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.

This paper describes some of the new features in the commercial electromagnetic software Altair Feko. These include the domain decomposition method (DDM) for non-conformal meshes, characteristic basis function method (CBFM) to reduce the number of unknowns, extending the characteristic mode analysis (CMA) to include lossy dielectrics, and improving the combined method of moments (MoM) and multiconductor transmission line (MTL) cable harness solution.

This work presents a numerical technique for the analysis of the Radar Cross Section (RCS) of large targets combining macro-basis functions, the multilevel fast multipole method and the generation of near-field preconditioners, using an approximate inverse matrix where the sparsity pattern is dynamic and computed considering an upper memory threshold. In order to improve the scalability, a group of rows is computed using the same least squares matrix minimising the Frobenius norm of the error, rendering each row group problem independent from the rest. This approach is applied to large and realistic problems in the test cases included. The presented preconditioner can be used to optimise the convergence of complex problems with respect to the hardware resources available in each case while being transparent to the user.

A technique for the reduction in the CPU-time in the analysis of electromagnetic problems using the Characteristic Basis Function Method (CBFM) is presented here, allowing for analysis of electrically large cases where an iterative solution process cannot be avoided. This technique is based on the use of the Adaptive Cross Approximation (ACA) for the fast computation of the coupling matrix between CBFs belonging to adjacent blocks, as well as the Multilevel Fast Multipole Method (MLFMM) for the computation of matrix−vector products in the solution of the full system. This combination allows for a noticeable reduction in the computational resources during the analysis of electrically large and complex scenarios while maintaining a very good degree of accuracy. A number of test cases serve to validate the presented approach in terms of accuracy, memory and CPU-time compared with conventional techniques.

A numerical approach for the reduction of the CPU time associated with the solution of electromagnetic problems with multiple right-hand sides is presented. This technique is especially suited to analyze the monostatic radar cross section (RCS) of electrically large cases, based on a novel interpolation approach over several directions and/or frequencies, reducing the total simulation time significantly while maintaining a good degree of accuracy. The test cases show that the approach provides accurate results for complex bodies and a noticeable reduction in the CPU time of the simulations.

This document presents a method for reducing the memory and CPU time required for the electromagnetic analysis of complex scenarios employing the Characteristic Basis Function Method. This technique introduces a novel procedure to accelerate the calculation of basis functions and the reduced matrix. The accuracy and computational cost associated with this approach are studied and validated through a number of test cases, making use of about five times less memory than with the conventional approach.

This paper presents a computationally efficient approach for the solution of electromagnetic problems based on the combination of the Characteristic Basis Functions and Adaptative Cross Approximation, allowing an improvement of the processing time and memory requirements with respect to the conventional MoM and CBFM approaches. The presented technique has been validated using a number of cases in order to assess its accuracy and efficiency.

A technique for the reduction of the CPU-time in the solution of complex electromagnetic problems using the Characteristic Basis Function Method is presented. This approach allows the analysis of electrically large cases iteratively using the Multilevel Fast Multipole Method to account for the matrix-vector products and defines a new procedure for the fast computation of the Characteristic Basis Functions and the reduced matrix. Some representative test cases show that the approach provides accurate results for complex bodies with a noticeable efficiency improvement.

This paper describes some of the latest features in the commercial electromagnetic software Altair Feko. These include the impedance sheet formulation to model multilayer frequency selective surface (FSS) radomes and coatings, method-of-moments (MoM) hybridised with faceted uniform theory of diffraction (UTD), shooting and bouncing rays (SBR) hybridised with standard ray tracing (SRT), and MLFMM parallel efficiency improvements.

This paper describes some of the latest features in the commercial electromagnetic software Altair Feko (including newFASANT). These include the surface impedance approach to compute SAR, surface roughness, PCB radiation emissions through an interface to Altair PollEx, and extensions to the characteristic basis function method to model radomes.

This article presents a technique for the computation of the monostatic radar cross section of complex objects based on a combination of macro-basis functions (MBFs) and the multilevel fast multipole algorithm. An initial pool of excitation-independent MBFs is first obtained, generating the corresponding reduced coupling matrix as well as the multipole data. For each excitation, ray-tracing processing is performed, extracting a number of critical points that are used to obtain a mask that allows to dynamically select the basis functions to be considered in the analysis. This strategy allows a noticeable reduction in the size of the problems with minimal CPU-time preprocessing overhead.

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.

This work details a technique tailored to the analysis of complex radome structures based on the non-overlapping separation of two different domains: antenna and radome. Both domains are analyzed isolated using the method of moments with the multilevel fast multipole algorithm (MoM-MLFMA) for the antenna domain and a modified characteristic basis function method with the multilevel fast multipole algorithm approach for the radome domain. An iterative procedure is then applied to compute the effect of each domain over the complementary domain. This approach usually converges into a few iterations, yielding very good results and significant efficiency improvements with respect to other efficient approaches such as a full-wave MoM-MLFMA analysis of the full problem. A realistic test case is included, considering a radome with an embedded frequency selective structure on one of its interfaces. The results show a very good agreement considering only three iterations between domains, requiring only one-third of the CPU-time needed by the conventional approach.

We present a new approach for the analysis and design of radome structures. It makes use of extended domain macro-basis functions obtained from the characteristic basis function method in order to represent the current distribution over the radome. This involves computational advantages due to the reduction in the number of unknowns compared to conventional approaches. This approach involves dividing the scenario into two domains, antenna and radome, and calculating the influence between them using a technique that iteratively corrects the error of the currents on each domain. This technique can be used to analyze arbitrary-shaped radome antennas including several material layers with different thicknesses and dielectric properties that can embed frequency selective surfaces on any interface. Several test cases are presented for the validation of the proposed technique.

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.

This work presents an efficient approach for the generation of distributed Sparse Approximate Inverse preconditioners based on the near-field coupling information for the analysis of electromagnetic problems on large computing clusters. This scheme combines the Message Passing Interface and Open Multi-Processing paradigms in order to minimise the CPU time and memory footprint of the preconditioner, making use of specific algorithms tailored to balance the load and reduce the amount ot information shared between nodes. Some representative examples provide insight into the scalability and performance of the described approach addressing large and realistic scenarios.

In recent years, the characteristic basis function method has been developed as an efficient approach for the solution of large electromagnetic radiation or scattering problems. According to this technique, the currents over the scenario under analysis are defined using a set of pre-computed characteristic basis functions, associated with a number of blocks into which the geometry is partitioned. This involves some computational advantages due to the reduction of the number of unknowns compared to conventional approaches. However, additional pre-processing time is introduced due to the computation of the CBFs and the reduced coupling matrix. A novel strategy is presented in this study in order to accelerate the generation of the reduced matrix, based on the application of the multilevel fast multipole algorithm.

This paper describes an iteration-free numerical approach for the analysis of the monostatic Radar Cross Section of arbitrary scenarios. The proposed method is based on a combination of the Sparse Approximate Inverse of the near-field coupling matrix and the Multilevel Fast Multipole Algorithm, and allows to bypass the iterative solution process maintaining a good degree of accuracy.

This letter presents an efficient approach for the electromagnetic analysis of complex scenarios involving transmitting antennas moving along predetermined trajectories. In order to efficiently reduce the size of the problem for each position of the antenna, we propose a technique based on macro basis functions that are dynamically generated using a ray-tracing analysis. The multilevel fast multipole algorithm is also included in order to reduce the memory consumption and speed up the solution process. Some representative test cases serve to validate the efficiency and performance of the proposed approach.