discretize.SimplexMesh.boundary_face_scalar_integral#
- property SimplexMesh.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.