Alfeld split on active mesh

NGSolve
1

Hello,

I want to use CutFEM for the Stokes problem using Scott-Vogelius elements on Alfeld splits. Currently, I have a working code that does

  1. Create a simplicial background mesh
  2. Create an Alfeld split of the background mesh
  3. Create an active mesh of the splitted background mesh given a levelset function.

This is done in the following way:

levelset = sqrt((x-0.5)**2 + (y-0.5)**2) - 0.25

square = SplineGeometry()
square.AddRectangle((0, 0), (1, 1), bcs=[])
mesh = Mesh(square.GenerateMesh(maxh=0.1, quad_dominated=False))
mesh.SplitElements_Alfeld()

lsetp1 = GridFunction(H1(mesh, order=1))
InterpolateToP1(levelset, lsetp1)

ci = CutInfo(mesh, lsetp1)
hasneg = ci.GetElementsOfType(HASNEG)

Vhbase = VectorH1(mesh, order=order, dirichlet=[])
Qhbase = L2(mesh, order=order - 1)

Vh = Restrict(Vhbase, hasneg)
Qh = Restrict(Qhbase, hasneg)

However, what I want to do is the following:

  1. Create a simplicial background mesh
  2. Create an active mesh of the background mesh given a levelset function.
  3. Create an Alfeld split of the active mesh.

Can anyone indicate how to do the Alfeld based on the active mesh, not the background mesh?

Thanks

2

Hi,

you could do the mesh manipulation yourself.
Here is a simple script for 2D barycenter refinement:
barycenter_ref.py (1.3 KB)

You can now adapt it to only act on active elements (and ignore the others for refinement or remove them completely).

Best,
Christoph