porepy.grids.grid_extrusion module

This module contains functionality to to increase the dimensions of grids by extrusion in the z-direction.

Both, single grids and mixed-dimensional grids can be extruded. The dimension of the highest-dimensional grid should be 2 at most.

The two functions performing above are

extrude_grid(g, z)[source]

Increases the dimension of a given grid by 1, by extruding the grid in the z-direction.

The original grid is assumed to be in the xy-plane, that is, any existing non-zero z-direction is ignored.

Both, the original and the new grid will have their geometry computed.

Parameters

  • g (Grid) – Original grid to be extruded. Must have dimension 0, 1 or 2.

  • z (ndarray) – An array containing z-coordinates per node for the extruded grid. Should be either non-negative or non-positive, and be sorted in increasing or decreasing order, respectively.

Raises

  • ValueError – If the z-coordinates for nodes contain both positive and negative values.

  • ValueError – If a 3D grid is provided for extrusion.

Returns

A 3-tuple containing

Grid:

The extruded grid of dimension g.dim + 1.

ndarray:

Cell mappings, such that that row i gives all indices of cells in the extruded grid that comes from cell i in the original grid.

ndarray:

Face mappings, s.t. row i gives all indices of faces in the extruded grid that come from face i in the original grid.

Return type

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

extrude_grid_bucket(mdg, z)[source]

Extrude a mixed-dimensional grid by extending all fixed-dimensional grids in the z-direction.

In practice, the original grid bucket will be 2D, and the result is 3D.

The returned mixed-dimensional grid is fully functional, including mortar grids on the mdg edges. The data dictionaries on subdomains and interfaces are mainly empty. Data can be transferred from the original md-grid via the returned map between old and new grids.

Parameters

  • mdg (MixedDimensionalGrid) – Mixed-dimensional grid to be extruded. The highest dimension should be 2D.

  • z (ndarray) – An array containing z-coordinates per node for the extruded grid. Should be either non-negative or non-positive, and be sorted in increasing or decreasing order, respectively.

Returns

A 2-tuple containing

MixedDimensionalGrid:

A mixed-dimensional grid with highest dimension 3. The data dictionaries on subdomains and interfaces are mostly empty.

dict:

Mapping from individual grids in the old mixed-dimensional grid to the corresponding extruded grids in the new one. The dictionary values are a named tuple with elements grid (new grid), cell_map and face_map, where the two latter describe mapping between the new and old grid, see extrude_grid() for details.

Return type

tuple[porepy.grids.md_grid.MixedDimensionalGrid, dict]