Parallel Automatic Mesh Re-Generation

This is a joint project with the Computer Science group composed of Vipin Kumar and George Karypis. The purpose of this project is to develop parallel automatic mesh re-generation tools. We use the term re-generation because we will not generate an entirely new grid from scratch (at least not at this time), but given an initial grid, we will re-generate both the element and nodal distribution in order to satisfy both an element quality and a nodal distribution quality criteria. The element quality criteria will initially be a Delaunay one, but eventually, other quality criteria choices will be made available (Max-min, Min-max, aspect-ratio, ...). The nodal distribution quality will be for the nodal distribution in the mesh (which defines mesh size) to conform to a user-defined function. This function will be either geometric based (based on the refinement of the surface grid), or some function (possibly representing accuracy in a field-simulation solution) which specify the density of the grid in all areas of the domain.

These tools will come about through a merger of the automatic mesh generation software of A. Johnson with the parallel mesh partitioning software of G. Karypis (Metis). Details of the exact algorithm will be forthcoming. These tools will run on any distributed memory (or shared memory) architecture that supports MPI.

These tools are designed for use in numerical simulations which require periodic and frequent changes in the mesh structure. One such application area is time-dependent flows around moving objects where the mesh has to deform in order to follow the movements of the objects. This periodic change in the mesh (remeshing) will be required when mesh distortion builds up due to the movement of the boundaries. Another application area is a solution-dependent mesh (adaptive refinement) where the mesh refinement is periodically changed in order to keep the error in a solution to a minimum as well as the size of the mesh.

The 3 stages in the development of these tools are:

1. Parallel Mesh Regularization. I use the term Regularization to mean a redistribution of the element connectivity in order to improve the quality of the grid (in this case, to turn it into a Delaunay mesh). The nodes in the beginning and ending mesh remain the same. We will accomplish this by combining Andrew's mesh generation routines, George's Metis, and mixing in some new parallel mesh redistribution routines.This first stage is finished.
2. Parallel Mesh Re-Generation. This second stage will be a continuation of the first, but along with a redistribution of the element connectivity, the actual nodes will also be created/destroyed/moved in order to satisfy a given nodal distribution function. This procedure will totally regenerate/redistribute both the elements and nodes. All mesh moving simulations that incorporate remeshing can be accomplished, in parallel, using stage 2 tools.
3. Parallel Automatic Mesh Generation. At stage 3 we may continue the development of a fully automatic parallel mesh generator. Instead of just modifying an existing mesh (as was the case in stage 2), stage 3 development tools will create an entire grid from scratch in parallel.

As stated earlier, this is a new project and more information will be posted as this project progresses.