Obtain the coodinates of boundary mesh with particular mesh marker

Question

This is a very simple question, however, I haven't been able to find straight forward documentation for this. I have a region that I have converted to an element mesh (which we can visualize with 'wireframe'):

reg = ImplicitRegion[True, {{x, -10, 10}, {y, -10, 10}}];
mesh1 = ToElementMesh[reg, 
   "BoundaryMeshGenerator" -> {"Continuation"}, MaxCellMeasure -> .5, 
   "MaxBoundaryCellMeasure" -> 0.3];
mesh1["Wireframe"]

I would like the coordinates of the mesh on at the boundary of y=-10. So I could write

bmesh1 = ToBoundaryMesh[mesh1]
linecoords = Select[bmesh1["Coordinates"], #[[2]] == -10. &]

However, I was wondering if there is a way to get the same result by using Element Markers instead of Select. Plotting with

mesh1["Wireframe"["MeshElement" -> "BoundaryElements", 
  "MeshElementMarkerStyle" -> Red]]

shows that the y=-10 boundary have element marker 1. So I would like to say something like linecoords = bmesh1["ElementMarker"==1]["Coordinates"], but I can't seem to find the right syntax for it.

Answer 1

Similar to this answer you can use:

Needs["NDSolve`FEM`"]
reg = ImplicitRegion[True, {{x, -10, 10}, {y, -10, 10}}];
mesh1 = ToElementMesh[reg, 
   "BoundaryMeshGenerator" -> {"Continuation"}, MaxCellMeasure -> .75,
    "MaxBoundaryCellMeasure" -> 0.5];
(*mesh1["Wireframe"]*)

mesh1["Wireframe"[ElementMarker == 1, 
  "MeshElement" -> "BoundaryElements", 
  "MeshElementMarkerStyle" -> Red]]

Or for point elements:

mesh1["Wireframe"[ElementMarker == 1, 
  "MeshElement" -> "PointElements", "MeshElementMarkerStyle" -> Red]]

Now, if you need the actual coordinates you could use the following helper functions:

getCoords[mesh_, meshElement_, whichMarker_] := Module[
  {pos, gc},
  pos = Flatten[{ElementMarker /. 
      Solve[whichMarker, ElementMarker]}];
  pos = Alternatives @@ pos;
  pos = Position[ElementMarkers[mesh[meshElement]], pos];
  gc = ElementMeshToGraphicsComplex[mesh, pos, 
    "MeshElement" -> meshElement];
  If[meshElement == "PointElements",
   gc[[1]][[Flatten[Flatten[gc[[2]]][[All, 1]], 1]]]
   ,
   gc[[1]][[#]] & /@ Flatten[Flatten[t][[All, 1]], 1]
   ]
  ]

You'd then

coords = getCoords[mesh1, "PointElements", ElementMarker == 1];
Graphics[Point[coords]]

It's not 100% ideal but it will do the job.

If you just want the coordinates, then this is probably a better way:

pts = mesh1["Coordinates"];
pEle = mesh1["PointElements"];
theseEle = MeshElementByMarkerPredicate[pEle, {_?(# == 1 &)}];
GetElementCoordinates[pts, Flatten[ElementIncidents[theseEle]]]

Hope this helps.