porepy.grids.mortar_grid module

A module containing the class for the mortar grid, a geometric representation of interfaces between two subdomains in the mixed-dimensional sense.

class MortarGrid(*args, **kwargs)

Bases: object

Parent class for mortar grids.

It contains two grids representing the left and right part of the mortar grid and the weighted mapping from the primary grid to the mortar grids and from the secondary grid to the mortar grids. The two mortar grids can be different. The primary grid is assumed to be one dimension higher than the mortar grids, while the secondary grid can either one dimension higher or the same dimension as the mortar grids.

Note

The mortar class is mostly tested for the case when the secondary grid has the same dimension as the mortar grid. Especially, the updating of any grid should not be expected to work and will most likely throw an error.

Parameters

• dim – Grid dimension.

• side_grids – Grid on each side.

• primary_secondary –

  default=None

  Cell-face relations between the higher dimensional grid and the lower dimensional grid. It is possible to not give the projection to create only the grid.

• codim –

  default=1

  Dimension difference between the primary grid secondary grid.

• name –

  default=''

  Name of the grid. Can also be used to set various information on the grid.

• face_duplicate_ind –

  default=None

  Which faces should be considered duplicates, and mapped to the second of the side_grids.

  If not provided, duplicate faces will be inferred from the indices of the faces.

  Will only be used if len(side_Grids)==2.

• tol –

  default=1e-6

  Tolerance used in geometric computations.

Raises

• ValueError – If dim==3 , The mortar grid can not be three-dimensional.

• ValueError – If the mortar grids have different dimensions.

• ValueError – If the number of sides is not 1 or 2.

• ValueError – If face_duplicate_ind is not None and the co-dimension is 2. In this case there are no faces to duplicate.

cell_diameters()

Returns

An array containing the diameters of each cell in the mortar grid and shape=(mortar_grid.num_cells,).

Return type

ndarray

compute_geometry()

Compute the geometry of the mortar grids.

We assume that they are not aligned with the x-axis (1D) or the x-y-plane (2D).

Performs calls to each grid’s compute_geometry().

Return type

None

mortar_to_primary_avg(nd=1)

Project values from the mortar to faces of primary, by averaging quantities from the mortar side.

The projection matrix is scaled so that the row sum is unity, that is, values on the primary side are computed as averages of values from the mortar side, according to the overlap between (in general several) mortar cells and a primary face.

This mapping is intended for intensive properties, e.g. pressures.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Projection matrix with row sum unity and shape=(nd*mortar_grid.num_cells, nd*g_primary.num_faces).

Return type

spmatrix

mortar_to_primary_int(nd=1)

Project values from the mortar to faces of primary, by summing quantities from the mortar side.

The projection matrix is scaled so that the column sum is unity, that is, values on the mortar side are distributed to the primary according to the overlap between a mortar cell and (in general several) primary faces.

This mapping is intended for extensive properties, e.g. fluxes.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Projection matrix with column sum unity and shape=(nd*mortar_grid.num_cells, nd*g_primary.num_faces).

Return type

spmatrix

mortar_to_secondary_avg(nd=1)

Project values from the mortar to secondary, by averaging quantities from the mortar side.

The projection matrix is scaled so that the row sum is unity, that is, values on the secondary side are computed as averages of values from the mortar side, according to the overlap between (in general several) mortar cells and a secondary cell.

This mapping is intended for intensive properties, e.g. pressures.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Projection matrix with row sum unity and shape=(nd*mortar_grid.num_cells, nd*g_secondary.num_faces).

Return type

spmatrix

mortar_to_secondary_int(nd=1)

Project values from the mortar to cells at the secondary, by summing quantities from the mortar side.

The projection matrix is scaled so that the column sum is unity, that is, values on the mortar side are distributed to the secondary according to the overlap between a mortar cell and (in general several) secondary cells.

This mapping is intended for extensive properties, e.g. fluxes.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Projection matrix with column sum unity and shape=(nd*mortar_grid.num_cells, nd*g_secondary.num_faces).

Return type

spmatrix

num_sides()

Shortcut to compute the number of sides. It has to be 2 or 1.

Returns

Number of sides.

Return type

int

primary_to_mortar_avg(nd=1)

Project values from faces of primary to the mortar, by averaging quantities from the primary side.

The projection matrix is scaled so that the row sum is unity, that is, values on the mortar side are computed as averages of values from the primary side, according to the overlap between (in general several) primary faces and a mortar cell.

This mapping is intended for intensive properties, e.g. pressures.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Projection matrix with row sum unity and shape=(nd*g_primary.num_faces, nd*mortar_grid.num_cells).

Return type

spmatrix

primary_to_mortar_int(nd=1)

Project values from faces of primary to the mortar, by summing quantities from the primary side.

The projection matrix is scaled so that the column sum is unity, that is, values on the primary side are distributed to the mortar according to the overlap between a primary face and (in general several) mortar cells.

This mapping is intended for extensive properties, e.g. fluxes.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Projection matrix with column sum unity and shape=(nd*g_primary.num_faces, nd*mortar_grid.num_cells).

Return type

spmatrix

project_to_side_grids()

Generator for the side grids and projection operators from the mortar cells, combining cells on all the sides, to the specific side grids.

Yields

A 2-tuple containing

csc_matrix:

Projection from the mortar cells to this side grid.

Grid:

PorePy grid representing one of the sides of the mortar grid. Can be used for standard discretizations.

Return type

Generator[tuple[scipy.sparse._base.spmatrix, porepy.grids.grid.Grid], None, None]

secondary_to_mortar_avg(nd=1)

Project values from cells at the secondary to the mortar, by averaging quantities from the secondary side.

The projection matrix is scaled so that the row sum is unity, that is, values on the mortar side are computed as averages of values from the secondary side, according to the overlap between (in general several) primary cells and the mortar cells.

This mapping is intended for intensive properties, e.g. pressures.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Projection matrix with row sum unity and shape=(nd*g_secondary.num_cells, nd*mortar_grid.num_cells).

Return type

spmatrix

secondary_to_mortar_int(nd=1)

Project values from cells on the secondary side to the mortar, by summing quantities from the secondary side.

The projection matrix is scaled so that the column sum is unity, that is, values on the secondary side are distributed to the mortar according to the overlap between a secondary cell and (in general several) mortar cells.

This mapping is intended for extensive properties, e.g. sources.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Projection matrix with column sum unity and shape=(nd*g_secondary.num_cells, nd*mortar_grid.num_cells).

Return type

spmatrix

sign_of_mortar_sides(nd=1)

Assign positive or negative weight to the two sides of a mortar grid.

This is needed e.g. to make projection operators into signed projections, for variables that have no particular defined sign conventions.

This function defines a convention for what is a positive jump between the mortar sides.

Example

Take the difference between right and left variables, and project to the secondary grid by

>>> mortar_to_secondary_avg() * sign_of_mortar_sides()

Notes

The flux variables in flow and transport equations are defined as positive from primary to secondary. Hence, the two sides have different conventions, and there is no need to adjust the signs further.

This method will probably not be meaningful if applied to mortar grids where the two side grids are non-matching.

Parameters

nd (int) –

default=1

Spatial dimension of the projected quantity. Defaults to 1 (mapping for scalar quantities).

Returns

Diagonal matrix with positive signs on variables belonging to the first of the side_grids and shape=(nd*mortar_grid.num_cells, nd*mortar_grid.num_cells).

Return type

spmatrix

update_mortar(new_side_grids, tol=None)

Update the low_to_mortar_int and high_to_mortar_int maps when the mortar grids are changed.

Parameters

• new_side_grids (dict[porepy.grids.mortar_grid.MortarSides, porepy.grids.grid.Grid]) – A dictionary containing for each side (identified with the enumeration MortarSides) a matrix representing the new mapping between the old and new mortar grids.

• tol (Optional[float]) –

  default=None

  Tolerance used for matching the new and old grids.

  If not provided, tol is used.

Raises

• ValueError – If the old and new mortar grids are not of the same dimension.

• ValueError – If the mortar grid is not of dimension 0,1 or 2.

Return type

None

update_primary(g_new, g_old, tol=None)

Update the _primary_to_mortar_int map when the primary (higher-dimensional) grid is changed.

Parameters

• g_new (Grid) – The new primary grid.

• g_old (Grid) – The old primary grid.

• tol (Optional[float]) –

  default=None

  Tolerance used for matching the new and old grids.

  If not provided, tol is used.

Raises

• ValueError – For 0d mortar grids, if the faces of the old primary grid do not correspond to the same physical point.

• NotImplementedError – If the dimension of the mortar grid is >1 (this has not been implemented yet).

Return type

None

update_secondary(new_g, tol=None)

Update the mappings between mortar and secondary grid when the latter is changed.

Note

This function assumes that the secondary grid is only updated once: A change from matching to non-matching between the mortar and secondary grids is okay, but replacing a non-matching secondary grid with another one will not work.

Parameters

• new_g (Grid) – The new secondary grid.

• tol (Optional[float]) –

  default=None

  Tolerance used for matching the new and old grids.

  If not provided, tol is used.

Raises

• NotImplementedError – If the new secondary grid and the mortar grid are not of the same dimension.

• ValueError – If the old and new secondary grids are not of the same dimension.

• ValueError – If the mortar grid is not of dimension 0,1 or 2.

Return type

None

cell_centers: ndarray

Cell centers of each cell in the side grids.

cell_volumes: ndarray

Cell volumes of each cell in the side grids.

codim

The co-dimension of the mortar grid.

dim

The ambient dimension of the mortar grid.

property id

Grid ID.

The returned attribute must not be changed. This may severely compromise other parts of the code, such as sorting in md grids.

The attribute is set in __new__(). This avoids calls to the super constructor in child classes.

name: list[str]

The name of mortar grid stored as a list of relevant information.

num_cells: int

Total number of cells in all side grids.

side_grids: dict[porepy.grids.mortar_grid.MortarSides, porepy.grids.grid.Grid]

A dictionary containing for each enumeration MortarSides the respective side grid.

sides: ndarray

An array containing the enumeration of each side grid (keys of side_grids).

tol

The tolerance given at instantiation.

class MortarSides(value)

Bases: Enum

A custom enumeration for the left, the right and empty side of an interface represented by a mortar grid.

LEFT_SIDE

NONE_SIDE

RIGHT_SIDE