Tagging Isolated Volumes

[ConnorMallon]

given a geometry, is it possible to tag isolated volumes in the domain that are not connected to the main volume of the domain (e.g the volume shown in red below)

[fverdugo]

It is possible to define a domain with disconnected components, but you would need to impose sufficient boundary conditions to solve a PDE on it.

[ConnorMallon]

Is it possible to tag these isolated volumes? I mean to somehow know which sections of the domain are part of a set ISOLATED (red) or the set NOT ISOLATED (blue). It would be so that we could deal with them separately to make sure the problem is well posed.

[santiagobadia]

@fverdugo we need this classification to make the problems solvable in topopt 😄

[santiagobadia]

I think that this algorithm should rely on the sub-partition of cells into simplices (with the current implementation). We could have singular cases in which the intersection of one cell with the domain could in fact be a disconnected set. Do you think we can deal with this case now?

[oriolcg]

One way of doing this is by using a "filling" algorithm, but I don't know if it would be useful for your case

[fverdugo]

Ok, you want to find the components of a domain described by a single level-set right?

[fverdugo]

I think you can do this without computing the sub-triangulation, just working with the nodal values and the graph that defines de connections between nodes (i.e. the sparsity pattern of an operator on the background mesh).

[santiagobadia]

I think that the problem is the same. I am not sure we are properly dealing with cells such that its interior is disconnected. We can probably talk, it is going to be easier.