Free and/or moving boundary problems occur in a wide range of applications. These boundaries can obey either local or global conditions. In this dissertation, new numerical techniques for solving some of these problems are developed, analyzed, implemented and tested. The new techniques for free and moving boundary problems are 1) a second order method for solving moving boundary problems and 2) a hybrid level set/boundary element method for solving some free boundary problems. The main tool used in both is the Fast Marching method, a fast algorithm for solving the eikonal equation. An application using Fast Marching to solve a model for sand pile formation in domains with obstacles is shown. A new, second order Fast Marching scheme for domains with obstacles is introduced. We look at the stability and accuracy of discretizations commonly used with Fast Marching. The performance of Fast Marching is compared that of Fast Sweeping, another eikonal solver. The second order method for solving moving boundary problems is applied to some simple examples. Finally, a globally defined free boundary problem inspired by fluid dynamics, the Bernoulli problem, is solved using the hybrid method.
| Identifer | oai:union.ndltd.org:NCSU/oai:NCSU:etd-04262006-083221 |
| Date | 10 July 2006 |
| Creators | Kuster, Christopher M. |
| Contributors | Stephen L. Campbell, Pierre A. Gremaud, Zhilin Li, Carl T. Kelley |
| Publisher | NCSU |
| Source Sets | North Carolina State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://www.lib.ncsu.edu/theses/available/etd-04262006-083221/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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