10 ParFUM

ParFUM is the name for the latest version of FEM. ParFUM includes additional features including parallel mesh modification and adaptivity (geometrical). ParFUM also contains functions which generate additional topological adjacency information. ParFUM cannot be built separate from CHARM++ since it uses various messaging mechanisms that MPI does not readily support. It is important to note that ParFUM adaptivity at the moment has some limitations. It works only for meshes which are two-dimensional. The other limitation is that the mesh on which it works on must have one layer of node-deep ghosts. Most applications reqire no or one layer ghosts, so it is really not a limitation, but for applications that need multiple layers of ghost information, the adaptivity operations cannot be used.

10.1 Adaptivity Initialization

If a FEM application wants to use parallel mesh adaptivity, the first task is to call the initialization routine from the driver function. This creates the node and element adjacency information that is essential for the adaptivity operations. It also initializes all the mesh adaptivity related internal objects in the framework.

void FEM_ADAPT_Init(int meshID)
Initializes the mesh defined by meshID for the mesh adaptivity operations.

10.2 Preparing the Mesh for Adaptivity

For every element entity in the mesh, there is a desired size entry for each element. This entry is called meshSizing. This meshSizing entry contains a metric that decides the element quality. The default metric is the average of the size of the three edges of an element. This section provides various mechanisms to set this field. Some of the adaptive operations actually use these metrics to maintain quality. Though there is another metric which is computer for each element and maintained on the fly and that is the ratio of the largest length to the smallest altitude and this value during mesh adaptivity is not allowed to go beyond a certain limit. Because the larger this value after a cecrtain limit, the worse the element quality.

void FEM_ADAPT_SetElementSizeField(int meshID, int elem, double size);
For the mesh specified by meshID, for the element elem, we set the desired size for each element to be size.

void FEM_ADAPT_SetElementSizeField(int meshID, double *sizes);
For the mesh specified by meshID, for the element elem, we set the desired size for each element from the corresonponding entry in the sizes array.

void FEM_ADAPT_SetReferenceMesh(int meshID);
For each element int this mesh defined by meshID set its size to the average edge length of the corresponding element.

void FEM_ADAPT_GradateMesh(int meshID, double smoothness);
Resize mesh elements to avoid jumps in element size. i.e. avoid discontinuities in the desired sizes for elements of a mesh by smoothing them out. Algorithm based on h-shock correction, described in Mesh Gradation Control, Borouchaki et al.

10.3 Modifying the Mesh

Once the elements in the mesh has been prepared by specifying there desired sizes, we are ready to use the actual adaptivity operations. Currently we provide delauney flip operations, edge bisect operations and edge-coarsen operations all of which are implemented in parallel, but the user has access to these wrapper functions which interlligently decide when and in which region of the mesh to use the adaptivity operations to generate a mesh with higher quality elements while achieving the desired size (which is usually average edge length per element), or it could even be the area of each element.

void FEM_ADAPT_Refine(int meshID, int qm, int method, double factor,double *sizes);
Perform refinements on the mesh specified by meshId. Tries to maintain/improve element quality by refining the mesh as specified by a quality measure qm. If method = 0, refine areas with size larger than factor down to factor If method = 1, refine elements down to sizes specified in the sizes array. In this array each entry corresponds to the corresponding element. Negative entries in sizes array indicate no refinement.

void FEM_ADAPT_Coarsen(int meshID, int qm, int method, double factor,double *sizes);
Perform refinements on the mesh specified by meshId. Tries to maintain/improve element quality by coarsening the mesh as specified by a quality measure qm. If method = 0, coarsen areas with size smaller than factor down to factor If method = 1, coarsen elements up to sizes specified in the sizes array. In this array each entry corresponds to the corresponding element. Negative entries in sizes array indicate no coarsening.

void FEM_ADAPT_AdaptMesh(int meshID, int qm, int method, double factor,double *sizes);
It has the same set of arguments as required by the previous two operations, namely refine and coarsen. This function keeps using the above two functions till we have all elements in the mesh with as close to the desired quality. Apart from using the above two operations, it also performs a mesh repair operation where it gets rid of some bad quality elements by delauney flip or coarsening as the geometry in the area demands.

int FEM_ADAPT_SimpleRefineMesh(int meshID, double targetA, double xmin, double ymin, double xmax, double ymax);
A region is defined by (xmax, xmin, ymax, ymin) and the target area to be achieved for all elements in this region in the mesh specified by meshID is given by targetA. This function only performs a series of refinements on the elements in this region. If the area is larger, then no coarsening is done.

int FEM_ADAPT_SimpleCoarsenMesh(int meshID, double targetA, double xmin, double ymin, double xmax, double ymax);
A region is defined by (xmax, xmin, ymax, ymin) and the target area to be achieved for all elements in this region in the mesh specified by meshID is given by targetA. This function only performs a series of coarsenings on the elements in this region. If the area is smaller, then no refinement is done.

10.4 Verifiy correctness of the Mesh

After adaptivity operations are performed and even before adaptivity operations, it is important to first verify that we are working on a mesh that is consistent geometrically with the types of mesh that the adaptivity algorithms are designed to work on. There is a function that can be used to test various properties of a mesh, like area, quality, geometric consistency, idxl list correctness, etc.

void FEM_ADAPT_TestMesh(int meshID);
This provides a series of tests to determine the consistency of the mesh specified by meshID.

These four simple steps define what needs to be used by a program that wishes to use the adaptivity features of ParFUM.

10.5 ParFUM developers

This manual is meant for ParFUM users, so developers should look at the source code and the doxygen generated documentaion.