`pymor.discretizers.builtin.grids.oned`¶

Module Contents¶

Classes¶

 `OnedGrid` One-dimensional `Grid` on an interval.
class pymor.discretizers.builtin.grids.oned.OnedGrid(domain=(0, 1), num_intervals=4, identify_left_right=False)[source]

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.

dim = 1[source]
reference_element[source]
__reduce__(self)[source]

Helper for pickle.

__str__(self)[source]

Return str(self).

size(self, codim=0)[source]

The number of entities of codimension `codim`.

subentities(self, codim, subentity_codim)[source]

`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)`

embeddings(self, codim)[source]

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.

bounding_box(self)[source]

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

orthogonal_centers(self)[source]

`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.)

visualize(self, U, codim=1, **kwargs)[source]

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 1).

kwargs