Eliseo Garcia

An Iterative Solution for Electrically Large Problems Combining the Characteristic Basis Function Method and the Multilevel Fast Multipole Algorithm

An iterative scheme for the rigorous computation of electrically large problems is presented. The approach is based on a combination of the characteristic basis function method (CBFM) and the multilevel fast multipole algorithm (MLFMA) that can deal with very large problems that require an iterative solution process, even considering that the application of the CBFM entails an important reduction of the number of unknowns when compared to Method of Moments approaches based on subdomain functions. This reduction is due to the fact that the number of macro-basis functions, called characteristic basis functions (CBFs), is lesser than the number of low-level subsectional functions used to sample the geometry. In addition, the use of the MLFMA avoids the need to calculate and store the coupling terms in the reduced matrix that are not on or close to the diagonal, thereby optimizing the CPU time and the memory storage requirements. non-uniform rational B-splines (NURBS) surfaces are employed for the representation of the geometry and the CBFs are described in terms of curved rooftops generated in the parametric space. The associated macro-testing functions are defined as aggregations of curved razor-blade functions.

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.

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.

Calculation of the RCS from the double reflection between planar facets and curved surfaces

A method to obtain the contribution to the monostatic radar cross section (RCS) due to double reflections between plane facets and curved surfaces is presented. This method is applied to arbitrary targets modeled by NURBS (non-uniform rational B-spline) surfaces. The method developed is a combination of geometrical optics (GO) and the stationary phase method (SPM).

AN EFFICIENT HYBRID-SCHEME COMBINING THE CHARACTERISTIC BASIS FUNCTION METHOD AND THE MULTILEVEL FAST MULTIPOLE ALGORITHM FOR SOLVING BISTATIC RCS AND RADIATION PROBLEMS

A numerically e-cient approach for the rigorous compu- tation of bi-static scattering and radiation problems is presented. The approach is based on an improvement of a previous method scheme that combines the Characteristic Basis Function Method (CBFM) and the Multilevel Fast Multipole Algorithm (MLFMA). The approach com- bines Characteristic Basis Functions (CBFS) and subdomains func- tions for reducing the CPU time in the pre-process and in the solving iterative process for simple or multiple excitations. It is intended for use in very large cases where an iterative solution process cannot be avoided, even considering the matrix size reduction achieved by the CBFM. This reduction is particularly important for solving radiation or bistatic problems in which an integral equation is solved once.

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.

Hybrid Iterative Approach Combined With Domain Decomposition for the Analysis of Large Electromagnetic Problems

In this paper, we propose a technique for the electromagnetic analysis of large objects considering the interactions between separate parts of the geometry (which in this context will be referred to as domains). A number of unknowns is associated to each domain, and only the basis functions included within the same domain are considered fully coupled (i.e., a full-wave analysis is performed for every domain, isolating it from the rest of the geometry). An iterative process is then applied to determine the total currents over the object, considering the currents induced by the external sources and those due to interactions between different domains. Once a current distribution is obtained over a given domain it is essential to identify those passive domains with which the interaction active-domain-passive-domain will yield a significant contribution to the final result (scattered field, radiation pattern, S-parameters, etc.). In this work, we utilize a ray-tracing method combined with the multipole expansion of the active currents over a number of points located on the radiating surface to speed up the solution of large and realistic problems.

Hierarchical scheme for the application of the Characteristic Basis Function Method based on a multilevel approach

We have presented herein a procedure for the generation of high-level Characteristic Basis Functions by using a chained SVD-based technique. The proposed method reduces the overall number of basis functions to be considered for the generation of the reduced matrix and, furthermore, it is very well suited for combining it with a CBFM-MLFMA implementation, because of the similarities between the hierarchical aggregation of CBFs and the expansion in terms of multipoles for several levels.

Efficient combination of acceleration techniques applied to high frequency methods for solving radiation and scattering problems

Abstract 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.

Characteristic Basis Function Method

An efficient technique for solving large electromagnetic problems, called Characteristic Basis Function Method (CBFM), is presented. It is a rigorous technique, based on Method of Moments (MoM), which can solve electrically very large problems using less computer resources than MoM. The key step in the CBFM consists of defining a relatively small number of high-level Characteristic Basis Functions (CBFs) to represent the induced currents on the surface of the problems. The advantages in terms of computational improvements and in the reduction of the complexity of the problems are showed for different kind of problems. Several results and computational analysis are presented in order to illustrate the accuracy and the benefits of the technique.