Second order meshing of 2D domains (with multiple subdomains)

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1

Hi everyone,
I was trying to generate a second order mesh for a domain comprising of a circle inside square. But was facing an issue. Here is the MWE with a very coarse mesh to delineate the problem:

from ngsolve import *
from netgen.geom2d import SplineGeometry

periodic = SplineGeometry()
pnts = [ (0,0), (1,0), (1,1), (0,1) ]
pnums = [periodic.AppendPoint(*p) for p in pnts]

top = periodic.Append( ["line", pnums[2], pnums[3]], bc="outer")
right = periodic.Append ( ["line", pnums[1], pnums[2]], bc="periodic")
btom = periodic.Append( ["line", pnums[1], pnums[0]], leftdomain=0, rightdomain=1, copy=top, bc="outer")
left = periodic.Append( ["line", pnums[0], pnums[3]], leftdomain=0, rightdomain=1, copy=right, bc="periodic")

# adding the circle
periodic.AddCircle((0.5, 0.5), 0.3, leftdomain=0, rightdomain=1, bc = "inner")

msh = periodic.GenerateMesh(maxh=5)
msh.SecondOrder()

This, however, generates a mesh where the mid-points of the edges along the circle aren’t properly placed. I am guessing it has to do with how I am defining the geometry

Any suggestions on what could be going wrong.

Thank you

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2

[attachment=undefined]paraview_Ordered.png[/attachment]I think I confused triplot of the corresponding linear mesh with the actual mesh. However I noticed something. The ordering of vertices is slightly different than what one would expect in Paraview (vertices followed by edge midpoints in the same order as the vertices)

For instance:

points = []
cell_arr = []

for pt in msh.Points():
    points.append([*pt])

points = np.array(points)

for elem in msh.Elements2D():
    cell_arr.append([int(str(i)) for i in elem.points])

points = points[:, :2]
cell_arr = np.array(cell_arr, int)-1

when fed to paraview gives:

whereas adjusting the last 2 points as

cell_arr = cell_arr[:, [0,1,2,5,3,4]]  #the last three points are ordered different than what one would expect

gives the desired ordering

[attachment=undefined]paraview_Ordered.png[/attachment]