porepy.grids.md_grid module

A module to store the grid hierarchy formed by a set of fractures and their intersections along with a surrounding matrix in the form of a mixed-dimensional grid.

class MixedDimensionalGrid[source]

Bases: object

Container for the hierarchy of grids formed by fractures and their intersections along with a surrounding matrix.

add_interface(intf, sd_pair, primary_secondary_map)[source]

Add an interface to the mixed-dimensional grid.

Note

If the grids have different dimensions, the coupling will be defined with the higher-dimensional grid as the first (primary) subdomain. For equal dimensions, the ordering of the subdomains is the same as in input grids.

Parameters

intf (MortarGrid) – MortarGrid that represents this interface.
sd_pair (tuple[porepy.grids.grid.Grid, porepy.grids.grid.Grid]) –
len==2

A 2-tuple containing grids to be connected. The ordering is arbitrary.
primary_secondary_map (spmatrix) –
Identity mapping between faces in the higher-dimensional grid and cells in the lower-dimensional grid. No assumptions are made on the type of the object at this stage.

In the grids[0].dim = grids[1].dim case, the mapping is from faces of the first grid to faces of the second one. In the co-dimension 2 case, it maps from cells to cells.

Raises

ValueError – If the interface is not specified by exactly two grids
ValueError – If the interface already exists.
ValueError – If the two grids are not between zero and two dimensions apart.

Return type

None

add_subdomains(new_subdomains)[source]

Add new subdomains to the mixed-dimensional grid.

Parameters: new_subdomains (Union[Grid, Iterable[Grid]]) – The subdomains to be added. None of these should have been added previously.
Raises: ValueError – If a subdomain is already present in the mixed-dimensional grid.
Return type: None

argsort_grids(grids)[source]

Return indices that would sort the subdomains or interfaces.

Sorting is done according to two criteria:

Descending dimension.

Ascending (mortar) grid ID (for each dimension). The ID is assigned on instantiation of a (mortar) grid. The codimension is not considered for interfaces.

Example

>>> inds = mdg.argsort_grids(subdomain_list)
>>> sorted_subdomains = [subdomain_list[i] for i in inds]

Parameters: grids (Iterable[Union[Grid, MortarGrid]]) – List of subdomain grids.
Returns: Array that sorts the grids with shape=(len(grids),).
Return type: ndarray

boundaries(dim=None)[source]

Get a sorted list of boundary grids in the mixed-dimensional grid.

Optionally, the boundary grids can be filtered by dimension.

Sorting by descending boundary dimension and increasing BoundaryGrid id, see argsort_grids().

Parameters

dim (Optional[int]) –

default=None

If provided, only boundary grids of the specified dimension will be returned.

Returns

A list of boundary grids.

Return type

list[porepy.grids.boundary_grid.BoundaryGrid]

compute_geometry()[source]

Compute geometric quantities for each contained grid.

Return type: None

copy()[source]

Make a shallow copy of the mixed-dimensional grid. The underlying subdomain and interface grids are not copied.

Returns: Copy of this mixed-dimensional grid.
Return type: MixedDimensionalGrid

diameter(cond=None)[source]

Compute the cell diameter (mesh size) of the mixed-dimensional grid.

A function can be passed to filter subdomains and/or interfaces.

Parameters

cond (Optional[Callable[[Union[Grid, MortarGrid]], bool]]) –

default=None

Predicate with a subdomain or interface as input.

Returns

The diameter of the mixed-dimensional grid.

Return type

float

dim_max()[source]

Get the maximal dimension represented in the grid.

Returns: Maximum dimension of the grids present in the hierarchy.
Return type: int

dim_min()[source]

Get the minimal dimension represented in the mixed-dimensional grid.

Returns: Minimum dimension of the grids present in the hierarchy.
Return type: int

interface_data(intf)[source]

Getter for the interface data dictionary.

Parameters: intf (MortarGrid) – The mortar grid associated with the interface.
Returns: The data dictionary associated with the interface.
Return type: dict

interface_to_subdomain_pair(intf)[source]

Obtain the subdomains of an interface.

The subdomains will be given in descending order with respect to their dimension. If the interface is between grids of the same dimension, ascending subdomain ordering (as defined by sort_subdomain_tuple()) is used.

Parameters

intf (MortarGrid) – The mortar grid associated with an interface.

Returns

A 2-tuple containing

The primary subdomain neighboring this interface. Normally, this will be the subdomain with the higher dimension.

The secondary subdomain neighboring this interface. Normally, this will be the subdomain with the lower dimension.

Return type

tuple[porepy.grids.grid.Grid, porepy.grids.grid.Grid]

interfaces(return_data: Literal[False] = False, dim: Optional[int] = None) → list[porepy.grids.mortar_grid.MortarGrid][source]

interfaces(return_data: Literal[True], dim: Optional[int] = None) → list[tuple[porepy.grids.mortar_grid.MortarGrid, dict]]

Get a sorted list of interfaces in the mixed-dimensional grid.

Optionally, the interfaces can be filtered on dimension. Also, the data dictionary belonging to the interfaces can be returned.

Sorting by descending interface dimension and increasing MortarGrid ID, see argsort_grids().

Parameters

return_data –
default=False

If True, the data dictionary of the interface will be returned together with the interface mortar grids. Defaults to False.
dim –
default=None

If provided, only interfaces of the specified dimension will be returned.

Returns

Either a list of mortar grids associated with interfaces (default), or (if return_data=True) list of tuples, where the first tuple item is the interface mortar grid, the second is the associated data dictionary.

neighboring_subdomains(sd, only_higher=False, only_lower=False)[source]

Get the subdomain neighbors of a subdomain (going through interfaces).

Optionally, return only neighbors corresponding to higher or lower dimension. At most one of only_higher and only_lower can be True.

Parameters

sd (Grid) – Subdomain in the mixed-dimensional grid.
only_higher (bool) –
default=False

Consider only the higher-dimensional neighbors.
only_lower (bool) –
default=False

Consider only the lower-dimensional neighbors.

Raises

ValueError – If both only_higher and only_lower are True.

Returns

Subdomain neighbors of sd.

Return type

list[porepy.grids.grid.Grid]

num_interface_cells(cond=None)[source]

Compute the total number of mortar cells of the mixed-dimensional grid.

A function can be passed to filter interfaces.

Parameters

cond (Optional[Callable[[MortarGrid], bool]]) –

default=None

Predicate with an interface as input.

Returns

The total number of mortar cells of the grid bucket.

Return type

int

num_interfaces()[source]

Returns: Total number of interfaces in the mixed-dimensional grid.
Return type: int

num_subdomain_cells(cond=None)[source]

Compute the total number of subdomain cells of the mixed-dimensional grid.

A function can be passed to filter subdomains.

Parameters

cond (Optional[Callable[[Grid], bool]]) –

default=None

Predicate with a subdomain as input.

Returns

The total number of subdomain cells of the grid bucket.

Return type

int

num_subdomains()[source]

Returns: Total number of subdomains in the mixed-dimensional grid.
Return type: int

remove_subdomain(sd)[source]

Remove a subdomain and related interfaces from the mixed-dimensional grid.

Parameters: sd (Grid) – The subdomain to be removed.
Return type: None

replace_subdomains_and_interfaces(sd_map=None, intf_map=None, tol=1e-6)[source]

Replace grids and/or mortar grids in the mixed-dimensional grid.

Parameters

sd_map (Optional[dict[porepy.grids.grid.Grid, porepy.grids.grid.Grid]]) –
default=None

Mapping between the old and new grids. Keys are the old grids, and values are the new grids.
intf_map (Optional[dict[porepy.grids.mortar_grid.MortarGrid, Union[porepy.grids.mortar_grid.MortarGrid, dict[porepy.grids.mortar_grid.MortarSides, porepy.grids.grid.Grid]]]]) –
default=None

Mapping between the old mortar grid and new (side grids of the) mortar grid. Keys are the old mortar grids, and values are dictionaries with side grid number as keys, and side grids as values. Optionally, the mapping can be directly from old to new mortar grid (sometimes it is easier to construct the new mortar grid right away, before replacing it in the mixed-dimensional grid).
tol (float) –
default=1e-6

Geometric tolerance used when updating mortar projections.

Return type

None

sort_interfaces(interfaces)[source]

Sort interfaces.

Sorting by descending interface dimension and increasing MortarGrid ID, see argsort_grids().

Parameters: interfaces (list[porepy.grids.mortar_grid.MortarGrid]) – list of interfaces.
Returns: List containing the same interfaces, sorted.
Return type: list[porepy.grids.mortar_grid.MortarGrid]

sort_subdomain_tuple(subdomains)[source]

Sort two subdomains.

Sorting by descending subdomain dimension and increasing node ID, see argsort_grids().

Parameters

subdomains (tuple[porepy.grids.grid.Grid, porepy.grids.grid.Grid]) –

len=2

Tuple of two subdomains.

Returns

Tuple containing the same two subdomains, sorted.

Return type

tuple[porepy.grids.grid.Grid, porepy.grids.grid.Grid]

sort_subdomains(subdomains)[source]

Sort subdomains.

Sorting by descending subdomain dimension and increasing node ID, see argsort_grids().

Parameters: subdomains (list[porepy.grids.grid.Grid]) – List of subdomains.
Returns: List containing the same subdomains, sorted.
Return type: list[porepy.grids.grid.Grid]

subdomain_data(sd)[source]

Getter for the subdomain data dictionary.

Parameters: sd (Grid) – The subdomain grid.
Returns: The data dictionary associated with the subdomain.
Return type: dict

subdomain_pair_to_interface(sd_pair)[source]

Get an interface from a pair of subdomains.

Parameters: sd_pair (tuple[porepy.grids.grid.Grid, porepy.grids.grid.Grid]) – Pair of subdomains. Should exist in the mixed-dimensional grid.
Raises: KeyError – If the subdomain pair is not represented in the mixed-dimensional grid.
Returns: The interface that connects the subdomain pairs, represented by a MortarGrid.
Return type: MortarGrid

subdomain_to_boundary_grid(sd)[source]

Get the boundary grid associated with a subdomain.

Parameters: sd (Grid) – A subdomain in the mixed-dimensional grid.
Returns: The boundary grid associated with this subdomain.
Return type: BoundaryGrid

subdomain_to_interfaces(sd)[source]

Iterator over the interfaces of a specific subdomain.

Parameters: sd (Grid) – A subdomain in the mixed-dimensional grid.
Returns: Sorted list of interfaces associated with the subdomain (see sort_interfaces()).
Return type: list[porepy.grids.mortar_grid.MortarGrid]

subdomains(return_data: Literal[False] = False, dim: Optional[int] = None) → list[porepy.grids.grid.Grid][source]

subdomains(return_data: Literal[True], dim: Optional[int] = None) → list[tuple[porepy.grids.grid.Grid, dict]]

Get a sorted list of subdomains in the mixed-dimensional grid.

Optionally, the subdomains can be filtered by dimension. Also, the data dictionary belonging to the subdomain can be returned.

Sorted by descending subdomain dimension and increasing Grid ID, see argsort_grids().

Parameters

return_data –
default=False

If True, the data dictionary of the subdomain will be returned together with the subdomain grids.
dim –
default=None

If provided, only subdomains of the specified dimension will be returned.

Returns

Either a list of grids associated with subdomains (default), or (if return_data=True) list of tuples, where the first tuple item is the subdomain grid, the second is the associated data dictionary.

name: Name of the md-grid, initiated as 'Mixed-dimensional grid'.