Metodologias de discretização espacial sem malha baseadas nos potenciais de Coulomb e Lennard-Jones para o método radial de interpolação por pontos (RPIM) aplicadas para solução numérica das equações de Maxwell

Abstract

In this thesis, three new particle interaction methods based on the Coulomb's and Lennard- Jones' potentials have been developed (and computationally implemented), aiming to generate meshless spatial discretization which can be used to the Radial Point Interpolation Method (RPIM) for solving partial di erential equations. These new methods, called Coulomb Law Discretization Method (CLDM), Electric Charge Gaussian Gradation Method (ECGGM) e Lennard-Jones Discretization Method (LJDM),employ adapted versions of Coulomb's and Lennard-Jones' vector forces equations for obtaining a balanced distribution of nodes in space (equilibrium state), in order to achieve high discretization quality of space and complex structures. For this aim, a new quality metrics is introduced. This doctoral thesis is presented as an aggregation of three scienti c papers, which present respectively the methods: CLDM, ECGGM and LJDM. The RPIM and the uniaxial perfectly matched layers (UPML) are used for solving Maxwell's equations in time domain for 2D (TMz mode) and 3D problems. The CLDM, ECGGM and LJDM methods (each in conjunction with the RPIM method) are applied to electromagnetic scattering problems, based on circular, elliptic and triangular metal cylinders (2D case). The LJDM / RPIM method is applied to the 3D case. The obtained results are in accordance with analytical solutions.