Graphene is a single atomic layer of graphite and has many extraordinary properties. Many graphene based applications have been proposed in recent years and the need of a time domain simulation tool for studying graphene based devices emerges. This thesis focuses on developing a simulation framework for graphene based devices using finite-difference time-domain (FDTD) method. Formulation for a perfectly matched layer (PML) for the sub-cell FDTD method for thin dispersive layers has been derived and implemented. Such a PML is useful when thin layers extend to the boundaries of the computational domain. Using the sub-cell PML formulation to model the graphene thin layers significantly reduces the computational cost compared to using the conventional FDTD. The proposed formulation is accompanied by detailed validation and error analysis studies. Several graphene applications are simulated using the new framework and the results show good agreement with the respective analytical models.

Graphene is a single atomic layer of graphite and has many extraordinary properties. Many graphene based applications have been proposed in recent years and the need of a time domain simulation tool for studying graphene based devices emerges. This thesis focuses on developing a simulation framework for graphene based devices using finite-difference time-domain (FDTD) method. Formulation for a perfectly matched layer (PML) for the sub-cell FDTD method for thin dispersive layers has been derived and implemented. Such a PML is useful when thin layers extend to the boundaries of the computational domain. Using the sub-cell PML formulation to model the graphene thin layers significantly reduces the computational cost compared to using the conventional FDTD. The proposed formulation is accompanied by detailed validation and error analysis studies. Several graphene applications are simulated using the new framework and the results show good agreement with the respective analytical models.

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In the field of antenna design and analysis, often the need arises to numerically extrapolate the far-zone performance of a radiating structure from its known (or assumed known) near-zone electromagnetic field. Mathematical processes developed to accomplish such a task are known in the literature as near-zone to far-zone transformations (NZ-FZTs) as well as near-field far-field (NF-FF) transformations. These processes make use of sampled near-zone field quantities along some virtual surface, viz., the transformation surface, that surrounds the radiating structure of interest. Depending upon the application, samples of the required near-zone field quantities are supplied via analytical, empirical, or computational means. Over the years, a number of NZ-FZT processes have been developed to meet the demands of many applications. In short, their differences include, but are not limited to, the following: (1) the size and shape of the transformation surface, (2) the required near-zone field quantities and how they are sampled, (3) the computational methodology used, and (4) the imbedding of various application-driven features. Each process has its pros and cons depending upon its specific application as well as the type of radiation structure under consideration. In this dissertation we put forth a new and original NZ-FZT process that allows the transformation surface along which the near-zone is sampled to be spheroidal in shape: namely a prolate or oblate spheroid. Naturally, there are benefits gained in doing so. Our approach uses a formulated eigenfunction expansion of spheroidal wave-harmonics to develop two distinct, yet closely related, NZ-FZT algorithms for each type of spheroidal transformation surface. The process only requires knowledge of the E-field along the transformation surface and does not need the corresponding H-field. Given is a systematic exposition of the formulation, implementation, and verification of the newly developed NZ-FZT process. Accordingly, computer software is developed to implement both NZ-FZT algorithms. In the validation process, analytical and empirical radiation structures serve as computational benchmarks. Numerical models of both benchmark structures are created by integrating the software with a field solver, viz., a finite-difference time-domain (FDTD) code. Results of these computer models are compared with theoretical and empirical data to provide additional validation. / Ph. D.

This dissertation is about efficient computation of the electromagnetic fields with the locally corrected Nyström (LCN) method as a point-based boundary element method (BEM). The concept of surface integral equations is discussed and the electric field integral equation (EFIE) is derived from the Maxwell’s equations. Due to its point-based nature, the LCN discretization of the EFIE has some advantages over discretizing the EFIE by the method-of-moments (MoM) which is an element-based BEM. On the other hand, due to maturity of the MoM, a large body of work is available to resolve the numerical issues arising in MoM while there has been less work related to the relatively new LCN. To combine the benefits of the LCN method and the classical Rao-Wilton-Glisson MoM, equivalence between these BEMs are established and their exact relationships are derived. Both the vector-potential EFIE and the mixed-potential EFIE are covered. Various aspects of achieving HO convergence to the correct answer using high-order (HO) LCN method are discussed. In particular, the patch size limitation, predicting the optimal degrees of freedom, and the effect of dynamic range in the solution are discussed both analytically and numerically to provide concrete motivations towards HO LCN. The benefits of an HO BEM can not be realized unless an HO geometry representation is used in conjunction with the BEM. Non-uniform rational b-spline (NURBS) surfaces are the most widely adopted HO geometry modelling technique in various disciplines due to their many advantages. However, a typical mesh created out of NURBS surfaces contain both triangular and quadrilateral elements while formulating LCN based on Gaussian quadrature rules on triangular elements have limitations. As a result, the LCN community has mostly adopted LCN based on curvilinear quadrilateral modelling of the geometry. A new class of Newton-Cotes quadrature rules for triangles is proposed to facilitate incorporating NURBS surfaces into the HO LCN. / May 2016

Modeling of the electromagnetic, structural, thermal, or acoustic response of the human body to various external and internal stimuli is limited by the availability of anatomically accurate and numerically efficient computational models. The models currently approved for use are generally of proprietary or fixed format, preventing new model construction or customization. 1. This dissertation develops a new Visible Human Project - Female (VHP-F) computational phantom, constructed via segmentation of anatomical cryosection images taken in the axial plane of the human body. Its unique property is superior resolution on human head. In its current form, the VHP-F model contains 33 separate objects describing a variety of human tissues within the head and torso. Each obejct is a non-intersecting 2-manifold model composed of contiguous surface triangular elements making the VHP-F model compatible with major commercial and academic numerical simulators employing the Finite Element Method (FEM), Boundary Element Method (BEM), Finite Volume Method (FVM), and Finite-Difference Time-Domain (FDTD) Method. 2. This dissertation develops a new workflow used to construct the VHP-F model that may be utilized to build accessible custom models from any medical image data source. The workflow is customizable and flexible, enabling the creation of standard and parametrically varying models facilitating research on impacts associated with fluctuation of body characteristics (for example, skin thickness) and dynamic processes such as fluid pulsation. 3. This dissertation identifies, enables, and quantifies three new specific computational bioelectromagnetic problems, each of which is solved with the help of the developed VHP-F model: I. Transcranial Direct Current Stimulation (tDCS) of human brain motor cortex with extracephalic versus cephalic electrodes; II. RF channel characterization within cerebral cortex with novel small on-body directional antennas; III. Body Area Network (BAN) characterization and RF localization within the human body using the FDTD method and small antenna models with coincident phase centers. Each of those problems has been (or will be) the subject of a separate dedicated MS thesis.

The discontinuous Galerkin method (DGM) is applied to a number of problems in computational electromagnetics. This is achieved by obtaining numerical solutions to Maxwell's equations using the DGM. The aim of these simulations is to highlight the strengths of the method while showing its resilience in handling problems other schemes may not be able to accurately model. Although no method will ever be the best choice for every problem in electromagnetics, the discontinuous Galerkin method is able to accurately approximate any problem, although the computational costs can make the scheme impractical for some. Like other time domain schemes, the DGM becomes inefficient on large domains where the solution contains small wavelengths. We demonstrate that all of the different types of boundary conditions in electromagnetic wave propagation can be implemented into the DGM. Reflection and transmission boundaries fit easily into the framework, whereas perfect absorption requires a more advanced technique known as the perfectly matched layer. We begin by simulating mirrors with several different geometries, and analyze how the DGM method performs, and how it offers a more complete evaluation of the behavior in this problem than some other methods. Since Maxwell's equations describe the macroscopic features of electromagnetics, our simulations are able to capture the wave features of electromagnetics, such as interference and diffraction. We demonstrate this by accurately modelling Young's double slit experiment, a classic experiment which features well understood interference and diffraction phenomena. We also extend the basic electromagnetic wave propagation simulations to include situations where the waves travel into new media. The formulation of the DGM for Maxwell's equations allows the numerical solutions to accurately resolve the features at the interface of two media as predicted by the Fresnel coefficients. This allows the DGM to model lenses and other sources of refraction. We predict that the DGM will become an increasingly valuable method for computational electromagnetics because of its wide range of applicability as well as the lack of undesirable features in the numerical solutions. Furthermore, the only limiting factor for applying DGM, its computational cost, will become less influential as computing power continues to increase, allowing us to apply the DGM to an increasing set of applications.

This thesis presents a full-vectorial mode matching method for whispering gallery microcavity analysis. With this technique, optical properties such as resonance wavelength, quality factor and electromagnetic field distribution of an arbitrarily shaped microcavity can be computed with high accuracy. To illustrate this, a mode matching analysis that involves a single propagating whispering gallery mode is performed on a microtoroid in the presence of individual nonplasmonic nanoparticle on its surface. This method is also extended to the analysis of cavity adsorbed by a plasmonic nanoparticle at a wavelength close to plasmon resonance where the resulting field distortion invalidates other approaches. The simulation demonstrates high efficiency and is in close agreement with experimental measurements reported in previous work. Furthermore, we extend our mode matching analysis to the case where multiple whispering gallery modes are involved in the course of light propagation. The new formalism is performed on a cavity-waveguide coupling system to investigate the light delivery from a tapered optical waveguide to a microcavity at high precision. A novel hybrid integration scheme to implement an ultra-high quality factor microcavity on a silicon-on-insulator platform is proposed based on the related modelling results. / Graduate / 0752 / 0544 / duxuanmax@gmail.com

The discontinuous Galerkin method (DGM) is applied to a number of problems in computational electromagnetics. This is achieved by obtaining numerical solutions to Maxwell's equations using the DGM. The aim of these simulations is to highlight the strengths of the method while showing its resilience in handling problems other schemes may not be able to accurately model. Although no method will ever be the best choice for every problem in electromagnetics, the discontinuous Galerkin method is able to accurately approximate any problem, although the computational costs can make the scheme impractical for some. Like other time domain schemes, the DGM becomes inefficient on large domains where the solution contains small wavelengths. We demonstrate that all of the different types of boundary conditions in electromagnetic wave propagation can be implemented into the DGM. Reflection and transmission boundaries fit easily into the framework, whereas perfect absorption requires a more advanced technique known as the perfectly matched layer. We begin by simulating mirrors with several different geometries, and analyze how the DGM method performs, and how it offers a more complete evaluation of the behavior in this problem than some other methods. Since Maxwell's equations describe the macroscopic features of electromagnetics, our simulations are able to capture the wave features of electromagnetics, such as interference and diffraction. We demonstrate this by accurately modelling Young's double slit experiment, a classic experiment which features well understood interference and diffraction phenomena. We also extend the basic electromagnetic wave propagation simulations to include situations where the waves travel into new media. The formulation of the DGM for Maxwell's equations allows the numerical solutions to accurately resolve the features at the interface of two media as predicted by the Fresnel coefficients. This allows the DGM to model lenses and other sources of refraction. We predict that the DGM will become an increasingly valuable method for computational electromagnetics because of its wide range of applicability as well as the lack of undesirable features in the numerical solutions. Furthermore, the only limiting factor for applying DGM, its computational cost, will become less influential as computing power continues to increase, allowing us to apply the DGM to an increasing set of applications.