pymor.discretizers.builtin.grids.oned

Module Contents

class pymor.discretizers.builtin.grids.oned.OnedGrid(domain=(0, 1), num_intervals=4, identify_left_right=False)

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

One-dimensional Grid on an interval.

Parameters:

• domain – Tuple (left, right) containing the left and right boundary of the domain.

• num_intervals – The number of 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 = 1

reference_element

bounding_box()

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

embeddings(codim)

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=1, **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 1).

• kwargs – See visualize