Nodal point swarm not working on cubed sphere mesh

[bknight1]

Discussed in https://github.com/underworldcode/underworld3/discussions/307

^{Originally posted by chenxi-kong April 20, 2025}
Hi! When I was trying to solve the advection-diffusion equation on a cubed sphere mesh (which by default is using the semi Lagrangian method), I found that the nodal point swarm can not be constructed if its tracked variable is defined on this type of mesh. This issue can be reproduced by running:

import underworld3 as uw
import numpy as np
import sympy

mesh = uw.meshing.uw.meshing.CubedSphere(
    radiusOuter=1.0,
    radiusInner=0.547,
    numElements=10,
    refinement=0,
    simplex=False,
    verbose=False,
)

t_soln = uw.discretisation.MeshVariable("T", mesh, 1, degree=3)
nswarm = uw.swarm.NodalPointSwarm(t_soln, True)

and it says:

ValueError                                Traceback (most recent call last)
Cell In[39], line 1
----> 1 nswarm = uw.swarm.NodalPointSwarm(t_soln, True)

File [~/miniconda3/envs/uw3p/lib/python3.11/site-packages/underworld3/swarm.py:2035](http://localhost:8083/home/ckong/miniconda3/envs/uw3p/lib/python3.11/site-packages/underworld3/swarm.py#line=2034), in NodalPointSwarm.__init__(self, trackedVariable, verbose)
   2032 nswarm.dm.migrate(remove_sent_points=True)
   2034 with nswarm.access(nX0, nI0):
-> 2035     nX0.data[:, :] = coords
   2036     nI0.data[:, 0] = range(0, coords.shape[0])
   2038 self._nswarm = nswarm

ValueError: could not broadcast input array from shape (50442,3) into shape (43710,3)

I am wondering if there is an problem with using semi Lagrangian method for variables on cubed sphere mesh, or it is just because I am not doing it right somewhere?

Thanks!!

[bknight1]

The number of particles from tracked field is larger than the created swarm.

I'm able to reproduce this error for this mesh, and it also occurs on some other meshes, most likely due particles being removed close to the boundary. If I set the degree= 1 and continuous=false then the code runs fine, suggesting particles being removed.

@lmoresi @julesghub I think we can solve this issue by changing 2034 to 2036 to:

        with nswarm.access(nX0, nI0):
            nX0.data[:, :] = nswarm.data[:, :]
            nI0.data[:, 0] = range(0, nswarm.data[:, :].shape[0])

This will then use the created swarm particle locations instead of the original coordinate list

[lmoresi]

Let's add this to the hackathon to-do list

[knepley]

When is the hackathon?

[julesghub]

Agreed let's talk about it at the hackathon.

        with nswarm.access(nX0, nI0):
            nX0.data[:, :] = nswarm.data[:, :]
            nI0.data[:, 0] = range(0, nswarm.data[:, :].shape[0])

Also I don't think the nswarm.data[:,:].shape[0] is required. Only nswarm.data.shape[0]. Does that make sense?

[julesghub]

When is the hackathon?

Next week @ Curtain University, Perth.

[lmoresi]

I think we need to be careful not to fix the problem without checking the underlying cause which is (probably) the fact that a lot of points near the surfaces can move outside the mesh due to the mesh being first order. We can discuss suitable fixes for this.