Slobodan V. Savić was born in Belgrade, Serbia, in 1985. He received the B.Sc.E.E., M.Sc.E.E. and Ph.D. degrees from the School of Electrical Engineering, University of Belgrade, Serbia, in 2008, 2009, and 2015, respectively.
In 2010, he joined the School of Electrical Engineering, University of Belgrade, as a Teaching Assistant. He was promoted to an Assistant Professor in 2016 and to an Associate Professor in 2021.
His main areas of interest are computational electromagnetics, antennas and active and passive microwave circuits and components.
We have implemented the curl-conforming max-ortho basis functions in the higher order large-domain FEM for the first time. Additionally, we have developed the novel two-term recurrent formula which simplifies this implementation and enables fast and accurate calculation of max-ortho basis functions for arbitrary high field-expansion orders. We have also examined the performance of the three types of basis functions: classical, near-ortho, and max-ortho, within the FEM framework, showing that the usage of the max-ortho basis functions results in the smallest condition number of a mass matrix (in eigen-value problems) and a final FEM matrix (in driven problems), and fastest convergence of iterative solvers. In the higher order large-domain FEM, a mass matrix with the lowest possible condition number (in special cases independent of N and as low as 1) is mostly desirable, especially when relatively high field-expansion orders are used in the p-refinement, so there is additional motivation to construct meshes with as many as possible FEs with orthogonal axes. Moreover, we have discussed all the benefits of the max-ortho basis functions and their limitations in the context of curved-element modeling. We have also shown that max-ortho basis function can reduce the number of iterations necessary for the iterative solver to converge. Additionally, due to sparse storage schemes typically employed in the FEM, the usage of the max-ortho basis functions can lead to reduction in the number of non-zero matrix entries and thus to reduction of used memory, which is not the case in the MoM-SIE. Hence, we conclude that the max-ortho basis functions fully enable the use of meshes with a small number of electrically large FEs with very high field-expansion orders, and thus exploit to the full potential all the benefits of higher order large-domain FEM modeling, especially in conjunction with iterative solvers.
We have presented, implemented, and validated by representative numerical experiments, a nonrigorous symmetric second-order ABC in combination with large-domain higher-order FEM technique for frequency domain EM scattering analysis. In the proposed method, the ABC is implemented nonrigorously, without imposing the normal field continuity and without introducing additional variables. The required divergence of the nonconformal field components is computed numerically on the faces of elements belonging to the ABS, using simple finite differences. Numerical experiments have shown that the nonrigorous second-order ABC performs significantly better compared to the first-order ABC and that the proposed method results mach very good with referent numerical solution of high accuracy. Moreover, the examples have shown that the errors in computation of the RCS can be significantly lower if the divergence term is included in the ABC, as described, than if it is omitted. This conclusion is in contrast with results reported thus far in the literature, where examples with small-domain FEM meshes have been utilized exclusively. Finally, examples with a dielectric cubical scatterer and the NASA almond have shown that the proposed method can be successfully applied in analysis of scatterers with sharp edges and tips.
This paper has presented a novel conformal cubical transformation-based metamaterial invisibility cloak and its rigorous full-wave numerical validation and evaluation in both the near field and the far field based on a higher order large-domain FEM-MoM modeling approach. The numerical characterization has been carried out employing large anisotropic continuously inhomogeneous generalized hexahedral finite elements, with no need for a discretization of the permittivity and permeability profiles of the cloak (subdivision into very small finite elements), typical for conventional approaches to FEM analysis of transformation-based cloaks, and the analysis has required about 30 times fewer unknowns to obtain the results of a similar accuracy when compared to the COMSOL Multiphysics® solution. Numerical results have shown a very substantial reduction, of five to ten orders of magnitude, in the backscattering cross section of the cloaked cube, with both lossless and lossy cloaks, in the entire analyzed range of wavelengths. They have also demonstrated the accuracy and efficiency of a simple 24-element large-domain model of the cubical cloak yielding a backscatter so low that it is on par with the best numerical approximation of the zero backscatter from an empty cubical region of the same size as the original scatterer, as verified by WIPL-D and a pure surface (MoM) model. The fact that the far-field numerical FEM-MoM results for the cubical cloak are similar or better than the respective results for the linear spherical cloak has been attributed to an exact geometrical representation of the cubical cloak vs. an approximate modeling of the spherical geometry using fourth-order Lagrange quadrilateral patches. The results have also shown the bistatic behavior of the lossless and lossy (with several characteristic loss tangents) cubical cloaks consistent with the corresponding results for the spherical and cylindrical cloaks – the incorporation of loss does not degrade the backscattering performance of the cloak, while a smooth degradation of the cloak's forward scattering performance occurs with the increase of loss in the cloak material. It is believed that the presented novel cubical cloak and its rather unconventional validation and evaluation can be of a significant interest and value in investigations of coordinate transformations needed for the conformal cloaking of cubical structures or similar objects with sharp edges and corners, as well as in developments of conformal transformation-based PMLs.
This paper has proposed and demonstrated a highly efficient and versatile 3-D numerical model of a cloaking structure. In particular, it has presented higher order FEM-MoM computational electromagnetic analysis of a spherical transformation-based metamaterial cloak, with the continuously inhomogeneous anisotropic cloaking region modeled using large curved finite elements that allow continuous spatial variations of complex permittivity and permeability tensors and high-order field approximations throughout their volumes. The flexibility of the technique has enabled a very effective modeling of the cloak by means of only six FEM elements and six MoM patches over the volume and external surface, respectively, of the cloaking layer, and a very small number of unknowns. Numerical results have shown a very significant reduction (three to five orders of magnitude for the 6-element model and five to seven orders of magnitude for the 24-element model) in the scattering cross section of the cloaked PEC sphere in a quite broad range of wavelengths, thus providing a broadband characterization of a 3-D cloaking device. Given the introduced explicit approximations in modeling of the spherical geometry and continuous material tensor profiles (both by fourth-order Lagrange interpolating functions), and inherent numerical approximations involved in the FEM and MoM techniques and codes, a conclusion is that the cloaking effects can be predicted rather accurately by the presented full-wave numerical analysis method. The method and numerical model can be readily adapted for analysis and design of electrically larger and/or more complex 3-D cloaking devices (which can be arbitrarily inhomogeneous and can include sharp edges and reentrant corners) with proper h-, p-, and hp-refinements [28] of simple initial models.
This letter has introduced a constant speed parametrization mapping of MoM-SIE boundary surfaces in analysis of antennas and scatterers and its approximation using large Lagrange-type quadrilateral patches, and has demonstrated, on simple examples of line-to-curve and square-to-surface mappings, the importance of achieving, at least approximately, the constant speed parametrization (arc-length parametrization) along the surface coordinate lines. The proper placement of interpolation nodes that ensures minimum mapped parametric space distortion is especially important when large high-order curvilinear elements are constructed and applied. In the scattering example, the CSP mapping has resulted in on average five times lower percentage error in RCS computations than with the ray casting parametrization mapping. The RCS results have confirmed all conclusions and expectations derived from the analysis of geometrical results in Fig. 3. Moreover, we realize that what appeared as slight geometrical inaccuracies in the model actually translates into rather considerable errors in the RCS, which emphasizes even more the importance of proper geometrical mapping, namely, CSP mapping in the higher order MoM-SIE case. The proposed CSP mapping concept for 3-D MoM-SIE modeling, developed and implemented in this work for the cube-to-sphere mapping, can be extended to arbitrary curves and surfaces, taking into account specific changes of the curvature radii in the parametric space.
Motivated by an intention to check exactly to what extent is the choice of antenna array elements important in the design of very large millimeter-wave LOS-MIMO arrays, we have modeled and rigorously simulated three types of antenna array elements. Deliberately, general antenna types were studied, while noting modification possibilities for an improved operation. In addition to the trade-offs at the system level, in the number of antennas, sizes of sub-array elements, powering schemes and others, it has been shown that a trade-off should be performed at an antenna design level as well, for the optimal performance of the antenna sub-arrays. The obtained results unambiguously confirm the anticipated benefits in the utilization of highly efficient, wideband, antennas, which often require more complex designing approaches and design optimization for the best results. It is profitable to invest additional time and effort into the antenna sub-array design, to improve the characteristics of an overall array and increase the system capacity.
We have proposed a simple and inexpensive wire-based internal matching network for axial-mode helical antennas. We have also formulated an equivalent thin-wire-based EM model of internally matched helical antennas. The proposed model yields results which are in an excellent agreement with the complete full-wave FEM simulations. The accuracy of the proposed model has also been validated by measurements on a fabricated antenna. In the presented example, the proposed model reduces the simulation run time by more than 100 times and 400 times, compared to FEM and MoM full-wave analysis of complete models, respectively, while maintaining excellent accuracy. We remark that when employing the equivalence from [15], as done here, high-permittivity dielectrics may yield unacceptably large wire radii in the equivalent model. This can be bypassed by using the method from [22], which would, however, require modification of the available commercial software.
We have outlined the guidelines for teaching hard-to-grasp concepts of analytically solving EM problems that involve inhomogeneous media in electrostatic fields, stationary current fields, and stationary magnetic fields. These problems are the essence of the Fundamentals of Electrical Engineering 1 and 2 coursework, which most of the first-year students in Electrical Engineering have to take. At the introductory level, the coursework focuses on simply recognizing classes of problems that can be solved in closed form. Once recognized, the problems can be solved by applying simple rules, based on comparison with solutions in homogeneous media. In addition, we have presented strict mathematical proofs, based on vector calculus, regarding the types of problems that can be analytically solved. These proofs can be presented in an intermediate level course (e.g., in the third year Electromagnetics course). Although the presented physical concepts and rigorous mathematical proofs are extremely important for unambiguous comprehension of the fundamentals of EM field analysis (and as such they are adopted as parts of our regular undergraduate introductory and intermediate level courses in Electrical Engineering), to the best of our knowledge, they have not been addressed previously in such a unified and clear manner in any EM textbooks or educational papers.
In this paper, the influence of mechanical activation on microstructure, kinetics, and formation of spinel, along with the site occupancy in the resulting MgAl2O4 spinel, was investigated in detail. The main conclusions are: (1) 60 minutes of mechanical activation lead to mechanochemical reaction within the initial powder; its microstructure appeared to be homogeneous with a reduction in agglomerate and particle size, compared to the non-activated one. (2) DTA indicated several processes taking place during heating: humidity evaporation, desorption, diffusion, decomposition of Mg(OH)2, and carbonation of a portion of MgO. In addition, an exothermic peak corresponding to the spinel formation was observed, shifting from 1100–1400°C to 950–1150°C, with a corresponding reduction in value of Ea from 580 to 420 kJ mol −1. (3) Analysis of microstructures showed that AM–0–1600 and AM–60–1600 had no open porosity, indicating that the final stage sintering was reached. As density increased, the pores became more regular in shape. The increased density also lead to increases in the dielectric permittivity, from the lowest values of less than 3 after sintering at 1200°C to values of more than 6 after sintering at 1600°C. (4) Inverse spinel, with additional Raman peak at 724 cm–1, was observed in all of sintered samples, with an increase in inverse spinel content with increase in sintering temperature and higher inverse spinel content in mechanically activated samples. Detailed analysis of Raman spectra indicated the breaking point for ordering of crystal structure to be around 1500°C for non-activated samples, while that point for activated samples is shifted to 1400°C. (5) Finally, the mechanical activation, as a preparation process, has a strong influence on all hierarchical levels within the powders and sintered samples: it affects the chemical reaction, lowers the temperature of the spinel formation by about 200°C, and lowers the temperature of arrangement of the crystal lattice by about 100°C.
"Zbirka ispitnih pitanja i zadataka iz Mikrotalasne tehnike,"
Belgrade: Academic Mind, 2022.
ISBN: 978-86-7466-938-9;
"Mikrotalasna elektronika,"
Belgrade: Academic Mind, 2016.
ISBN: 978-86-7466-625-8;