pymor.discretizers.builtin.grids.tria

Module Contents

class pymor.discretizers.builtin.grids.tria.TriaGrid(num_intervals=(2, 2), domain=([0, 0], [1, 1]), identify_left_right=False, identify_bottom_top=False)

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

Basic implementation of a triangular grid on a rectangular domain.

The global face, edge and vertex indices are given as follows

6---------10----------7---------11----------8
| \                 / | \                 / |
|    22   10    18    |    23   11    19    |
|       \     /       |       \     /       |
3    14   11     6    4    15   12     7    5
|       /     \       |       /     \       |
|    14    2    26    |    15    3    27    |
| /                 \ | /                 \ |
3----------8----------4----------9----------5
| \                 / | \                 / |
|    20    8    16    |    21    9    17    |
|       \     /       |       \     /       |
0    12    9     4    1    13   10     5    2
|       /     \       |       /     \       |
|    12    0    24    |    13    1    25    |
| /                 \ | /                 \ |
0----------6----------1----------7----------2

Parameters:

• num_intervals – Tuple (n0, n1) determining a grid with n0 x n1 codim-0 entities.

• domain – Tuple (ll, ur) where ll defines the lower left and ur the upper right corner of the domain.

• identify_left_right – If True, the left and right boundaries are identified, i.e. the left-most codim-0 entities become neighbors of the right-most codim-0 entities.

• identify_bottom_top – If True, the bottom and top boundaries are identified, i.e. the bottom-most codim-0 entities become neighbors of the top-most codim-0 entities.

Methods

bounding_box	Returns a (2, dim)-shaped array containing lower/upper bounding box coordinates.
embeddings	Return embeddings.
orthogonal_centers	Return orthogonal centers.
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

bounding_box()

Returns a (2, dim)-shaped array containing lower/upper bounding box coordinates.

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.

orthogonal_centers()

Return orthogonal centers.

retval[e] is a point inside the codim-0 entity with global index e such that the line segment from retval[e] to retval[e2] is always orthogonal to the codim-1 entity shared by the codim-0 entities with global index e and e2.

(This is mainly useful for gradient approximation in finite volume schemes.)

size(codim=0)

The number of entities of codimension codim.

subentities(codim, subentity_codim)

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 U.shape[1] > 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 number of time points per array must match.

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

• kwargs – See visualize