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.
|
