Monge-Ampere boundary movement for non-rectangular domains

[jwallwork23]

Consider solving Poisson on a mesh of a non-rectangular, polygonal domain.

If all straight line boundary segments are uniquely tagged then the Monge-Ampere mover will fix the corners and only allow boundary movement tangential to each segment. However, this does not avoid the situation in the following plot, where the tangential movement passes a corner.

It isn't obvious how to fix this, but here are a few possibilities:

• Fix all boundary nodes (undesirable, but possible, thanks to #12).
• Add a weighting to the tangential movement condition, so that it goes to zero at the corners.
• Penalise mesh tangling, perhaps in the monitor function.

[jwallwork23]

I think this should be fixed now? Presumably the image was generated with an old version of Movement.

[jwallwork23]

@ddundo will try to replicate this issue.

[jwallwork23]

We discussed in the meeting and determined that the DirichletBC for the EquationBC doesn't guarantee that nodes don't get moved beyond the corners (it doesn't know that the values have to do with mesh entities).

[jwallwork23]

It's possible that there's no way to guarantee this effect doesn't manifest, i.e., problem is ill-posed.

[ddundo]

I tried to replicate this using this code: https://gist.github.com/ddundo/bef044545395ad94e0d28553a80d8578

It all looks good to me! I also tried other monitor functions that focus adaptation more towards the boundary. But please let me know if I missed/did something wrong :)

[ddundo]

Edit: sorry, boundary segments aren't marked in the gmsh code below.

---

Hmm just saw that there is some normal movement on this example:

Same code as in the gist above, but mesh created like this:

from math import cos, sin

import gmsh

gmsh.initialize()
gmsh.model.add("heptagon")

r = 1  # Radius of the circumscribed circle
n_sides = 7
lc = 0.1  # Characteristic length

points = []
for i in range(n_sides):
    angle = 2 * 3.14159 * i / n_sides
    x = r * cos(angle)
    y = r * sin(angle)
    points.append(gmsh.model.geo.addPoint(x, y, 0, lc))

lines = []
for i in range(n_sides):
    lines.append(gmsh.model.geo.addLine(points[i], points[(i + 1) % n_sides]))

loop = gmsh.model.geo.addCurveLoop(lines)
surface = gmsh.model.geo.addPlaneSurface([loop])

gmsh.model.geo.synchronize()
gmsh.model.mesh.generate(2)

gmsh.write("heptagon.msh")
gmsh.finalize()

[jwallwork23]

Thanks for this @ddundo. Which branch are you using here?

[ddundo]

Thanks for this @ddundo. Which branch are you using here?

On 112_fix-specific-segment :)

[jwallwork23]

Hm it looks like the mesh doesn't have any boundary tags. It needs to have Physical ID tags on boundary segments for that to work properly.

Added a warning on the branch cfdc231.

[ddundo]

Yeah I forgot about that in the second example, sorry. But the first one does have boundaries marked - and it works well I think