Análise de campos eletromagnéticos em regiões limitadas pelo método dos elementos finitos.

Abstract

This thesis presents three variational finite element formulations for analysis of bounded, loss-free and linear electromagnetic field problems, enclosing otherwise general non-homogeneous and/or anisotropic media. The treatment is general and can be applied to both static and time-harmonic fields in longitudinally homogeneous and infinite transmission lines or waveguides. In applying the method of finite elements (FEM) to bounded waveguides, transversely non-homogeneous and/or anisotropic, the most suitable formulation is expressed in terms of three components of the magnetic field H, due to the hybrid nature of the modes in such waveguides. In order to eliminate the spurious solutions, inherent to vector variational formulations, one introduces the transverse penalty method w i t h selective reduced integration on lagrangian elements (STRIP), as well as the regularized mixed method (RMM). Some typical problems are solved and the results are compared with the ones obtained by the selective reduced integration penalty (RIP) and edge finite element methods. The quality of the approximations and the computational performance, confirm the theoretical estimates of errors and convergence rates, obtained through numerical analysis on each one of the formulations presented. The mixed method presents a numerical stability identical to that of the RIP method, when one uses moderately distorted elements. One has observed that the STRIP finite element method provides more accurate eigenvalues than the ones calculated with the edge finite element method. Unfortunately, the same does not happen to the eigenvectors, due to the decoupling between the transverse and longitudinal components of the magnetic field H. Although mathematically inconsistent, the STRIP finite element method plays a rather critical role with respect to the edge elements finite element methods, whose adepts claim that could solve any kind of electromagnetic boundary value problem.