This work presents a set of algorithmic and architectural improvements to the Physical Optics (PO) method, aimed at enhancing its applicability to industrial-scale electromagnetic simulations. Building on previous research in diffraction modeling, relational databases-specifically PostgreSQL with its geospatial extension PostGIS-have been adopted to manage large volumes of geometric and intermediate data efficiently. The Gordon integral has been implemented natively in C within the database engine, significantly reducing computation time. Additionally, native spatial indexing and memory-aware data structures have enabled the simulation of complex scenarios on standard desktop hardware. An interpolation strategy has been introduced to accelerate ISAR image generation, allowing the reuse of previously computed integrals under small variations in frequency and scattering direction. The proposed framework eliminates memory bottlenecks and improves scalability, demonstrating its effectiveness through radar cross-section (RCS) and ISAR benchmarks. These results confirm the viability of database-driven PO simulations for real-world applications.

A new ray-tracing acceleration technique is presented for electromagnetic simulation problems using the Uniform Theory of Diffraction and meshes of planar facets. The innovation involves using relational databases to accurately store spatial information, enabling spatial indexing through space partitioning with R-trees. This technique effectively reduces the computational cost of several critical phases, including the shadowing test. Additionally, there are multiple advantages to utilizing this technology, such as automated memory and disk management along with a query planner that organizes the instructions automatically. Direct rays, multiple reflections, multiple transmissions, simple diffraction, and combinations of these effects have been implemented in PostgreSQL and its spatial library PostGIS. Compared to traditional techniques that employ Angular Z-Buffer acceleration and store information solely in RAM using a lowlevel language, this approach decreases memory usage by more than 90% in complex scenarios. It also shows a decrease in execution time by more than half when the scenario is sufficiently complex.

When applying the Uniform Theory of Diffraction asymptotic technique, the ray-tracing computational step is the most intensive in terms of computer resources and execution time. This step consists of calculating every possible ray path between a source and an observation point. The second step consists of calculating the electromagnetic contribution of each path, and is generally negligible in relation to the first one.

A refinement for the computation of the rigorous part of the multi-level fast multipole method (MLFMM) of analyzing volumetric objects is presented. A scheme based on the fast Fourier technique (FFT) is proposed with the objective of reducing the computational resources required to accurately analyze large homogeneous and non-homogeneous dielectric volumes. In order to reduce the memory requirements, the storage of the near-field terms of the method of moments (MoM) matrix is performed only for the positions corresponding to a parallelepiped with the size of the level 1 block of the MLFMM, computed with the vacuum permittivity, taking advantage of the Toeplitz symmetry present in regular hexahedral meshes. The FFT avoids applying the near-field MoM matrix in the iterative solution process. The application of this approach results in huge improvements in terms of memory usage, but also a speeds up the iterative solution process because the use of three-dimensional (3D) FFTs is very efficient for computing convolutions when the number of unknowns of the problems becomes very large as happens in volumetric problems. We also propose a new approach for the numerical treatment of the transition of the dielectric permittivity between different dielectrics or between a dielectric and a free space. To validate the computation technique, the radar cross section (RCS) of several dielectric bodies is computed using the classical MLFMM approach and it is compared with the presented FFT-based-MLFMM solution. The results demonstrate that the efficient memory and computation time usage of the proposed approach.

Fast computation of the coefficients of the reduced impedance matrix of the method of moment (MM) is proposed by expanding the basis functions (BFs) in pulses and solving an equivalent periodic problem (EPP) for analyzing large multilayer structures with non-uniform rational basis spline (NURBS) modeling of the embedded layout. These coefficients are required by the computation of sparse approximate inverse (SAI) preconditioner, which leads an efficient iterative version of the MM. This reduced coefficient matrix only considers the near field part of the MM matrix. Discrete functions of small sizes are required to implement the pulse expansion and EPP. These discrete functions of small size lead to discrete cyclic convolutions that are computed in a very fast way by fast Fourier transform (FFT)-accelerated matrix–vector multiplication. Results obtained using a conventional laptop show an analysis of very large multilayer structures with resonant layouts, as whole reflectarrays of electrical size 40 times the vacuum wavelengths, where the iterative MM with a SAI preconditioner can be 22.7 times faster than the pure iterative MM without any preconditioner.

A comparison between Ma-Rokhlin-Wandzura (MRW) and double exponential (DE) quadrature rules for numerical integration of method of moments (MoM) matrix entries with singular behavior is presented for multilayer periodic structures. Non Uniform Rational B-Splines (NURBS) modelling of the layout surfaces is implemented to provide high-order description of the geometry. The comparison is carried out in order to show that quadrature rule is more suitable for MoM matrix computation in terms of sampling, accuracy of computation of MoM matrix, and CPU time consumption. The comparison of CPU time consumption shows that the numerical integration with MRW samples is roughly 15 times faster than that numerical integration using DE samples for results with similar accuracies. These promising results encourage to carry out a comparison with results obtained in previous works where a specialized approach for the specific analysis of split rings geometries was carried out. This previous approach uses spectral MoM version with specific entire domain basis function with edge singularities defined on split ring geometry. Thus, the previous approach provides accurate results with low CPU time consumption to be compared. The comparison shows that CPU time consumption obtained by MRW samples is similar to the CPU time consumption required by the previous work of specific analysis of split rings geometries. The fact that similar CPU time consumptions are obtained by MRW quadrature rules for modelling of general planar geometries and by the specialized approach for split ring geometry provides an assessment for the usage of the MRW quadrature rules and NURBS modelling. This fact provides an efficient tool for analysis of reflectarray elements with general planar layout geometries, which is suitable for reflectarray designs under local periodicity assumption where a huge number of periodic multilayer structures have to be analyzed.

BICGSTAB-FFT method of moment (MM) scheme is proposed to analyze several levels of planar generic layouts embedded in large multilayer structures when the layout geometries are modeled by NURBS surfaces. In this scheme, efficient computation of normalized error defined in iterative bi-conjugate gradient stabilized (BICGSTAB) method for large multilayer structure analysis problems is implemented. The efficient computation is based on pulse expansion with dense equi-spaced mesh of generalized rooftop basis functions (BFs) defined on NURBS surfaces and equivalent periodic problem (EPP) in order to apply fast Fourier transforms (FFT). Moreover, efficient computation of Green's functions for multilayer structure is implemented for near and far field regions. Experimental and numerical validations of whole printed reflect array antennas of electrical size between 8 and 16 times the vacuum wavelengths are shown. In these validations, CPU time consumptions of the proposed method are obtained with results between few minutes and half an hour using a conventional laptop.

In this paper, an efficient technique of computation of method of moments (MM) matrix entries for multilayer periodic structures with NURBS surface and Bézier patches modelling is proposed. An approximation in terms of constant pulses of generalized rooftop basis functions (BFs) defined on Bézier patches is proposed. This approximation leads discrete convolutions instead of usual continuous convolution between Green’s functions and BFs obtained by the direct mixed potential integral equation (MPIE) approach. An equivalent periodic problem (EPP) which contains the original problem is proposed to transform the discrete convolutions in discrete cyclic convolutions. The resultant discrete cyclic convolutions are computed by efficiently using the Fast Fourier Transform (FFT) procedure. The performance of the proposed method and direct computation of the MM entries are compared for phases of reflection coefficient. The proposed method is between 9 and 50 times faster than the direct computation for phase errors less than 1 deg. The proposed method exhibits a behaviour of CPU time consumption of O(NbLog10Nb) as the number Nb of BFs increases. This behaviour provides significant CPU time savings with respect to the expected behaviour of O(Nb2) provided by the direct computation of the MM matrix entries.

Multi-beams antennas are currently being used for direct broadcast satellite, personal communication satellite, military communication satellite, and high-speed internet applications. In this work, a circularly polarized (CP) multi-spot beam satellite parabolic reflectarray antenna is designed to provide six spot beams at 19.7 GHz. For this purpose, an easy technique to compute the required phase shifts to produce two focused beams in specular directions for a CP parabolic reflectarray is proposed. These required phase shifts are added to the reflected fields by the variable rotation of the reflectarray elements printed on the surface of a parabolic antenna which are fed by a dual-CP feed-horn. For this purpose, a reflectarray cell made of a conductive cross embedded in a grounded multilayered substrate is optimized to produce very linear phase-shift and low cross-polarization level. To demonstrate the multibeam capacity, a 1.8-meter offset parabolic reflectarray made of the optimized reflectarray element was designed to generate six focused beams in dual-CP with three dual-CP feed-horns. The six main spots fulfill the typical multi spot satellite requirement with angular separation less than 0.56°, 0.4 dB loss in the gain, and cross-polarization level below 35 dB with respect to the maximum of radiation.

The design of a Compact Dual-band Equatorial helix antenna using Computational Electromagnetic Methods together with multiobjective optimization algorithms is presented. These antennas are used for Telemetry, Tracking, and Control of satellites from the terrain base station. In order to optimize the parameters an antenna, a simulation-optimization process is shown along a real case study. The para...

A novel approach for the analysis and design of radomes is presented. It uses full domain macro-basis functions obtained from the Characteristic Basis Function Method (CBFM), for modeling the radome structure. The presented approach can be used to analyze arbitrary-shaped radome antennas with several material layers composed by different thickness and different dielectrics. Some cases of study are presented in order to validate the new method.

The concept of generating two spaced beams in dual-CP by variable rotation technique (VRT) is validated for the first time by manufacturing and measuring. A reflectarray demonstrator has been designed, manufactured, and tested to deviate +/- 10 degrees the beam of a dual-CP multiflared horn at 19.7 GHz. The proposed reflectarray cell for VRT is made of a conductive cross printed on a grounded dielectric. The experimental results show that two adjacent beams in dual-CP maintain the correct directions in the prescribed frequency band (19.2-20.2 GHz). The results are satisfactory and validate the concept for generating two spaced beams in orthogonal CP by VRT with a single feed.

A design technique has been proposed to generate two closely spaced beams in orthogonal circular polarization using the variable rotation technique (VRT) in reflectarrays printed on arbitrary shaped surfaces fed by a single dual circular polarized (CP) horn. The proposed reflectarray cell for VRT is made of a conductive cross printed on a grounded dielectric. A 1.8-meter offset parabolic reflectarray has been designed to generate six beams in circular polarization with three dual-CP feed-horns, with very promising results for multi spot beam satellite antennas in Ka-band.

In this work, a computer tool for the simulation of the responses of Frequency Modulated-Continuous Wave radar systems in Urban Traffic Scenes is presented. The radar echoes including frequency shifts due to distance and object speeds are computed using a new hybrid technique that combines Method of Moments, Physical Optics and Geometrical Theory of Diffraction. Arbitrarily time-shaped radar sequences can be set for obtaining output parameters like Doppler Spectrum, beat signals in frequency and time domains, distances and speeds of echoes, etc. The technique is efficient and accurate for solving the electrically large and multiscale problem that appears in the simulation of these systems in urban complex scenarios. Representative results are presented.

It is presented a new hybrid technique combining Method of Moments, Physical Optics and Geometrical Theory of Diffraction for the analysis of the vehicle to vehicle and vehicle to infraestructure radio-wave channel in urban traffic scenes. The technique is efficient and accurate for solving the electrically large and multiscale problem that appears in the analyses of these channels. Representative results and cross validations are presented.

Most computer codes in Radar Cross Section (RCS) prediction use Physical Optics (PO) and Physical theory of Diffraction (PTD) combined with Geometrical Optics (GO) and Geometrical Theory of Diffraction (GTD). The latter approaches are computationally cheaper and much more accurate for curved surfaces, but not applicable for the computation of the RCS of all surfaces of a complex object due to the presence of caustic problems in the analysis of concave surfaces or flat surfaces in the far field. The main contribution of this paper is the development of a hybrid method based on a new combination of two asymptotic techniques: GTD and PO, considering the advantages and avoiding the disadvantages of each of them. A very efficient and accurate method to analyze the RCS of complex structures at high frequencies is obtained with the new combination. The proposed new method has been validated comparing RCS results obtained for some simple cases using the proposed approach and RCS using the rigorous technique of Method of Moments (MoM). Some complex cases have been examined at high frequencies contrasting the results with PO. This study shows the accuracy and the efficiency of the hybrid method and its suitability for the computation of the RCS at really large and complex targets at high frequencies.

The design of a Compact Dual-band Equatorial helix antenna is presented. These antennas are used for Telemetry, Tracking, and Control (TTC) of satellites from the terrain base station. A simulation-optimization process is presented, a simulation tool named MONURBS is linked with a well-known multi-objective algorithm (NSGA-II) in order to design and optimize the parameters of the antenna. The size of the antenna that fulfills radiation patterns needed for the communication are obtained using simulation together with a multi-objective algorithm. In this work, a comparison with previous designs and the antenna prototype are be presented showing that this approach can achive solutions expediting the process.

An improved ray-tracing method applied to high-frequency techniques such as the Uniform Theory of Diffraction (UTD) is presented. The main goal is to increase the speed of the analysis of complex structures while considering a vast number of observation directions and taking into account multiple bounces. The method is based on a combination of the Angular Z-Buffer (AZB), the Space Volumetric Partitioning (SVP) algorithm and the A∗ heuristic search method to treat multiple bounces. In addition, a Master Point strategy was developed to analyze efficiently a large number of Near-Field points or Far-Field directions. This technique can be applied to electromagnetic radiation problems, scattering analysis, propagation at urban or indoor environments and to the mutual coupling between antennas. Due to its efficiency, its application is suitable to study large antennas radiation patterns and even its interactions with complex environments, including satellites, ships, aircrafts, cities or another complex electrically large bodies. The new technique appears to be extremely efficient at these applications even when considering multiple bounces.