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 ϕn be a discrete scalar quantity that lives on mesh nodes. average_node_to_cell constructs a discrete linear operator Anc that projects ϕf to cell centers, i.e.:

ϕc=Ancϕn

where ϕc 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