puncturedfem.PlanarMesh

Planar mesh geometry and topology.

The edges of the mesh are permitted to be curved, and mesh cells are permitted to be multiply connected.

edges meet at an interior angle strictly between 0 and 2 pi (no slits or cusps). Hanging nodes (i.e. an interior angle of pi) are permitted. Looped edges (edges with identical endpoints) are permitted under the same restrictions.

The mesh geometry is determined by the parameterization of the edges. The mesh topology is automatically determined by observing that each Edge is shared by the boundary of exactly two MeshCells.

Computations on the mesh dictate that the boundary of each MeshCell have an oriented boundary (counterclockwise on the outer boundary, clockwise on the inner boundary). Rather than storing the parameterization of each Edge twice (once for each MeshCell), we record the orientation of each Edge relative to the boundary of each MeshCell.

For instance, if the Edge is oriented counterclockwise to a MeshCell boundary, with that Edge lying on the outer boundary of this MeshCell, then the Edge is said to have positive orientation with respect to that MeshCell. Each Edge object stores the MeshCell index of the MeshCell on either side of the Edge, one positive and one negative. If the Edge is on the boundary of the domain, the "missing" MeshCell is assigned a negative MeshCell index.

Usage

See examples/ex0-mesh-building.ipynb for an example of how to build a mesh.

Attributes:

Name	Type	Description
num_edges	int	Number of edges in the mesh.
num_cells	int	Number of MeshCells in the mesh.
num_verts	int	Number of Vertices in the mesh.
edges	list[Edge]	List of edges in the mesh.
vert_idx_list	list[int]	List of vertex indices in the mesh, excluding Vertices of loops.
cell_idx_list	list[int]	List of MeshCell indices in the mesh.

Notes

• The vertex indices are taken to be nonnegative integers. These indices are not necessarily 0, 1, ...., num_verts - 1, but instead are determined by the indices assigned to the endpoints of the edges.
• The MeshCell indices are taken to be nonnegative integers, except for the case of edges on the boundary of the domain. In this case, the MeshCell index is assigned to be negative. Similar to the vertex indices, the MeshCell indices are not necessarily 0, 1, ...., num_cells - 1, but instead are determined by the indices assigned to the edges in the pos_cell_idx and neg_cell_idx attributes.

__init__(edges, verbose=True)

Initialize a PlanarMesh object.

Parameters:

Name	Type	Description	Default
edges	list[Edge]	List of edges in the mesh.	required
verbose	bool, optional	If True, print information about the mesh. Default is True.	True

__str__()

Return a string representation of the PlanarMesh object.

add_edge(e)

Add an Edge to the mesh.

Parameters:

Name	Type	Description	Default
e	Edge	Edge to add to the mesh.	required

add_edges(edges)

Add a list of edges to the mesh.

Parameters:

Name	Type	Description	Default
edges	list[Edge]	List of edges to add to the mesh.	required

edge_is_on_boundary(edge_idx)

Return True if the Edge with index edge_idx is on the boundary.

Parameters:

Name	Type	Description	Default
edge_idx	int	Index of the Edge.	required

Returns:

Type	Description
bool	True if the Edge is on the boundary, False otherwise.

get_abs_cell_idx(cell_idx)

Return the absolute MeshCell index of cell_idx.

Parameters:

Name	Type	Description	Default
cell_idx	int	Index of the MeshCell to return.	required

Returns:

Type	Description
int	Absolute index of the MeshCell.

get_cell(cell_idx)

Return the MeshCell with index cell_idx.

Parameters:

Name	Type	Description	Default
cell_idx	int	Index of the MeshCell to return.	required

Returns:

Type	Description
MeshCell	MeshCell with index cell_idx.

vert_is_on_boundary(vert_idx)

Return True if the vertex with index vert_idx is on the boundary.

Parameters:

Name	Type	Description	Default
vert_idx	int	Index of the vertex.	required

Returns:

Type	Description
bool	True if the vertex is on the boundary, False otherwise.