Lacunae Based Stabilization of PMLs

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dc.contributor.advisor Pierre Gremaud, Committee Member en_US
dc.contributor.advisor Shamim Rahman, Committee Member en_US
dc.contributor.advisor Dmitri Zenkov, Committee Member en_US
dc.contributor.advisor Ralph Smith, Committee Member en_US
dc.contributor.advisor Semyon Tsynkov, Committee Chair en_US Qasimov, Heydar Rafiq oglu en_US 2010-04-02T19:01:39Z 2010-04-02T19:01:39Z 2008-11-11 en_US
dc.identifier.other etd-10152008-134023 en_US
dc.description.abstract Perfectly matched layers (PML) enclose the computational domain for simulating electromagnetic phenomena defined over unbounded regions. While being overall very successful, this procedure has sometimes been reported to develop instabilities and exhibit a physically unaccountable growth of the solution inside the layer over long integration times. In the thesis, we conduct a numerical as well as analytical study of the PML's response after a long time of integration. The physical and mathematical PMLs are implemented with several well-known schemes: Yee, leap-frog, Lax-Wendroff, and Runge-Kutta in time with central differences in space. Then, the eigen-structure of each discretization at quiescent state is studied to gain an insight into the nature of instability, the sources of growth of the solution and the potential contamination of the domain of interest. The results of this investigation provide useful information regarding the better and worse performers among the specific combinations of schemes and PMLs, yet they do not precisely identify the mechanism behind the growth of the solution. Therefore, the main focus of the thesis is to build a methodology that would inhibit the instability of the PML regardless of its source. The approach is based on the concept of numerical integration that exploits the presence of lacunae in the solutions. It applies to hyperbolic partial differential equations and systems that satisfy the Huygens' principle, in particular, the Maxwell's system of equations that governs the propagation of electromagnetic waves. The methodology does not modify the equations inside the layer and hence, while eliminating the undesirable growth, it fully preserves all the advantageous properties of a given PML, such as matching at the interface and the degree of absorption. A practical algorithm is constructed in the thesis, and a theorem is proved that guarantees a temporally uniform error bound over the domain of interest. The theoretical findings are corroborated numerically, and the potential for extending the methodology is discussed en_US
dc.rights 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, dis sertation, 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. en_US
dc.subject hyperbolic PDE en_US
dc.subject Maxwell's Equations en_US
dc.subject Artificial Boundary Conditions en_US
dc.subject Lacunae en_US
dc.subject Absorbing Layers en_US
dc.subject PML en_US
dc.title Lacunae Based Stabilization of PMLs en_US PhD en_US dissertation en_US Applied Mathematics en_US

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