Meshless methods have recently received much attention but are yet to reach their full potential as the required problem setup (i.e. collocation point distribution) is still significant and far from automated. The distribution of points still closely resembles the nodes of finite volume-type meshes and the free parameter, c, of the radial-basis expansion functions (RBF) still must be tailored specifically to a problem. The localized meshless collocation method investigated requires a local influence region, or topology, used as the expansion medium to produce the required field derivatives. Tests have shown a regular cartesian point distribution produces optimal results, however, in order to maintain a locally cartesian point distribution a recursive quadtree scheme is herein proposed. The quadtree method allows modeling of irregular geometries and refinement of regions of interest and it lends itself for full automation, thus, reducing problem setup efforts. Furthermore, the construction of the localized expansion regions is closely tied up to the point distribution process and, hence, incorporated into the automated sequence. This also allows for the optimization of the RBF free parameter on a local basis to achieve a desired level of accuracy in the expansion. In addition, an optimized auto-segmentation process is adopted to distribute and balance the problem loads throughout a parallel computational environment while minimizing communication requirements.
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:etd-1760 |
| Date | 01 January 2006 |
| Creators | Mitteff, Eric |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
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