pymor.discretizers.builtin.grids.unstructured

Module Contents

class pymor.discretizers.builtin.grids.unstructured.UnstructuredTriangleGrid(sizes, subentity_data, embedding_data)

Bases: pymor.discretizers.builtin.grids.interfaces.Grid

A generic unstructured, triangular grid.

Use from_vertices to instantiate the grid from vertex coordinates and connectivity data.

Methods

embeddings	Return embeddings.
from_vertices	Instantiate grid from vertex coordinates and connectivity data.
size	The number of entities of codimension codim.
subentities	Return subentities.
visualize	Visualize scalar data associated to the grid as a patch plot.

dim = 2

reference_element

embeddings(codim=0)

Return embeddings.

Returns tuple (A, B) where A[e] and B[e] are the linear part and the translation part of the map from the reference element of e to e.

For codim > 0, we provide a default implementation by taking the embedding of the codim-1 parent entity e_0 of e with lowest global index and composing it with the subentity_embedding of e into e_0 determined by the reference element.

classmethod from_vertices(vertices, faces)

Instantiate grid from vertex coordinates and connectivity data.

Parameters:

• vertices – A (num_vertices, 2)-shaped NumPy array containing the coordinates of all vertices in the grid. The row numbers in the array will be the global indices of the given vertices (codim 2 entities).

• faces – A (num_faces, 3)-shaped NumPy array containing the global indices of the vertices which define a given triangle in the grid. The row numbers in the array will be the global indices of the given triangles (codim 0 entities).

size(codim=0)

The number of entities of codimension codim.

subentities(codim=0, subentity_codim=None)

Return subentities.

retval[e,s] is the global index of the s-th codim-subentity_codim subentity of the codim-codim entity with global index e.

The ordering of subentities(0, subentity_codim)[e] has to correspond, w.r.t. the embedding of e, to the local ordering inside the reference element.

For codim > 0, we provide a default implementation by calculating the subentities of e as follows:

1. Find the codim-1 parent entity e_0 of e with minimal global index

2. Lookup the local indices of the subentities of e inside e_0 using the reference element.

3. Map these local indices to global indices using subentities(codim - 1, subentity_codim).

This procedures assures that subentities(codim, subentity_codim)[e] has the right ordering w.r.t. the embedding determined by e_0, which agrees with what is returned by embeddings(codim)

visualize(U, codim=2, **kwargs)

Visualize scalar data associated to the grid as a patch plot.

Parameters:

• U – NumPy array of the data to visualize. If U.dim == 2 and len(U) > 1, the data is visualized as a time series of plots. Alternatively, a tuple of NumPy arrays can be provided, in which case a subplot is created for each entry of the tuple. The lengths of all arrays have to agree.

• codim – The codimension of the entities the data in U is attached to (either 0 or 2).

• kwargs – See visualize

pymor.discretizers.builtin.grids.unstructured.compute_edges(subentities)