simpeg.maps.InjectActiveFaces.inverse

InjectActiveFaces.inverse(u)

Compute the inverse projection operation.

Recover the model parameters (active faces) from a set of physical property values defined on the entire mesh.

For a discrete set of model parameters \(\mathbf{m}\) defined on a set of active faces, the mapping \(\mathbf{u}(\mathbf{m})\) is defined as:

\[\mathbf{u}(\mathbf{m}) = \mathbf{Pm} + \mathbf{d} \,m_\perp\]

where \(\mathbf{P}\) is a (nF , nP) projection matrix from active faces to all mesh faces, and \(\mathbf{d}\) is a (nR , 1) matrix that projects the inactive face value \(m_\perp\) to all mesh faces.

The inverse mapping is given by:

\[\mathbf{m}(\mathbf{u}) = \mathbf{P^T u}\]

Parameters:

u(mesh.nF) numpy.ndarray

A vector which contains physical property values for all mesh faces.