Contribución al análisis de problemas electromagnéticos mediante el método de los momentos con bajo coste computacional

Abstract

The present thesis is related with the development of numerical techniques which porpouse is focused on the analysis of boarded antennas on 3D perfectly conductive geornetries which shape can become totaily arbitrary. One of the more popular techniques employed to analyze radiation and scattering problems is the Method of Moments (MoM). This method has a high computational cost when the electrical size of the structure increases. Therefore, this thesis shows a way to implernent a efficjent and versatjle method that overcome this limitation of the MoM, to allow the designer of boarded antennas the fast determination of those configurations that satisfy the specifications in terms of radiation patterns, coupling factors couple among antennas. The geometric representation, used to model the 3D structuresaccurately and without too much information, is based on a set of parametric surfaces named NURBS. Most of the CAGD (Computer Aided Geometric Design) software packages available on the rnarket incorporate this format as the standard output in order to describe the body. That provides the advantage of working directly with the format generated by this tools. In the developrnent of the thesis a method was implemented with the porpouse to overcorne the problem of the calculation of geometric parameters in degenerated NTJRBS surfaces. It exist sorne electromagnetism formulations based on MoM that use current rooftops as base functions and razor blaze as weighting functions. In the developed work, one of the main contributions is the formulation of a new weighting function to discretize the magnetic fleid integral equation (MFIE) that overcomes certain limitations of the razor blaze function when acting over subdomines next to edges. An approximated formulation has also been applied, so much in the electric fleid integral equation (EFIE), like in the magnetic fleld integral equation (MFIE) and in the combined one(CFIE), consisting in the representation of the induced current by means of equivalent electric dipolares moments, that simplifies notoriusly the evaluation of each coupling factor (Dipolar Moments Technique, MD). The computacional efficiency is achieved, mainly in memory, due to the calculation of the complete coupling matrix at each step of the iterative method. Importants reductions in memory storage are achieved respect to the MoM, with the results behaving in a similar way. Another method presented to combine with MoM trying to achieve the same advantage is the Fast Multipole Method (FMM). It is based on an approach to the far away subodomines coupling. Applying FMM is possible to reduce the requirements on memory storage when the electrical size of the structure increases. Another of the most important contributions in this thesis is the application to the MoM of new equations resolution methods. The purpose is focused on the reduction of the execution time. It exist a lot of CGM based tools that solve the equations system that generates the MoM discretization. This is a method that assures convergence, but it requires of a lot of execution time when the number of unknowns is big. In this thesis, SIM-AR method is presented, that reduces the number of necessary iterations as well as the execution time. The way to combinate thismethod with MD or FMM techniques is shown in this thesis. In this way, it is possible to reduce memory storage too. At the end of the memory, conclusions about the most outstanding points developed is presented. We think that the most important is the reduction in memory storage and execution time achieved respect to the traditional MoM.