1. ParFUM: High-level Adaptivity Algorithms for Unstructured Meshes
Terry L. Wilmarth, Nilesh Choudhury, Isaac Dooley, Sayantan Chakravorty
Parallel Programming Laboratory
University of Illinois at Urbana-Champaign

2. Adaptivity Goals for ParFUM
Work with applications scientists to discover realistic adaptivity needs
Develop rich set of algorithms for flexible mesh adaptivity interface
Easy to use: minimal extra work for user
Fast, efficient, scalable
Modular, extensible implementation

3. Example: 1D Wave Propagation

4. Mesh Sizing
Many adaptivity operations strive to achieve a certain mesh sizing
Specified in mesh edge length
Set at mesh elements
Mesh sizing can be used to:
Direct refinement and coarsening
Maintain regional sizing
Maintain a reference mesh

5. Mesh Sizing, cont'd Setting mesh sizing:
FEM_ADAPT_SetElementSizeField(i nt meshID, int elem, double size)
FEM_ADAPT_SetElementsSizeField( int meshID, double *sizes)
Allows user to set sizing directly, however, adaptivity operations support special sizing techniques

6. Example: Flexible Sizing

7. Example: Flexible Sizing

8. Example: Flexible Sizing

9. Example: Flexible Sizing

10. Example: Flexible Sizing

11. Refinement and Coarsening
Simple algorithms guided by mesh sizing requirements and quality measures
Refinement: longest edge bisection (Rivara)
Coarsening: shortest edge contraction

12. Refinement and Coarsening, cont'd
An element is added to a list of elements to be refined/coarsened if:
Its average edge length is not within some tolerance of the sizing field
Its quality is low
These elements are sorted by:
Longest/shortest edge weighted appropriately by quality measure

13. Refinement and Coarsening, cont'd
Adaptation proceeds in passes
After a pass, elements are re- evaluated
Refinement adds new elements which must be examined in the next pass
Coarsening modifies shape of existing elements
Both algorithms may skip adapting certain elements (locking, inversion, quality)

14. Refinement and Coarsening, cont'd
API:
FEM_ADAPT_Refine(int qm, int method, double factor, double *sizes)
FEM_ADAPT_Coarsen(int qm, int method, double factor, double *sizes)
Method allows for modifying mesh to a uniform size, to use mesh sizing, to perform scaling, or combinations of these

15. Example: Remeshing/Repair

16. Example: Remeshing/Repair

17. Example: Remeshing/Repair

18. Example: Remeshing/Repair

19. Example: Remeshing/Repair

20. Example: Remeshing/Repair

21. Mesh Quality
These simple algorithms can be used strategically to improve mesh quality:
Coarsening removes elements, particularly skinny isosceles triangles
Refinement makes flat slivers into skinny isosceles that can be later removed by coarsening

22. Data Transfer
Automatic data transfer built in to low-level mesh modification operations
Linear interpolation of nodal data
Duplication of element data for bisection
Framework for user to override/specify data transfer mechanisms
Provides mechanism to push element data to nodes and pull it back again

23. Ongoing Efforts Translation of current functionality into 3D
Remesh/Repair, Smoothing, etc.
Element-to-element data transfer
Support for adaptivity in “thicker” ghost layers
Load balancing and dynamic repartitioning