discretize.TreeMesh.average_node_to_cell#
- TreeMesh.average_node_to_cell#
Averaging operator from nodes to cell centers (scalar quantities).
This property constructs a 2nd order averaging operator that maps scalar quantities from nodes to cell centers. This averaging operator is used when a discrete scalar quantity defined on mesh nodes must be projected to cell centers. Once constructed, the operator is stored permanently as a property of the mesh. See notes.
- Returns:
- (
n_cells
,n_nodes
)scipy.sparse.csr_matrix
The scalar averaging operator from nodes to cell centers
- (
Notes
Let
be a discrete scalar quantity that lives on mesh nodes. average_node_to_cell constructs a discrete linear operator that projects to cell centers, i.e.:where
approximates the value of the scalar quantity at cell centers. For each cell, we are simply averaging the values defined on its nodes. The operation is implemented as a matrix vector product, i.e.:phi_c = Anc @ phi_n