Engineering Mathematics 1 Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering by Sergei Silvestrov and Milica Rancic

Chapter 1 Frequency Domain and Time Domain Response of the Horizontal Grounding Electrode Using the Antenna Theory Approach

This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. In particular, it features mathematical methods and models of applied analysis, probability theory, differential equations, tensor analysis and

computational modelling used in applications to important problems concerning electromagnetics, antenna technologies, fluid dynamics, material and continuum physics and financial engineering.

The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods

and results discussed.

Chapters 1–10 are concerned with applied mathematics methods and models applied in electrical engineering, electromagnetism and antenna technologies. Chapter 1 by Dragan Poljak is concerned with applications of integro-differential equations and numerical analysis methods to the analysis of grounding systems important in the design of lightning protection systems. The analysis of horizontal

grounding electrodes has been carried out using the antenna theory approach in the frequency and time domain respectively. The formulation is based on the corresponding space-frequency and space-time Pocklington integro-differential equations.

The integro-differential relationships are numerically handled via the Galerkin– Bubnov scheme of the Indirect Boundary Element Method. Frequency domain and time domain analysis is illustrated by computational examples. Chapter 2 by Silvestar Šesnić and Dragan Poljak deals with the use of analytical methods for solving various integro-differential equations in electromagnetic compatibility, with the emphasis on the frequency and time domain solutions of the thin-wire configurations buried in a lossy ground. Solutions in the frequency domain are carried out via certain mathematical manipulations with the current function appearing in corresponding integral equations. On the other hand, analytical solutions in the time domain are undertaken using the Laplace transform and Cauchy residue theorem. Obtained analytical results are compared to those calculated using the numerical solution of the frequency domain Pocklington equation, where applicable.

Also, an overview of analytical solutions to the Grad-Shafranov equation for tokamak plasma is provided. In Chap. 3 by Milica Rančić, Radoslav Jankoski, Sergei Silvestrov and Slavoljub Aleksić, a new simple approximation that can be used for modelling one type of Sommerfeld integrals typically occurring in the expressions that describe sources buried in the lossy ground, is proposed. The proposed approximation has a form of a weighted exponential function with an additional complex constant term. The derivation procedure for this approximation is explained in detail, and the validation is supplied by applying it to the analysis of a bare conductor fed in the centre and immersed in the lossy ground at arbitrary depth. In Chap. 4 by Radoslav Jankoski, Milica Rančić, Vesna Arnautovski-Toseva and Sergei Silvestrov, high frequency analysis of a horizontal dipole antenna buried in lossy ground is performed. The soil is treated as a homogenous half-space of known electrical parameters.

The authors compare the range of applicability of two forms of transmission line models, a hybrid circuit method, and a point-matching method in this context. Chapter 5 by Pushpanjali G.

 pertains to an experimental implementation and evaluation of geometrically designed antennas. A novel design for an equilateral triangular microstrip antenna is proposed and tested. The antenna is designed, fabricated and tested for single and multiband operation. A theory for such antennas based on the experimental results is also considered. Chapter 6 by Nenad Cvetković, Miodrag Stojanović, Dejan

Jovanović, Aleksa Ristić, Dragan Vučković and Dejan Krstić provides a brief review of the derivation of two groups of approximate closed form expressions for the electrical scalar potential Green’s functions that originates from the current of the point ground electrode in the presence of a spherical ground inhomogeneity, proposes approximate solutions and considers known exact solutions involving infinite series sums. 

The exact solution is reorganized in order to facilitate comparison to the closed form solutions, and to estimate the error introduced by the approximate solutions, and error estimation is performed comparing the results for the electrical scalar potential obtained applying the approximate expressions and the accurate calculations. This is illustrated by a number of numerical experiments. In Chap. 7 by Mario Cvetković and Dragan Poljak, the electromagnetic thermal dosimetry model for the human brain

exposed to electromagnetic radiation is developed. 

The electromagnetic model based on the surface integral equation formulation is derived using the equivalence theorem for the case of a lossy homogeneous dielectric body. The thermal dosimetry model of the brain is based on the form of Pennes’ equation of heat transfer in biological issue. The numerical solution of the electromagnetic model is carried out using the Method of Moments, while the bioheat equation is solved using the finite element method. The electromagnetic thermal model developed here has been applied in internal dosimetry of the human brain to assess the absorbed electromagnetic energy and consequent temperature rise.