Connectivity Representations

While meshes are primarily defined as a collection of elements, with each element being defined by referencing the nodes that comprise it, a variety of data structures can be constructed to represent connections between different mesh entities, such as nodes, elements, edges, and faces which may be useful for performing different mesh operations or analysis. Each connectivity type is represented as a 2D data structure, with each row corresponding one entity and containing indices associated with another (e.g. each row of NodeConn corresponds to an element and contains indices associated with the list of nodes). Most of these data structures are non-rectangular (or “ragged”) as the number of connections per entity may vary. The connectivities listed in the following table can all be obtained from the the node connectivity list (NodeConn) using either the mesh class (see Working with the mesh class) or the converter module.

Connectivity Type	Row Correspondence	Index Association
Node Connectivity (NodeConn)	Element	Node
Node Neighbors (NodeNeighbors)	Node	Node
Element Connectivity (ElemConn)	Node	Element
Element Neighbors (ElemNeighbors)	Element	Element
Edges (Edges) [1]	Edge	Node
Edge Connectivity ( EdgeConn )	Element	Edge
Edge-Element (EdgeElemConn)	Edge	Element
Faces (Faces) [1]	Face	Node
Face Connectivity (FaceConn)	Element	Face
Face-Element (FaceElemConn)	Face	Element

[1] (1,2)

Edges and faces can be represented as “half-edges” and “half-faces” where at shared edges/faces, there multiple two half-edges/faces with each one being associated with only one element and having a specific orientation. When obtained through the mesh class (Edges, Faces), they are the “full” rather than the “half” representation. Half-edges and half-faces can be obtained through converter.solid2edges() and converter.solid2faces() and converted to full-edges and full-faces using converter.edges2unique() and converter.faces2unique().

2D Example

The below example shows several connectivity representations of the same mesh consisting, of three triangular elements. In each case, the entity corresponding to the first row is indicated in blue and the associated connections are indicated in red.

NodeCoords = [[0,0,0], [1,.1,0], [.9,.9,0], [-.1,1,0], [-.5,.5,0]]
NodeConn = [[0, 1, 3], [1, 2, 3], [0, 3, 4]]

NodeNeighbors = [[3, 4, 1],
                 [0, 2, 3],
                 [1, 3],
                 [1, 2, 0, 4],
                 [3, 0]]

ElemNeighbors = [[1, 2],
                 [0],
                 [0]]

ElemConn = [[0, 2],
            [0, 1],
            [1],
            [0, 1, 2],
            [2]]

Edges = [[0, 1],
         [3, 0],
         [4, 0],
         [1, 2],
         [1, 3],
         [2, 3],
         [3, 4]]

EdgeConn = [[0, 4, 1],
            [3, 5, 4],
            [1, 6, 2]]

EdgeElemConn = [[0],
                [0, 2],
                [2],
                [1],
                [0, 1],
                [1],
                [2]]