How to divide a region in FEM with a parametric curve?

Question

I'm using NDSolve with finite element to try to solve a heat transfer problem. The region I have is a rectangle where the four vertices are at (-0.5,0), (0.5,0), (0.5, 3), (-0.5,3). The rectangle is divided into two regions (different thermal conductivity) by a parametric curve y=1-0.1*Cos[2*pi*x], where -0.5<=x<=0.5. There is an example similar to this case in the official documentation using ToBoundaryMesh, but the region is divided by a straight line, not a curve. I also tried something like

ir = ParametricRegion[{t, 1 + \[Delta] Cos[2 \[Pi] t]}, {{t, -0.5, 0.5}}]
coords = DiscretizeRegion[ir]

But then I'm not sure how to supply the coordinates to ToBoundaryMesh or other functions.

How can I generate the mesh for use in NDSolve?

Answer 1

Maybe this will get you started:

(* If you do not have the FEMAddOns installed get then with: *)
(*  ResourceFunction["FEMAddOnsInstall"][] *)

Needs["FEMAddOns`"]
(* Create Regions *)
dom = Rectangle[{-0.5, 0}, {0.5, 3}];
bot = DiscretizeRegion@
   ImplicitRegion[(-0.5 <= x <= 0.5) && (0 <= y <= 
       1 + 0.1 Cos[2 \[Pi] x]), {x, y}];
bmesh1 = ToBoundaryMesh[dom];
bmesh2 = ToBoundaryMesh[bot];
bmesh = BoundaryElementMeshJoin[bmesh1, bmesh2]
bmesh["Wireframe"]