Creation of nested meshes

mesh
1

Introduction
I want to do adaptive mesh refinement, and keep the meshes nested, which means that every node in the coarser mesh, should also be present in the finer mesh. I have a 2d domain with a circle inside a rectangle, created like this:

domain_width = 10
domain_height = 5
domain.addRectangle(
            x=-domain_width / 2,
            y=-domain_height,
            z=0,
            dx=domain_width,
            dy=domain_height,
            tag=1
)
tag = domain.addDisk(xc = 0,yc = -0.8,zc =  0, rx = 0.2, ry= 0.2)

Then at some point, i create a first mesh and i have a local refinement function which looks like:

circle_cells = cell_markers.indices[cell_markers.values == cicle_tag]
mesh.topology.create_connectivity(mesh.topology.dim,1)
edges = compute_incident_entities(mesh.topology,circle_cells,2,1)
mesh, parent_cell, parent_facet = refine(msh = mesh,edges = edges, option = RefinementOption.parent_cell_and_facet)
mesh.topology.create_connectivity(1, 2)
cell_markers = transfer_meshtag(cell_markers, mesh, parent_cell)
facet_markers = transfer_meshtag(facet_markers, mesh, parent_cell, parent_facet)

The original mesh and the refined mesh:

meshes
meshes1603×1977 404 KB

Problem
I now have the problem that the new points in the refined mesh, are placed at edges of the coarser mesh, therefore, if i refine, the circle will not look more like a circle. The “circle” will keep the same shape.

Desired solution
I want that in the refined mesh, the circle looks more like a circle then in the coarser mesh. So the new nodes should be (partially) placed on the originally defined circle.

Is it possible to achieve this in some way ? It is important that the meshes remain nested. I see functionality for specifying mesh sizes in different subdomains, with the gmsh.model.mesh.field functionality. I could use that mutiple times, then, the circle will look more like a circle in the finer meshes, but i lose the nested property, which is very important for our case.

2

Hello Jordi,
The refinement routines of Dolfinx do not support any specific geometric control over the placement of refined mesh nodes. If you want to stick to the Dolfinx routines your best tools for this task is the refinement routine you mentioned or the usage of different (non hierarchical) meshes, in this case the non matching mesh interpolation might be of interest, see here.

If the transfer with the non-matching interpolation is not suitable in your use case, I would have a look into constrained Delaunay triangulations to produce meshes that fulfill your requirements. This is however not a FEniCS functionality and work on geometric multi grid support is still work in progress, see for example here for the computation of the necessary node to node inclusion mapping that might be of interest for two self contained meshes.

3

Thanks ! I will look into the links you shared.