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Title: Higher order H^1 and H(¿^) FEM techniques with EM applications
Keywords: FEM, Electromagnetics, Higher Order
Issue Date: 25-Jun-2010
Citation: DAVOOD ANSARI OGHOL BEIG (2010-06-25). Higher order H^1 and H(¿^) FEM techniques with EM applications. ScholarBank@NUS Repository.
Abstract: There is an ongoing endeavor to eliminate or elevate the limitations associated with exploitation of the advantages of HO FEM. In the context of hierarchical FEs, this has lead to the development of hp-adaptive methods while in the context of spectral FEs the problem can also be seen from a slightly different angle. The emergence of DDM has raised the possibility of applying HO FEs onto sub-domains where at least some the abovementioned limitations can be partially elevated. In this regard, this research will be focused on the following main objectives: 1. Improving the condition numbers of HO FE and IE matrices. 2. Developing schemes for efficient evaluation of element matrices with complex geometries and/or material properties. 3. Also, in order to avoid the difficulties associated with spurious modes, FE simulation of EM problems requires proper treatment of the null-space of the curl operator. Hence, we shall introduce a new dual-grid based the T/C decomposition method for higher order spectral elements. Item 1 is the focus of chapter 4 and part of chapter 3 where the properties of interpolation nodal sets are exploited for construction of improved FE and IE basis functions. The results are promising and indicate that condition number improvements could be significant. FE modeling of wave and scattering phenomena is made possible by means of special mesh truncation techniques. Here, the IE method was chosen because of its similarity with FEs that allowed the extension of the nodal set-based matrix conditioning technique into IEs. The issue of spurious modes in FE solution of Maxwell equation must be addressed by means of an appropriate null-space treatment. This is systematically done through T/C decomposition. In chapter 2 a new dual-grid based T/C technique for HO spectral elements is introduced. FEM matrices can often be computed by analytical methods. Moreover, material properties are traditionally treated as element-wise constant functions which is in contrast to the nature of FEs. In chapter 5, a new universal matrix approach for evaluation of FE matrices is introduced. The approach is validated on a model Luneburg lens problem and shows perfect compatibility with the physics of the lens. There are a number of advantages for the approach among which here I suffice to mention the ease of universal coding and improved flexibility for multi-physical problems.
Appears in Collections:Ph.D Theses (Open)

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