

  • \(\mathbf{M_{e\sigma}}\) is the inner-product matrix for conductivities projected to edges

Parameters:
resistivity(n_cells,) numpy.ndarray

Electrical resistivities defined at cell centers

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

The system matrix.