discretize.base.BaseRegularMesh.boundary_face_scalar_integral

property BaseRegularMesh.boundary_face_scalar_integral

Represent the operation of integrating a scalar function on the boundary.

This matrix represents the boundary surface integral of a scalar function multiplied with a finite volume test function on the mesh.

Returns:

(n_faces, n_boundary_faces) scipy.sparse.csr_matrix

Notes

The integral we are representing on the boundary of the mesh is

\[\int_{\Omega} u\vec{w} \cdot \hat{n} \partial \Omega\]

In discrete form this is:

\[w^T * P @ u_b\]

where w is defined on all faces, and u_b is defined on boundary faces.