Assigning Element Markers to 3D FEM Mesh

Question

I have created a 3D graphic using GraphicsComplex and then use ToElementMesh to generate a 3D Mesh that I want to solve a PDE on, but I cannot figure out how to apply ElementMarkers to the Boundaries. I am aware of the boundaryMarkerFunction but cannot seem to apply it correctly. Nice would be to apply the ElementMarkers to the faces of the 3D Graphic which is then Discretized using DiscretizeGraphics. Most examples of the boundaryMarkerFunction floating around seem to be for 2D meshes. In particular I would like to assign different boundary conditions to the base and fins of the object, therefore need appropriate ElementMarkers.

My Code is

Needs["NDSolve`FEM`"]

ft = 0.002;
fb = 0.005;
fh = 0.04;
bt = 0.005;
fins = 8;
w = 0.1;
l = 0.1;

g = (w - (fins*fb))/(fins - 1);
dfx = (fb - ft)/2;
dx = 2*dfx + ft + g;
nodes = 4*fins + 2;

base = {{0, y, 0}, {w, y, 0}, {w, y, bt}};
lastfin = {{dfx + ft, y, bt + fh}, {dfx, y, bt + fh}, {0, y, bt}};

restfins = 
Flatten[Table[{{w - dfx - i*dx, y, bt + fh}, {w - dfx - ft - i*dx, 
  y, bt + fh}, {w - 2*dfx - ft - i*dx, y, 
  bt}, {w - 2*dfx - ft - g - i*dx, y, bt}}, {i, 0, fins - 2}], 1];

 face1 = Join[base, restfins, lastfin] /. y -> 0;
 face2 = Join[base, restfins, lastfin] /. y -> l;
 fintops = 
 Table[{4 + 4 i, 4 + nodes + 4 i, 5 + nodes + 4 i, 5 + 4 i}, {i, 0, 
fins - 1}];
 basetops = 
 Table[{6 + 4 i, 6 + nodes + 4 i, 7 + nodes + 4 i, 7 + 4 i}, {i, 0, 
fins - 2}];
 finsidesright = 
 Table[{5 + 4 i, 5 + nodes + 4 i, 6 + nodes + 4 i, 6 + 4 i}, {i, 0, 
fins - 2}];
 finsidesleft = 
 Table[{7 + 4 i, 7 + nodes + 4 i, 8 + nodes + 4 i, 8 + 4 i}, {i, 0, 
fins - 2}];

 heatsink = 
 Graphics3D[
 GraphicsComplex[Join[face1, face2], 
 Polygon[Join[{Table[i, {i, 1, nodes}], 
  Table[i, {i, nodes + 1, 2*nodes}], {1, 2, 2 + nodes, 
   1 + nodes}, {2, 2 + nodes, 3 + nodes, 3}, {3, 3 + nodes, 
   4 + nodes, 4}, {1, 1 + nodes, nodes + nodes, nodes}, {nodes, 
   2*nodes, 2*nodes - 1, nodes - 1}}, fintops, basetops, 
 finsidesright, finsidesleft]]]]

DiscretizeGraphics[heatsink] looks a bit strange:

Fortunately, however, ToElementMesh looks okay

mesh = ToElementMesh[DiscretizeGraphics[heatsink]]["Wireframe"]

Any tips on how I can assign the faces / boundaries "ElementMarkers" would be most appreciated.

Note at first I used Regions to create the object but it seemed to get distorted during meshing unless a very fine mesh was used.

Answer 1

A bit long for a comment: What I'd do is split all polygons into quad elements and use those directly. Roughly like this:

sidesback1 = Partition[Table[i, {i, 1, nodes}][[3 ;; -1]], 4];
sidesfront1 = 
  Partition[Table[i, {i, nodes + 1, 2*nodes}][[3 ;; -1]], 4];
bmesh = ToBoundaryMesh["Coordinates" -> Join[face1, face2], 
  "BoundaryElements" -> {
    QuadElement[sidesback1], QuadElement[sidesfront1], 
    QuadElement[fintops], QuadElement[basetops], 
    QuadElement[finsidesright], QuadElement[finsidesleft],
    QuadElement[{{1, 2, 2 + nodes, 1 + nodes}, {2, 2 + nodes, 
       3 + nodes, 3}, {3, 3 + nodes, 4 + nodes, 4}, {1, 1 + nodes, 
       nodes + nodes, nodes}, {nodes, 2*nodes, 2*nodes - 1, 
       nodes - 1}}]
    }]

What is missing here is that you still need to split the former {1,2,3,34} polygon and add nodes on the {1,2} edge such that this polygon can be split down. This has the advantage that you could address every face or collection of faces with markers. I may do it later, but I need to attend to other things first.

Answer 2

Thanks to those that responded. Applying the boundary in the pde as a formula is okay for simple geometries but for more complicated ones it is cumbersome. I have tried user21's first suggestion:

bmesh = ToBoundaryMesh[DiscretizeGraphics[heatsink], 
"BoundaryMarkerFunction" -> (2 & /@ # &)];

 emesh = ToElementMesh[bmesh];
 emesh["Wireframe"["MeshElement" -> "BoundaryElements", 
 "MeshElementMarkerStyle" -> Red]]

and get the following as required - Marker "2" on the boundary. Thats certainly a step for me in the right direction. Now I just need to work out how to apply that to specific regions on the boundary, i.e. EM = 1 on say the base. The other answer looks promising regarding this so I will try that and get back.