Some Details

Meshless/Mesh-free

Point clouds are easier to use (for the end user) compared to meshes. However, there are some drawbacks: 1) using meshes can achieve linear time complexity for mesh associations [1]; 2) numerical integrations are not easy; 3) handling cell-averaged data fields, e.g. solutions that come from FVM, potential can lead to problems.

[1]	Jiao X, Edelsbrunner X, Heath MT. Mesh association: formulation and algorithms. In 8th International Meshing Roundtable. Sandia Report, South Lake Tahoe, CA, 1999; 75–82.

For 3), typically, people assume cell-averaged data to be cell-centered data, which limits to 2nd-order of accuracy. (Notice that this is actually not a big problem in practice.)

Global IDs/Handles

MOAB uses global IDs for parallel communications as well as DTK2. Therefore, ParPyDTK2 expects the user to provide this information. For most applications, this can be computed offline.

The global IDs are unique handles of the vertices in a point cloud. For instance, if one wants to distribute two triangles, then each of them has local IDs from 0 to 2, but unique global IDs that range from 1 to 4.

Note

ParPyDTK2 uses 1-based indexing for global IDs

Treatment of Empty Partitions

Both MOAB and DTK2 don’t natively support empty partitions, which occur pretty frequently in practice. For instance, couple a serial solver with a parallel solver, or couple a commercial code with an open-sourced one through socket and the incoming data partition graph from the commercial code probably doesn’t align with that of the open-sourced side.

To support empty partitions, we duplicate the first node in the master process to the processes that are empty. However, this is not complete yet, because the user is not aware of this, so that the values between across duplicated nodes are not synchronized. Of course, we don’t want to let the user to explicitly handle this extra layer of communication. To resolve this, a member function, called resolve_empty_partitions(), is added to class IMeshDB and must be called collectively whenever the user updates the field values through assign_field().