Feixes de raios complexos para a aceleração de algoritmos MoMaplicados a problemas de espalhamento eletromagnético

Abstract

This research aims at evaluating the possibility of using the Complex Source Beam Method of Moments (CSB-MoM) for the analysis and prediction of electromagnetic fields on topographic profiles. Thus, we intend to verify if the method is suitable for the analysis of electromagnetic propagation and scattering problems over large terrains. The standard Method of Moments (MoM) is employed to convert integral equationsinto a linear system that can be numerically solved with the help of a computer. However, the method presents critical shortcomings regarding its aplicability given the restriction imposed by the electric size of the problem due to the storage requirement of O(N2), being N the number of unkowns and O(N3) the solution time. The CSB-MoM, on its turn, merges the MoM with the Complex Source Beam (CSB) expansion technique in the solution of large electromagnetic problems. Hence, we seek to obtain the equation system generated by the standard MoM and solve itwith the help of the complex source point hybrid method. Therefore, our objective was solving the problem in question, that is, calculating the electromagnetic field at any point in space when a source radiates in the presence of an irregular terrain. The results obtained show that the CSB-MoM is capable of accelerating the matrix-vector product (MVP) of the iterative solutions of standard MoM problems related to large geometries. The operational count of the matrix-vector product and the memory requirement were lessend to O(N3/2), for both memory and processingtime, as opposed to the standard MVP. After the results were known, the hybrid models performances were compared and disscussed in light of the beam expansion behavior and its properties, as well as its performance regarding the standard MoM.