Milan M. Ilic

Higher Order Hybrid FEM-MoM Technique for Analysis of Antennas and Scatterers

A novel higher order large-domain hybrid computational electromagnetic technique based on the finite element method (FEM) and method of moments (MoM) is proposed for three-dimensional analysis of antennas and scatterers in the frequency domain. The geometry of the structure is modeled using generalized curved parametric hexahedral and quadrilateral elements of arbitrary geometrical orders. The fields and currents on elements are modeled using curl- and divergence-conforming hierarchical polynomial vector basis functions of arbitrary approximation orders, and the Galerkin method is used for testing. The elements can be as large as about two wavelengths in each dimension. As multiple MoM objects are possible in a global exterior region, the MoM part provides much greater modeling versatility and potential for applications, especially in antenna problems, than just as a boundary-integral closure to the FEM part. The examples demonstrate excellent accuracy, convergence, efficiency, and versatility of the new FEM-MoM technique, and very effective large-domain meshes that consist of a very small number of large flat and curved FEM and MoM elements, with p-refined field and current distributions of high approximation orders. The reduction in the number of unknowns is by two orders of magnitude when compared to available data for low-order FEM-MoM modeling.

Enhancing the gain of helical antennas by shaping the ground conductor

We have observed that the size and shape of the ground conductor of axial mode helical antennas have significant impact on the antenna gain. By shaping the ground conductor, we have increased the gain of a helical antenna for as much as 4 dB. Theoretical results are verified by measurements.

Continuously Inhomogeneous Higher Order Finite Elements for 3-D Electromagnetic Analysis

A novel higher order entire-domain finite element technique is presented for accurate and efficient full-wave three-dimensional (3D) analysis of electromagnetic structures with continuously inhomogeneous material regions, using large generalized curved hierarchical curl-conforming hexahedral vector finite elements that allow continuous change of medium parameters throughout their volumes. This is the first general 3D implementation and numerical demonstration of the inherent theoretical ability of the finite element method (FEM) to directly treat arbitrarily (continuously) inhomogeneous materials. The results demonstrate considerable reductions in both number of unknowns and computation time of the entire-domain FEM modeling of continuously inhomogeneous materials over piecewise homogeneous models. They indicate that, in addition to theoretical relevance and interest, large curved higher order continuous-FEM elements also have great potential for practical applications that include structures with pronounced material inhomogeneities and complexities.

Higher Order Large-Domain Hierarchical FEM Technique for Electromagnetic Modeling Using Legendre Basis Functions on Generalized Hexahedra

A novel higher-order large-domain hierarchical finite-element technique using curl-conforming vector basis functions constructed from standard Legendre polynomials on generalized curvilinear hexahedral elements is proposed for electromagnetic modeling. The technique combines the inherent modeling flexibility of hierarchical elements with excellent orthogonality and conditioning properties of Legendre curl-conforming basis functions, comparable to those of interpolatory techniques. The numerical examples show the reduction of the condition number of several orders of magnitude for high field-approximation orders (e.g., 14 orders of magnitude for entire-domain models) when compared to the technique using field expansions based on simple power functions and the same geometrical elements.

Double-Higher-Order Large-Domain Volume/Surface Integral Equation Method for Analysis of Composite Wire-Plate-Dielectric Antennas and Scatterers

A novel double-higher-order large-domain Galerkin-type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for analysis of composite dielectric and metallic radiation/scattering structures combining the volume integral equation (VIE) approach for dielectric parts and the surface integral equation (SIE) approach for metallic parts of the structure. The technique employs Lagrange-type interpolation generalized hexahedra and quadrilaterals of arbitrary geometrical-mapping orders for the approximation of geometry and hierarchical divergence-conforming polynomial vector basis functions of arbitrary expansion orders for the approximation of currents within the elements. The double-higher-order VSIE (VIE-SIE) method is extensively validated and evaluated against the analytical solutions and the numerical results obtained by alternative higher order methods.

Optimal Modeling Parameters for Higher Order MoM-SIE and FEM-MoM Electromagnetic Simulations

General guidelines and quantitative recipes for adoptions of optimal higher order parameters for computational electromagnetics (CEM) modeling using the method of moments and the finite element method are established and validated, based on an exhaustive series of numerical experiments and comprehensive case studies on higher order hierarchical CEM models of metallic and dielectric scatterers. The modeling parameters considered are: electrical dimensions of elements (h -refinement), polynomial orders of basis functions (p-refinement), orders of Gauss-Legendre integration formulas (integration accuracy), and geometrical (curvature) orders of elements in the model. The goal of the study, which is the first such study of higher order parameters in CEM, is to reduce the dilemmas and uncertainties associated with the great modeling flexibility of higher order elements, basis and testing functions, and integration procedures (this flexibility is the principal advantage but also the greatest shortcoming of the higher order CEM), and to ease and facilitate the decisions to be made on how to actually use them, by both CEM developers and practitioners.

Efficient Time-Domain Analysis of Waveguide Discontinuities Using Higher Order FEM in Frequency Domain

A computational technique is presented for efficient and accurate time-domain analysis of multiport waveguide structures with arbitrary metallic and dielectric discontinuities using a higher order finite element method (FEM) in the frequency domain. It is demonstrated that with a highly efficient and appropriately designed frequency-domain FEM solver, it is possible to obtain extremely fast and accurate time-domain solutions of microwave passive structures performing computations in the frequency domain along with the discrete Fourier transform (DFT) and its inverse (IDFT). The technique is a higher order large-domain Galerkin-type FEM for 3- D analysis of waveguide structures with discontinuities implementing curl-conforming hierarchical polynomial vector basis functions in conjunction with Lagrange-type curved hexahedral finite elements and a simple single-mode boundary condition, coupled with standard DFT and IDFT algorithms. The examples demonstrate excellent numerical properties of the technique, which appears to be the first time-from- frequency-domain FEM solver, primarily due to (i) very small total numbers of unknowns in higher order solutions, (ii) great modeling flexibility using large (homogeneous and continuously inhomogeneous) finite elements, and (iii) extremely fast multifrequency FEM analysis (the global FEM matrix is filled only once and then reused for every subsequent frequency point) needed for the inverse Fourier transform.

Higher Order FEM-MoM Domain Decomposition for 3-D Electromagnetic Analysis

A novel higher order domain decomposition (DD) method based on a hybridization of the finite element method (FEM) and method of moments (MoM) is proposed for three-dimensional (3-D) modeling of antennas and scatterers. The method implements multiple FEM domains within a global unbounded MoM environment, based on the surface equivalence theorem. The presented analyses of 3-D and two-dimensional (2-D) finite periodic arrays of inhomogeneous dielectric scatterers demonstrate excellent accuracy, convergence, and efficiency of the new FEM-MoM-DD technique, and a substantial reduction in the memory requirements and computational time when compared to the higher order MoM solution.

On the optimal dimensions of helical antenna with truncated-cone reflector

This paper presents optimization of a helical antenna with a truncated-cone reflector. We have found that the dimensions of the truncated-cone reflector and the dimensions of the helical antenna need to be optimized simultaneously to obtain the optimal design. Furthermore, we have found that the truncated-cone reflector can significantly increase the gain of the helical antenna compared to a circular or a square flat reflector. A set of diagrams is made to enable simple design of helical antennas with truncated-cone reflectors. Finally, the results are experimentally verified.

Measurement and characterization of winter precipitation at MASCRAD Snow Field Site

We present our ongoing studies of winter precipitation using multi-angle snowflake camera (MASC), 2D-video disdrometer, computational electromagnetic scattering methods, and state-of-the-art polarimetric radars. The newly built and established MASCRAD (MASC + Radar) Snow Field Site is one of the currently best instrumented and most sophisticated field sites for winter precipitation measurements and analysis in the nation. We present and discuss MASCRAD measurements for the snow event on Nov 15, 2014 in La Salle, Colorado.