Thesis (M.S.)--University of Texas at El Paso, 2008. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Thesis (Ph. D.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 96-102). Also available on the World Wide Web.

Thesis (Ph.D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 1, 2007) Vita. Includes bibliographical references.

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Mak, Tsz Fan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 33-36). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Zhang Kai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 99-102). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 1.1 --- The Generalized PML Theory --- p.6 / Chapter 1.1.1 --- Background --- p.6 / Chapter 1.1.2 --- Derivation --- p.8 / Chapter 1.1.3 --- Reflection Properties --- p.11 / Chapter 1.2 --- Unified Formulation --- p.12 / Chapter 1.2.1 --- "Face-, Edge- and Corner-PMLs" --- p.12 / Chapter 1.2.2 --- Unified PML Equations in 3D --- p.15 / Chapter 1.2.3 --- Unified PML Equations in 2D --- p.16 / Chapter 1.2.4 --- Examples of PML Formulations --- p.16 / Chapter 1.3 --- Inhomogeneous Initial Conditions --- p.23 / Chapter 2 --- Numerical Analysis of PMLs --- p.25 / Chapter 2.1 --- Continuous PMLs --- p.26 / Chapter 2.1.1 --- PMLs for Wave Equations --- p.27 / Chapter 2.1.2 --- Finite PMLs for Wave Equations --- p.31 / Chapter 2.1.3 --- Berenger's PMLs for Maxwell Equations --- p.33 / Chapter 2.1.4 --- Finite Berenger's PMLs for Maxwell Equations --- p.35 / Chapter 2.1.5 --- PMLs for Acoustic Equations --- p.38 / Chapter 2.1.6 --- Berenger's PMLs for Acoustic Equations --- p.39 / Chapter 2.1.7 --- PMLs for 1-D Hyperbolic Systems --- p.42 / Chapter 2.2 --- Discrete PMLs --- p.44 / Chapter 2.2.1 --- Discrete PMLs for Wave Equations --- p.44 / Chapter 2.2.2 --- Finite Discrete PMLs for Wave Equations --- p.51 / Chapter 2.2.3 --- Discrete Berenger's PMLs for Wave Equations --- p.53 / Chapter 2.2.4 --- Finite Discrete Berenger's PMLs for Wave Equations --- p.56 / Chapter 2.2.5 --- Discrete PMLs for 1-D Hyperbolic Systems --- p.58 / Chapter 2.3 --- Modified Yee schemes for PMLs --- p.59 / Chapter 2.3.1 --- Stability of the Yee Scheme for Wave Equation --- p.61 / Chapter 2.3.2 --- Decay of the Yee Scheme Solution to the Berenger's PMLs --- p.62 / Chapter 2.3.3 --- Stability and Convergence of the Yee Scheme for the Berenger's PMLs --- p.67 / Chapter 2.3.4 --- Decay of the Yee Scheme Solution to the Hagstrom's PMLs --- p.70 / Chapter 2.3.5 --- Stability and Convergence of the Yee Scheme for the Hagstrom's PMLs --- p.75 / Chapter 2.4 --- Modified Lax-Wendroff Scheme for PMLs --- p.80 / Chapter 2.4.1 --- Exponential Decays in Parabolic Equations --- p.80 / Chapter 2.4.2 --- Exponential Decays in Hyperbolic Equations --- p.82 / Chapter 2.4.3 --- Exponential Decays of Modified Lax-Wendroff Solutions --- p.86 / Chapter 3 --- Numerical Simulation --- p.93 / Bibliography --- p.99

在本文中，我們為了三維空間的馬克士威方程組(Maxwell’s equation)制定和分析了一套新種類的交錯間斷伽遼金(discontinuous Galerkin)方法，同時考慮了時間依賴性和時間諧波的馬克士威方程組。我們用了空間離散上交錯笛卡兒網格，這種方法具有許多良好的性質。首先，我們的方法所得出的數值解保留了電磁能量，並自動符合了高斯定律的離散版本。第二，質量矩陣是對角矩陣，從而時間推進是顯式和非常有效的。第三，我們的方法是高階準確，最佳收斂性在這裏會被嚴格地證明。第四，基於笛卡兒網格，它也很容易被執行，並可視為是典型的Yee’s Scheme的以及四邊形的邊有限元的推廣。最後，超收斂結果也會在這裏被證明。 / 在本文中，我們還提供了幾個數值結果驗證了理論的陳述。我們計算了時間依賴性和時間諧波的馬克士威方程組數值收斂結果。此外，我們計算時間諧波馬克士威方程組特徵值問題的數值特徵值，並與理論特徵值比較結果。最後，完美匹配層(Perfect Matching Layer)吸收邊界的問題也有實行其數值結果。 / We develop and analyze a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell’s equations in this paper. Both time-dependent and time-harmonic Maxwell’s equations are considered. The spatial discretization is based on staggered Cartesian grids which possess many good properties. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Second, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Third, our method is high order accurate and the optimal order of convergence is rigorously proved. Fourth, it is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee’s scheme as well as the quadrilateral edge finite elements. Lastly, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. / In this paper, we also provide several numerical results to verify the theoretical statements. We compute the numerical convergence order using L2-norm and discrete-norm respectively for both the time-dependent and time-harmonic Maxwell’s equations. Also, we compute the numerical eigenvalues for the time-harmonic eigenvalue problem and compare the result with the theoretical eigenvalues. Lastly, applications to problems in unbounded domains with the use of PML are also presented. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Yu, Tang Fei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 46-49). / Abstracts also in Chinese. / Chapter 1 --- Introduction and Model Problems --- p.1 / Chapter 2 --- Staggered DG Spaces --- p.4 / Chapter 2.1 --- Review on Gauss-Radau and Gaussisan points --- p.5 / Chapter 2.2 --- Basis functions --- p.6 / Chapter 2.3 --- Finite Elements space --- p.7 / Chapter 3 --- Method derivation --- p.14 / Chapter 3.1 --- Method --- p.14 / Chapter 3.2 --- Time discretization --- p.17 / Chapter 4 --- Energy conservation and Discrete Gauss law --- p.19 / Chapter 4.1 --- Energy conservation --- p.19 / Chapter 4.2 --- Discrete Gauss law --- p.22 / Chapter 5 --- Error analysis --- p.24 / Chapter 6 --- Numerical examples --- p.29 / Chapter 6.1 --- Convergence tests --- p.30 / Chapter 6.2 --- Diffraction by a perfectly conducting object --- p.30 / Chapter 6.3 --- Perfectly matched layers --- p.37 / Chapter 7 --- Time Harmonic Maxwell’s equations --- p.40 / Chapter 7.1 --- Model Problems --- p.40 / Chapter 7.2 --- Numerical examples --- p.40 / Chapter 7.2.1 --- Convergence tests --- p.41 / Chapter 7.2.2 --- Eigenvalues tests --- p.41 / Chapter 8 --- Conclusion --- p.45 / Bibliography --- p.46

In the first part, an efficient and reliable a posteriori error estimate is derived for solving three-dimensional static Maxwell's equations based on the lowest order edge elements of the first family. We propose an adaptive finite element method and establish convergence of the adaptive scheme in energy norm under a restriction on the initial mesh size. Any prescribed error tolerance is thus achieved in a finite number of steps. For discretization based on the lowest order edge elements of the second family, a similar adaptive method is designed which guarantees convergence without any initial mesh size restriction. The proofs rely mainly on error and oscillation reduction estimates as well as the Galerkin orthogonality of the edge element approximation. For time-dependent Maxwell's equations, we deduce an efficient and reliable a posteriori error estimate, upon which an adaptive finite element method is built. / In this thesis, we will address three typical problems with discontinuous coefficients in a general Lipschitz polyhedral domain, which are often encountered in numerical simulation of electromagnetism. / The second part deals with a saddle point problem arising from Maxwell's equations. We present an adaptive finite element method on the basis of the lowest order edge elements of the first family and prove its convergence. The main ingredients of the proof are a novel quasi-orthogonality, which replaces the usual Pythagoras relation, which fails in this case, all error reduction depending on an efficient and reliable a posteriori error estimate and an oscillation reduction. We show that this adaptive scheme is a contraction for the sum of some energy error plus the oscillation. Likewise, the above result is generalized to the discretization by the lowest order edge elements of the second family. / We introduce in the third part an adaptive finite element method for solving the eigenvalue problem of the Maxwell system based on an inverse iterative method. By modifying the exact inverse iteration algorithm involving an inner saddle point solver, we construct an adaptive inverse iteration finite element algorithm, which consists of an inexact inner adaptive procedure for a discrete mixed formulation in place of the original saddle point problem. An efficient and reliable a posteriori error estimate is obtained and the convergence of the inner adaptive method is proved. In addition, the important convergence property of the algorithm is studied, which ensures the errors between true solutions (eigenfunction and eigenvalue) and iterative ones to fall below any given tolerance within a finite number of iterations. / Xu, Yifeng. / "June 2007." / Adviser: Jun Zou. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 166-175). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

A numerical method based on the the method of characteristics for hyperbolic systems of partial differential equations in four independent variables is developed and used for solving time domain Maxwell's equations. The method uses the characteristic hypersurfaces and the characteristic conditions to derive a set of independent equations relating the electric and magnetic field components on these hypersurfaces. A discretization scheme is developed to solve for the unknown field components at each time step. The method retains many of the good features of the original method of characteristics for hyperbolic systems in two independent variables, such as optimal time step, good behavior near data discontinuities and the ability to treat general boundary conditions. The method is exemplified by calculating the time domain response of a few typical planar interconnect structures to Gaussian and unit step excitations. Although the general emphasis is on interconnect problems, the method is applicable to a number of other transient electromagnetic field problems governed by Maxwell's equations. In addition to the method of characteristics a finite difference scheme, known in mathematic circles as the modified Richtmyer scheme, is applied to the time domain solution of Maxwell's equations. Both methods should be useful for efficient full wave analysis of three dimensional electromagnetic field problems. / Graduation date: 1994

The modeling of electromagnetic phenomena described by the Maxwell's equations is of critical importance in many practical applications. The numerical simulation of these equations is challenging and much more involved than initially believed. Consequently, many discretization techniques, most of them quite complicated, have been proposed. In this dissertation, we present and analyze a new methodology for approximation of the time-harmonic Maxwell's equations. It is an extension of the negative-norm least-squares finite element approach which has been applied successfully to a variety of other problems. The main advantages of our method are that it uses simple, piecewise polynomial, finite element spaces, while giving quasi-optimal approximation, even for solutions with low regularity (such as the ones found in practical applications). The numerical solution can be efficiently computed using standard and well-known tools, such as iterative methods and eigensolvers for symmetric and positive definite systems (e.g. PCG and LOBPCG) and reconditioners for second-order problems (e.g. Multigrid). Additionally, approximation of varying polynomial degrees is allowed and spurious eigenmodes are provably avoided. We consider the following problems related to the Maxwell's equations in the frequency domain: the magnetostatic problem, the electrostatic problem, the eigenvalue problem and the full time-harmonic system. For each of these problems, we present a natural (very) weak variational formulation assuming minimal regularity of the solution. In each case, we prove error estimates for the approximation with two different discrete least-squares methods. We also show how to deal with problems posed on domains that are multiply connected or have multiple boundary components. Besides the theoretical analysis of the methods, the dissertation provides various numerical results in two and three dimensions that illustrate and support the theory.