This thesis introduces a topology optimization approach to design, from scratch, efficient microwave devices, such as antennas and waveguide transitions. The design of these devices is formulated as a general optimization problem that aims to build the whole layout of the device in order to extremize a chosen objective function. The objective function quantifies some required performance and is evaluated using numerical solutions to the 3D~Maxwell's equations by the finite-difference time-domain (FDTD) method. The design variables are the local conductivity at each Yee~edge in a given design domain, and a gradient-based optimization method is used to solve the optimization problem. In all design problems, objective function gradients are computed based on solutions to adjoint-field problems, which are also FDTD discretization of Maxwell's equations but solved with different source excitations. For any number of design variables, the computation of the objective function gradient requires one solution to the original field problem and one solution to the associated adjoint-field problem. The optimization problem is solved iteratively using the globally convergent Method of Moving Asymptotes (GCMMA). By the proposed approach, various design problems, including tens of thousands of design variables, are formulated and solved in a few hundred iterations. Examples of solved design problems are the design of wideband antennas, dual-band microstrip antennas, wideband directive antennas, and wideband coaxial-to-waveguide transitions. The fact that the proposed approach allows a fine-grained control over the whole layout of such devices results in novel devices with favourable performance. The optimization results are successfully verified with a commercial software package. Moreover, some devices are fabricated and their performance is successfully validated by experiments.

This Master's thesis clarifies the significance of Frölicher-Nijenhuis bracket and its applications in problems of physics. The basic apparatus for these applications is differential geometry on manifolds, tensor calculus and differential forms, which are contained in the first part of the thesis. The second part summarizes the basic theory of calculus of variations on manifolds and its selected applications in the field of physics. The last part of the thesis is devoted to the applications of Frölicher-Nijenhuis bracket in the derivation of Maxwell's equations and to the description of the geometry of ordinary differential equations.

The main objective of this study is to learn about the theory of electromagnetic field and to create a model of propagation of ultra short waves in a biological tissue. Next point of this paper is to determine a specific absorption rate (SAR) using a valid sanitary standard. A particular model solution was realized in a model environment of the program Comsol Multiphysics 3.5. A human head and a cellular phone with an intern antenna were successfully created in this model environment. First of all were entered appropriate parameters which led to a successful representation of the distribution of electric field intensity. A value of specific absorption rate taken by a biological tissue was determined in the next step. This value was compared to the value listed in a valid sanitary standard to prevent its overrun. A development of a temperature in a biological tissue was determined as well, according to a six minutes long interval stated in a valid sanitary standard.

Title: Finite elements for electromagnetics compatible with de Rham di- agram Author: Vojtěch Rybář Department: Department of Numerical Mathematics Supervisor: prof. Ing. Ivo Doležel, CSc. Abstract: The present work is devoted to the lowest-order finite elements for solving time-harmonic Maxwell's equations in two dimensions. Suc- cessful approximation of these equations requires the finite element spaces to be compatible with the de Rham diagram. However, the most often used basis functions (the Whitney functions) do not comply with this diagram. Therefore, we construct compatible bases and study their prop- erties. Since the construction is not unique, we investigate the influence of the particular choice on the conditioning of the corresponding finite element matrices. Finally, we utilize the special structure of the stiffness matrices, propose a few iterative schemes, and compare their convergence. Keywords: Maxwell's equations, edge finite element, de Rham diagram, finite element basis 1

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Previous research in InGaN/GaN light emitting diodes (LEDs) employing semi-classical drift-diffusion models has used reduced polarization constants without much physical explanantion. This paper investigates possible physical explanations for this effective polarization reduction in InGaN LEDs through the use of the simulation software SiLENSe. One major problem of current LED simulations is the assumption of perfectly discrete transitions between the quantum well (QW) and blocking layers when experiments have shown this to not be the case. The In concentration profile within InGaN multiple quantum well (MQW) devices shows much smoother and delayed transitions indicative of indium diffusion and drift during common atomic deposition techniques (e.g. molecular beam epitaxy, chemical vapor deposition). In this case the InGaN square QW approximation may not be valid in modeling the devices' true electronic behavior. A simulation of a 3QW InGaN/GaN LED heterostructure with an AlGaN electron blocking layer is discussed in this paper. Polarization coefficients were reduced to 70% and 40% empirical values to simulate polarization shielding effects. QW shapes of square (3 nm), trapezoidal, and triangular profiles were used to simulate realistic QW shapes. The J-V characteristic and electron-hole wavefunctions of each device were monitored. Polarization reduction decreased the onset voltage from 4.0 V to 3.0 V while QW size reduction decreased the onset voltage from 4.0 V to 3.5 V. The increased current density in both cases can be attributed to increased wavefunction overlap in the QWs.

This thesis presents the research results on the development of a microwave tomography imaging algorithm capable of reconstructing the dielectric properties of the unknown object. Our focus was on the theoretical aspects of the non-linear tomographic image reconstruction problem with particular emphasis on developing efficient numerical and non-linear optimization for solving the inverse scattering problem. A detailed description of a novel microwave tomography method based on frequency dependent finite difference time domain, a numerical method for solving Maxwell's equations and Genetic Algorithm (GA) as a global optimization technique is given. The proposed technique has the ability to deal with the heterogeneous and dispersive object with complex distribution of dielectric properties and to provide a quantitative image of permittivity and conductivity profile of the object. It is shown that the proposed technique is capable of using the multi-frequency, multi-view, and multi-incident planer techniques which provide useful information for the reconstruction of the dielectric properties profile and improve image quality. In addition, we show that when a-priori information about the object under test is known, it can be easily integrated with the inversion process. This provides realistic regularization of the solution and removes or reduces the possibility of non-true solutions. We further introduced application of the GA such as binary-coded GA, real-coded GA, hybrid binary and real coded GA, and neural-network/GA for solving the inverse scattering problem which improved the quality of the images as well as the conversion rate. The implications and possible advantages of each type of optimization are discussed, and synthetic inversion results are presented. The results showed that the proposed algorithm was capable of providing the quantitative images, although more research is still required to improve the image quality. In the proposed technique the computation time for solution convergence varies from a few hours to several days. Therefore, the parallel implementation of the algorithm was carried out to reduce the runtime. The proposed technique was evaluated for application in microwave breast cancer imaging as well as measurement data from university of Manitoba and Institut Frsenel's microwave tomography systems.

This thesis presents the research results on the development of a microwave tomography imaging algorithm capable of reconstructing the dielectric properties of the unknown object. Our focus was on the theoretical aspects of the non-linear tomographic image reconstruction problem with particular emphasis on developing efficient numerical and non-linear optimization for solving the inverse scattering problem. A detailed description of a novel microwave tomography method based on frequency dependent finite difference time domain, a numerical method for solving Maxwell's equations and Genetic Algorithm (GA) as a global optimization technique is given. The proposed technique has the ability to deal with the heterogeneous and dispersive object with complex distribution of dielectric properties and to provide a quantitative image of permittivity and conductivity profile of the object. It is shown that the proposed technique is capable of using the multi-frequency, multi-view, and multi-incident planer techniques which provide useful information for the reconstruction of the dielectric properties profile and improve image quality. In addition, we show that when a-priori information about the object under test is known, it can be easily integrated with the inversion process. This provides realistic regularization of the solution and removes or reduces the possibility of non-true solutions. We further introduced application of the GA such as binary-coded GA, real-coded GA, hybrid binary and real coded GA, and neural-network/GA for solving the inverse scattering problem which improved the quality of the images as well as the conversion rate. The implications and possible advantages of each type of optimization are discussed, and synthetic inversion results are presented. The results showed that the proposed algorithm was capable of providing the quantitative images, although more research is still required to improve the image quality. In the proposed technique the computation time for solution convergence varies from a few hours to several days. Therefore, the parallel implementation of the algorithm was carried out to reduce the runtime. The proposed technique was evaluated for application in microwave breast cancer imaging as well as measurement data from university of Manitoba and Institut Frsenel's microwave tomography systems.

Presented dissertation discusses the influence of electromagnetic fields on the weight of the particles, which are considered in this work as substances with the hub. Theoretical knowledge was practically tested on plant organisms (early somatic embryos, fungal pathogens), theoretically the influence of electromagnetic field on cell structure was modeled. It was subsequently confirmed by a practical experiment assumption about the influence of electromagnetic fields on the weight of the particles. These experiments were preceded by a theoretical study of the problem and the formulation of a solution using Maxwell's equations, from which other descriptive equations and formulas were derived. The results of the experiments were presented at several professional conferences and published in professional journals and proceedings.