Estudo e análises do MLPG aplicado a problemas eletromagnéticos de corpos de revolução

Abstract

This work combines, for the first time, axisymmetric electromagnetic analyses with meshless methods, which are relatively new and have only recently been applied as a tool for the obtention of numerical solutions in engineering. Electromagnetic problems with axial symmetries have successful been studied in the past using others numerical methods such as the Method of Moments and the Finite Element Method. However, the objective here is to develop simple and efficient meshless implementations, consolidating meshless methods as an excellent way to provide numeric solutions to these problems. These tasks are performed considering the Meshless Local Petrov Galerkin method. It does not require any type of grid or mesh for the construction of the approximate solution. However this work is added a background mesh that gives more stability to the method, especially in non-uniform nodes distribution that have a large variation in density. The MLPG is also known to produce sparse matrices as a result of a local analysis. MLPG is applied in electromagnetic problems with axial symmetry, being, first analyzed, problems in which fields also have axial symmetry, such as the analysis of a monopole over a perfect electric conductor plane excited by a coaxial guide operating in TEM mode and the analysis of a resonant cavity, a coaxil one. These analyses propitiated to evalute the accuracy, the convergence and stability of the method. One technique for addressing electromagnetic problems with axial symmetriy in which the fields do not have axial symmetry is also presented and two preliminary result is shown.