Topological basic operations

Subgraph and neighbours computation

The subgraph computation is done supposing that the mesh is topologically valid. The subgraph of a volume mesh is defined by a set of either faces, edges or vertices elements depending on the subgraph relative dimension.

The subgraph computation and the neighbours computation are tightly linked. The neighbours are defined as the elements that share a common lower dimensional element. For example, two volumes are neighbours if they share a common face, two faces are neighbours if they share a common edge, and so on.

In mefikit, the neighbours computation builds an adjacency graph, having as nodes the elements of the mesh and as edges the shared lower dimensional elements. Then, the neighbours of an element can be found by looking at its adjacent nodes in the graph.

Connectivity equivalence

There is different ways to represent the connectivity of an element. Here are the different class of equivalence:

• exact representation equality: two elements are equivalent if their connectivity is exactly the same, including the order of the nodes.
• rotational equivalence: two elements are equivalent if their connectivity can be made the same by rotating the order of the nodes. The topological shape is strictly equivalent under all operations, preserving the measure orientation.
• chiral equivalence: two elements are equivalent if their connectivity can be made the same by reversing the order of the nodes and rotating the nodes. This equivalence does not preserve the measure orientation (if it is positive or negative).
• node set equivalence: two elements are equivalent if they have the same set of nodes, regardless of the order. This equivalence is theoretical only, as it does not preserve the shape of the element. But it is very useful to detect duplicate elements in a mesh.