# DMPlexStratify#

Computes the strata for all points in the DMPLEX

## Synopsis#

#include "petscdmplex.h"
PetscErrorCode DMPlexStratify(DM dm)


Collective

## Input Parameter#

• dm - The DMPLEX

## Notes#

The strata group all points of the same grade, and this function calculates the strata. This grade can be seen as the height (or depth) of the point in the DAG.

The DAG for most topologies is a graded poset (https://en.wikipedia.org/wiki/Graded_poset), and can be illustrated by a Hasse Diagram (https://en.wikipedia.org/wiki/Hasse_diagram). Concretely, DMPlexStratify() creates a new label named “depth” containing the depth in the DAG of each point. For cell-vertex meshes, vertices are depth 0 and cells are depth 1. For fully interpolated meshes, depth 0 for vertices, 1 for edges, and so on until cells have depth equal to the dimension of the mesh. The depth label can be accessed through DMPlexGetDepthLabel() or DMPlexGetDepthStratum(), or manually via DMGetLabel(). The height is defined implicitly by height = maxDimension - depth, and can be accessed via DMPlexGetHeightStratum(). For example, cells have height 0 and faces have height 1.

The depth of a point is calculated by executing a breadth-first search (BFS) on the DAG. This could produce surprising results if run on a partially interpolated mesh, meaning one that had some edges and faces, but not others. For example, suppose that we had a mesh consisting of one triangle (c0) and three vertices (v0, v1, v2), and only one edge is on the boundary so we choose to interpolate only that one (e0), so that

  cone(c0) = {e0, v2}
cone(e0) = {v0, v1}


If DMPlexStratify() is run on this mesh, it will give depths

   depth 0 = {v0, v1, v2}
depth 1 = {e0, c0}


where the triangle has been given depth 1, instead of 2, because it is reachable from vertex v2.

DMPlexStratify() should be called after all calls to DMPlexSymmetrize()

DMPlex: Unstructured Grids, DM, DMPLEX, DMPlexCreate(), DMPlexSymmetrize(), DMPlexComputeCellTypes()