FEM Mesh - how to get elements belonging to ElementMarker

Question

I want to get a list of all boundary elements belonging to a certain ElementMarker of a boundary mesh.

This code creates a simple mesh and allows to inspect the ElementMarkers of the boundary mesh.

<< NDSolve`FEM`

cubi = Cuboid[{0, 0, 0}, {1, 1, 1}];
mesh = DiscretizeRegion[cubi, MaxCellMeasure -> 1];
bmesh = ToBoundaryMesh[mesh];

(*inspect element markers*)
groups = bmesh["BoundaryElementMarkerUnion"]
temp = Most[Range[0, 1, 1/(Length[groups])]];
colors = ColorData["BrightBands"][#] & /@ temp;
surfaces = 
  AssociationThread[groups, 
   bmesh["Wireframe"[ElementMarker == #, 
       "MeshElementStyle" -> FaceForm[colors[[#]]]]] & /@ groups];

Manipulate[
  Show[{bmesh["Edgeframe"], choices /. surfaces}],
  {{choices, groups}, groups, CheckboxBar},
  ControlPlacement -> Top
]

With bmesh["Wireframe"[ElementMarker == 1]] I can visualize a specific boundary part:

While bmesh["BoundaryElements"] returns all the triangles of the boundary:

{TriangleElement[{{5, 6, 1}, {5, 7, 6}, {4, 3, 8}, {4, 1, 3}, {4, 8, 
1}, {2, 3, 1}, {2, 7, 3}, {2, 6, 7}, {2, 1, 6}, {8, 3, 7}, {5, 1, 
8}, {5, 8, 7}}, {1, 2, 3, 4, 5, 4, 6, 6, 1, 3, 5, 2}]}

How can I use something like bmesh["BoundaryElements"] in a way that it gives me all the boundary elements that belong to a certain ElementMarker?

Answer 1

Two things you can do:

Group them by marker and extract what you want:

bele = bmesh["BoundaryElements"];
MeshElementSplitByMarker[bele]

{{TriangleElement[{{5, 6, 1}, {2, 1, 6}}, {1, 1}], 
  TriangleElement[{{5, 7, 6}, {5, 8, 7}}, {2, 2}], 
  TriangleElement[{{4, 3, 8}, {8, 3, 7}}, {3, 3}], 
  TriangleElement[{{4, 1, 3}, {2, 3, 1}}, {4, 4}], 
  TriangleElement[{{4, 8, 1}, {5, 1, 8}}, {5, 5}], 
  TriangleElement[{{2, 7, 3}, {2, 6, 7}}, {6, 6}]}}

or find the positions and extract what you want:

pos = Position[ElementMarkers[bele], Alternatives @@ {1, 6}];
elePart = Union[pos[[All, 1]]];
theseElements = 
 Function[{part}, 
   MeshElementByPart[bele[[part]], 
    Select[pos, First[#] == part &][[All, 2]]] ] /@ elePart

{TriangleElement[{{5, 6, 1}, {2, 7, 3}, {2, 6, 7}, {2, 1, 6}}, {1, 6, 
   6, 1}]}