pygeon.numerics.spanningtree module

Module for spanning tree computation.

class pygeon.numerics.spanningtree.SpanningTree(mdg, starting_faces='first_bdry')[source]

Bases: object

Class that can perform a spanning tree solve, aka a “grid sweep”. Useful to rapidly compute a flux field that balances a mass source.

__init__(mdg, starting_faces='first_bdry')[source]

Initializes a SpanningTree object.

Parameters:

mdg (pg.MixedDimensionalGrid | pg.Grid) – The mixed-dimensional grid.
starting_faces (np.ndarray | int | str) –
- “first_bdry” (default): Choose the first boundary face.
- ”all_bdry”: Choose all boundary faces.
- np.array or int: Indices of the starting faces.

setup_system(mdg, flagged_faces)[source]

Sets up the linear system for solving the spanning tree problem.

Parameters:

mdg (pg.MixedDimensionalGrid) – The mixed-dimensional grid.
flagged_faces (np.ndarray) – Array of flagged faces.

Returns:

None

find_starting_faces(mdg, starting_faces)[source]

Find the starting face for the spanning tree. By default, this method returns the indices of the boundary faces of the mesh.

Parameters:

mdg (pg.MixedDimensionalGrid) – The mixed-dimensional grid object.
starting_faces –
- “first_bdry” (default): Choose the first boundary face.
- ”all_bdry”: Choose all boundary faces.
- np.array or int: Indices of the starting faces.

Returns:

The indices of the starting faces for the spanning tree.

Return type:

np.ndarray

Raises:

KeyError – if starting_faces does not have the right type

find_starting_cells()[source]

Find the starting cell for the spanning tree.

Returns:: The indices of the starting cells.
Return type:: np.ndarray

add_outside_cell()[source]: Include a fictitious outside cell in the div operator. This cell will be used as the root of the tree.

remove_outside_cell()[source]: Remove the fictitious outside cell from the div operator and the tree

compute_tree()[source]

Construct a spanning tree of the elements.

Returns:: The computed spanning tree as a compressed sparse column matrix.
Return type:: sps.csc_array

flag_tree_faces()[source]

Flag the faces in the mesh that correspond to edges of the tree.

Returns:: A boolean array indicating the flagged faces in the mesh.
Return type:: np.ndarray

solve(f)[source]

Perform a spanning tree solve to compute a conservative flux field for given mass source.

Parameters:: f (np.ndarray) – Mass source, integrated against PwConstants.
Returns:: The post-processed flux field
Return type:: np.ndarray

assemble_SI()[source]

Assembles the operator S_I as a sparse array.

Returns:: S_I, a right inverse of the B-operator
Return type:: sps.sparray

Notes

This will be slow for large systems. If you only need the action of S_I, consider using self.solve() instead.

solve_transpose(rhs)[source]

Post-process the pressure by performing a transposed solve.

Parameters:: rhs (np.ndarray) – Right-hand side, usually the mass matrix times the flux minus boundary terms.
Returns:: The post-processed pressure field
Return type:: np.ndarray

class pygeon.numerics.spanningtree.SpanningTreeElasticity(mdg, starting_faces='first_bdry')[source]

Bases: SpanningTree

Represents a class for computing the spanning tree for the elastic problem.

setup_system(mdg, flagged_faces)[source]

Set up the system for the spanning tree algorithm.

Parameters:

mdg (pg.MixedDimensionalGrid) – The mixed-dimensional grid.
flagged_faces (np.ndarray) – Array of flagged faces.

Returns:

None

compute_expand(sd, flagged_faces)[source]

Compute the expanded matrix for spanning tree computation.

Parameters:

sd (pg.Grid) – The grid object.
flagged_faces (np.ndarray) – Array of flagged faces.

Returns:

The expanded matrix for spanning tree computation.

Return type:

sps.csc_array

compute_system(sd)[source]

Computes the system matrix for the given grid.

Parameters:: sd (pg.Grid) – The grid object representing the domain.
Returns:: The computed system matrix.
Return type:: sps.csc_array

class pygeon.numerics.spanningtree.SpanningTreeCosserat(mdg, starting_faces='first_bdry')[source]

Bases: SpanningTreeElasticity

Represents a class for computing the spanning tree for the Cosserat problem.

compute_expand(sd, flagged_faces)[source]

Compute the expanded matrix for spanning tree computation.

Parameters:

sd (pg.Grid) – The grid object.
flagged_faces (np.ndarray) – Array of flagged faces.

Returns:

The expanded matrix for spanning tree computation.

Return type:

sps.csc_array

compute_system(sd)[source]

Computes the system matrix for the given grid.

Parameters:: sd (pg.Grid) – The grid object representing the domain.
Returns:: The computed system matrix.
Return type:: sps.csc_array

class pygeon.numerics.spanningtree.SpanningWeightedTrees(mdg, spt, weights, starting_faces=None)[source]

Bases: object

Class that can perform a spanning weighted trees solve, based on one of the previously introduced classes SpanningTree and SpanningTreeElasticity. It works very similarly to the previous one by considering multiple trees instead.

__init__(mdg, spt, weights, starting_faces=None)[source]

Constructor of the class.

Parameters:

mdg (pg.MixedDimensionalGrid) – The mixed dimensional grid.
spt (object) – The spanning tree object to use.
weights (np.ndarray) – The weights to impose for each spanning tree, they need to sum to 1.
starting_faces (np.ndarray) – The set of starting faces, if not specified equi-distributed boundary faces are selected.

solve(f)[source]

Perform a spanning weighted trees solve to compute a conservative flux field for given mass source.

Parameters:: f (np.ndarray) – Mass source, integrated against PwConstants.
Returns:: The post-processed flux field.
Return type:: np.ndarray

assemble_SI()[source]

Assembles the operator S_I as a sparse array. NOTE: This will be slow for large systems. If you only need the action of S_I, consider using self.solve() instead.

Returns:: S_I, a right inverse of the B-operator
Return type:: sps.sparray

solve_transpose(rhs)[source]

Post-process the pressure by performing a transposed solve.

Parameters:: rhs (np.ndarray) – Right-hand side, usually the mass matrix times the flux minus boundary terms.
Returns:: The post-processed pressure field.
Return type:: np.ndarray

find_starting_faces(mdg, num)[source]

Find the starting faces for each spanning tree if None is provided in the constructor. By default, an equidistribution of boundary faces is constructed.

Parameters:

mdg (pg.MixedDimensionalGrid) – The (mixed dimensional) grid.
num (int) – Number of faces to be selected.

Returns:

The selected faces at the boundary.

Return type:

np.ndarray