pymor.discretizers.builtin.grids.subgrid

Module Contents

class pymor.discretizers.builtin.grids.subgrid.SubGrid(parent_grid, parent_entities)

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

A subgrid of a Grid.

Given a Grid and a list of codim-0 entities we construct the minimal subgrid of the grid, containing all the given entities.

Parameters:

• parent_grid – Grid of which a subgrid is to be created.

• parent_entities – NumPy array of global indices of the codim-0 entities which are to be contained in the subgrid.

parent_grid

The Grid from which the subgrid was constructed. SubGrid only stores a weakref to the grid, so accessing this property might return None if the original grid has been destroyed.

Methods

embeddings	Return embeddings.
indices_from_parent_indices	Maps indices of codim-codim entities of the parent grid to indices of the subgrid.
parent_indices	retval[e] is the index of the e-th codim-codim entity in the parent grid.
size	The number of entities of codimension codim.
subentities	Return subentities.

reference_element = None

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.

indices_from_parent_indices(ind, codim)

Maps indices of codim-codim entities of the parent grid to indices of the subgrid.

Parameters:

• ind – NumPy array of indices of codim-codim entities of the parent grid

• codim – codim of the entities indicated by ind

Raises:

ValueError – Not all provided indices correspond to entities contained in the subgrid.

parent_indices(codim)

retval[e] is the index of the e-th codim-codim entity in the parent grid.

size(codim)

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)

pymor.discretizers.builtin.grids.subgrid.make_sub_grid_boundary_info(sub_grid, parent_grid, parent_grid_boundary_info, new_boundary_type=None)

Derives a BoundaryInfo for a SubGrid.

Parameters:

• sub_grid – The SubGrid for which a BoundaryInfo is created.

• parent_grid – The parent Grid.

• parent_grid_boundary_info – The BoundaryInfo of the parent Grid from which to derive the BoundaryInfo

• new_boundary_type – The boundary type which is assigned to the new boundaries of subgrid. If None, no boundary type is assigned.

Returns:

|BoundaryInfo| associated with sub_grid.