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High-order accurate methods for solving Maxwell's equations and their applications.

机译：求解麦克斯韦方程组的高阶精确方法及其应用。

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摘要

This thesis contains two topics on high-order accurate methods for solving Maxwell's equations. The first topic is the application of high-order accurate methods to the modeling/designs of photonic crystals. The second topic is the development of thin layer approximations and implementation in discontinuous Galerkin method. Each topic consists of two parts as described below.;The first part, part I of the first topic, demonstrates the behavior and sensitivity of the frozen mode phenomenon in finite structures with anisotropic materials, including both magnetic materials and non-normal incidence. A discontinuous Galerkin method is used for solving Maxwell's equations in the time domain. The existence of the frozen mode phenomena is confirmed and the impact of finiteness and perturbations of periodicity is studied.;In the second part, part II of the second topic, PDE constrained nonlinear optimization techniques are implemented to optimized the design of electromagnetic crystals for the frozen mode phenomenon. We investigate both of gyrotropic photonic crystals and degenerate band edge crystals as well as the more complex case of the oblique incidence. We extend the investigation to the three-dimensional case to identify the first three-dimensional crystal exhibiting frozen mode behavior.;The third part, part I of the second topic, studies high-order accurate thin layer approximations for metal backed coatings in the time-domain. Isotropic materials and tangentially-oriented anisotropic materials are considered in one and two dimensions. The implementation of these models are discussed in the context of discontinuous Galerkin methods which are particularly well-suited for these approximations. The range of validity, accuracy, and stability of the resulting schemes is discussed through one- and two-dimensional examples.;The last part, part II of the second topic, also studies high-order accurate thin layer approximations, but for transmission layers. The thin layer formulation of 3rd order and 5th order for curvilinear transmission layers are derived. Also, similar to the previous part, computational results on the range of validity, accuracy, and stability is demonstrated on one- and two-dimensional cases.;This thesis is based on the following 4 papers: (1) S. Chun and J. S. Hesthaven, Modeling of the frozen mode phenomenon and its Sensitivity using Discontinuous Galerkin methods, commun. comput. phys., 2, 2007, pp. 611--639. (2) S. Chun and J. S. Hesthaven, PDE constrained optimization and design of frozen mode crystals, commun. comput. phys., 3, 2008, pp. 878--898. (3) S. Chun and J. S. Hesthaven, High-order accurate thin layer approximation for time-domain electromagnetics, Part I: General metal backed coatings, in preparation. (4) S. Chun, H. Haddar and J. S. Hesthaven, High-order accurate thin layer approximation for time-domain electromagnetics, Part II: Interface conditions, in preparation.
机译：本文包含两个主题，用于解决麦克斯韦方程组的高阶精确方法。第一个主题是将高阶精确方法应用于光子晶体的建模/设计。第二个主题是薄层近似的发展和不连续Galerkin方法的实现。每个主题包括以下两个部分：第一部分，第一个主题的第一部分，展示了各向异性材料（包括磁性材料和非法向入射）在有限结构中的冻结模式现象的行为和敏感性。不连续的Galerkin方法用于在时域中求解麦克斯韦方程。确认了冻结模式现象的存在，并研究了有限性和周期性扰动的影响。第二部分，第二部分第二部分，采用PDE约束的非线性优化技术对电磁晶体的设计进行了优化。冻结模式现象。我们研究了回旋光子晶体和简并的带边缘晶体以及更复杂的斜入射情况。我们将研究扩展到三维情况，以识别表现出冻结模式行为的第一个三维晶体。第三部分，第二个主题的第一部分，研究了当时金属背涂层的高阶精确薄层近似-域。各向同性材料和切向取向的各向异性材料被视为一维和二维的。这些模型的实现是在不连续Galerkin方法的背景下进行讨论的，该方法特别适合于这些近似值。通过一维和二维示例讨论了所得方案的有效性，准确性和稳定性的范围。第二部分的最后一部分，第二部分，也研究了高阶精确薄层近似，但对于传输层。推导了曲线透射层三阶和五阶的薄层公式。并且，与前一部分相似，在一维和二维情况下证明了有效性，准确性和稳定性的范围的计算结果。本文基于以下四篇论文：（1）S. Chun和JS Hesthaven，《使用不连续Galerkin方法对冻结模式现象及其灵敏度进行建模》，公共。计算。 phys。，2，2007，第611--639页。 （2）S. Chun和J. S. Hesthaven，PDE限制了冻结模式晶体的优化和设计。计算。 phys。，3，2008，第878--898页。 （3）S. Chun和J. S. Hesthaven，时域电磁学的高阶精确薄层近似，第I部分：常规金属底涂层，正在准备中。 （4）S. Chun，H。Haddar和J. S. Hesthaven，时域电磁学的高阶精确薄层近似，第二部分：界面条件，正在准备中。

著录项

  • 作者

    Chun, Sehun.;

  • 作者单位

    Brown University.;

  • 授予单位 Brown University.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2008
  • 页码 152 p.
  • 总页数 152
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;
  • 关键词

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