Felipe Cátedra

Generation of Characteristic Basis Functions Defined Over Large Surfaces by Using a Multilevel Approach

An efficient procedure for the generation of characteristic basis functions (CBFs) over large arbitrary surfaces is presented in this work. The first step is to partition the original object into subdomains and then derive the CBFs for these domains by solving for the currents induced by a set of components of the planewave spectrum (PWS). Next, we aggregate the adjacent domains to obtain enlarged CBFs by expanding the original ones in terms of the weighted planewaves used to compute them. This process can be performed iteratively and involves fast, non-expensive matrix manipulation. We obtain a progressive decrease of the number of unknowns, as we increase the domain size, by following the procedure described above.

Accurate Representation of the Edge Behavior of Current When Using PO-Derived Characteristic Basis Functions

A procedure for accurate solution of scattering problems involving geometries with sharp edges by using physical optics-based characteristic basis functions, which themselves do not possess edge singularities, is presented in this communication. Our strategy is to employ special types of blocks that contain the free edges of the object, within which we can accurately represent the behaviors of the currents with rapidly varying amplitudes, still by using physical optics (PO)-types functions for the initial bases. The set of geometrical blocks which are associated solely with the edges extend along each edge, but have a relatively small width. The final number of characteristic basis functions using this approach is only slightly greater than that needed in the conventional characteristic basis function method (CBFM), which does not utilize the edge-block strategy. However, the accuracy in the final results is notably improved in some cases.

Optimization of a Dual-Band Helical Antenna for TTC Applications at S Band

A compact dual-band equatorial helical antenna for TTC (telemetry, tracking, and control) applications in satellites is presented. The network feeding system of the antenna was also designed, analyzed, and measured to achieve circular polarization. A Moment Method code was used to evaluate the performance of both the helical antenna and the feed-circuit network. The whole system was optimized to fulfill rather strict specifications, while maintaining quite small size and weight. A prototype of the helical antenna was fabricated and measured. The design process of the geometrical model, and comparisons between the predicted and measured values, are presented. The results led to the conclusion that it is a very suitable antenna for operating at S band.

Fast ray-tracing for computing n-bounces between curved surfaces

A new ray-tracing method has been developed for the analysis of antennas on-board complex structures and to compute the propagation at indoor/outdoor environments considering n-bounces. The structures (satellites, ships, aircrafts, etc.) are modeled by planar and/or curved surfaces defined by perfectly electrical conductors or dielectric materials (with or without losses). The structures are defined as parametric surfaces, in particular by NURBS (Non-Uniform Rational B-Spline) surfaces. The approach is based on the Uniform Theory of Diffraction (UTD) for the field computation.

Development of an efficient rigorous technique based on the combination of CBFM and MLFMA to solve very large electromagnetic problems

A numerically efficient approach for the rigorous computation of scattering and radiation problems is presented. This technique is based on the combination of the Characteristic Basis Function Method (CBFM) and the Multilevel Fast Multipole Algorithm (MLFMA), and it is intended to deal with very large cases where an iterative solution process cannot be avoided, even considering the matrix size reduction reached by the CBFM. The combination of these techniques avoids the need of computing and storing the terms in the reduced coupling matrix that are not in or close to the diagonal, optimizing the CPU-time and the memory storage requirements.

Application of Asymptotic and Rigorous Techniques for the Characterization of Interferences Caused by a Wind Turbine in Its Neighborhood

This paper presents a complete assessment to the interferences caused in the nearby radio systems by wind turbines. Three different parameters have been considered: the scattered field of a wind turbine, its radar cross-section (RCS), and the Doppler shift generated by the rotating movements of the blades. These predictions are very useful for the study of the influence of wind farms in radio systems. To achieve this, both high-frequency techniques, such as Geometrical Theory of Diffraction/Uniform Theory of Diffraction (GTD/UTD) and Physical Optics (PO), and rigorous techniques, like Method of Moments (MoM), have been used. In the analysis of the scattered field, conductor and dielectric models of the wind turbine have been analyzed. In this way, realistic results can be obtained. For all cases under analysis, the wind turbine has been modeled with NURBS (Non-Uniform Rational B-Spline) surfaces since they allow the real shape of the object to be accurately replicated with very little information.

Fast Analysis of a Dual-Band Reflectarray Using Two Different Numerical Approaches Based on the Moment Method

This communication presents two efficient approaches for the electromagnetic field analysis of complex 3D bodies. The first method can provide a fast and accurate analysis of arbitrary metallic and dielectric/magnetic structures and combines the moment method (MM), the multilevel fast multipole algorithm (MLFMA), physics optics (PO) and the characteristic basis function method (CBFM) to solve very large scattering problems. The second technique is based on a domain decomposition approach that divides the geometry into several parts to minimize the vast computational resources required when applying the MM. A parallelization process was carried out by using the message passing interface (MPI) algorithm to minimize the memory and time requirements for each simulation. A dual-band reflectarray was successfully analyzed to compare the performance of both codes.

Combining the Characteristic Basis Function Method with rooftops and razor-blade testing functions over NURBS patches

The Characteristic Basis Function Method (CBFM) is an efficient technique for overcoming the great burden placed on the computational resources in the conventional Method of Moments (MoM) when used to solve electrically large problems. It is an iteration-free approach that does not suffer from convergence problems as many of the iterative techniques are known to do when dealing with ill-conditioned matrices. The underlying concept of the CBFM is the generation of macro-basis functions that are associated with the subdomains (blocks), in which the large geometry is divided. The CBFM has been continuously evolving, and new approaches to the generation of the CBFs have appeared in recent years, including one that combines high-frequency Physical Optics currents in smooth parts of the object, with MoM type of subdomain functions in regions with fine details. A novel implementation of the CBFM is presented in this communication, in which the Characteristic Basis Functions (CBFs) are represented by means of rooftops that are generated from Non-Uniform Rational B-Splines (NURBS) in the parametric (u,v) domain. The testing procedure makes use of razor-blade functions corresponding to each rooftop.

Design and Optimization of an EBG Antenna with an Efficient Electromagnetic Solver

A novel electromagnetic bandgap (EBG) antenna has been designed, optimized, and analyzed using an efficient electromagnetic solver based on the moment method. Very good agreement between simulations and measurements in anechoic chamber has been obtained. Comparisons of the antenna with and without the EBG structure have been conducted to study its influence in terms of gain. This new EBG antenna is an excellent candidate for several applications due to its high gain and good polarization purity.

Incorporating the multilevel fast multipole method into the characteristic basis function method to solve large scattering and radiation problems

This communication focuses on the problem of reducing the computational cost of generating the reduced matrix in the context of CBFM for very large scatterers using two different approaches: (i) MLFMM to compute the far-field interactions between distant functions; and (ii) stabilized bi-conjugated gradient method (BiCGM) to solve the reduced matrix equation iteratively. Additionally, the CBFM is combined with a geometrical description of the objects using non-uniform rational B-splines (NURBS) defined over a parametric domain, which is well suited for setting up an adaptive mesh without the need of external software tools (C. Delgado et al., 2006). A class of rooftop functions-located on the parametric domain-together with razor-blades serve as the low-level basis and testing functions, respectively, employed to construct the CBFs and subsequently used to generate the reduced matrix.