| Author | Ottmar Klaas and Mark S. Shephard |
|---|---|
| Title | Automatic Generation of Partition of Unity Discretizations for Three Dimensional Domains |
| Year | 1998 |
| Pages | 119-131 |
| Editor | - - |
| Abstract | The Partition of Unity Method (PUM), also referred to as mesh free methods, is based on the definition of overlapping patches _i comprising a cover {_i } of the domain _. For an efficient implementation it is very important that the interaction between the patches themselves, and between the patches and the boundary, is well understood and easily accessible during the runtime of the program. We will show that an octree representation of the domain with a tetrahedral mesh at the boundary is an efficient means to provide the needed information. It subdivides an arbitrary domain into simply shaped topological objects (cubes, tetrahedrons) giving a non overlapping discrete representation of the domain on which efficient numerical integration schemes can be employed. The octants serve as the basic unit to construct the overlapping partitions. The structure of the octree allows the efficient determination of patch interactions. |