Constraints on hybrid region placement

[adamjgnoel]

A mesoscopic subvolume adjacent to a microscopic region needs that region to cover the entirety of every face that is adjacent to that region (i.e., part of the adjacent face should not also be adjacent to some other region). Otherwise the hybrid interface will not have proper transitions for two reasons:

1. The subvolumes might not be detected as neighbors
2. If they are detected as neighbors, then the transition rate out of the mesoscopic subvolume will be calculated assuming that the shared face is fully shared with the corresponding microscopic region.

This constraint is challenging to relax without adding significant computational requirements to the neighbor detection algorithm, especially if the mesoscopic region is a child of the microscopic region.

[adamjgnoel]

One possible solution is to enforce this constraint explicitly. Check for partial overlap between mesoscopic subvolumes that are along the boundary of a child region against the boundaries of the other children, their parent, their parent's neighbors, and their parent's neighbors children.