Coulomb´s Law Discretization Method: a New Methodology of Spatial Discretization for the Radial Point Interpolation Method

In this paper, a new particle interaction method based on Coulombs force law has been developed and computationally implemented for performing meshless spatial discretization. The new methodology, which is named Coulombs Law Discretization Method (CLDM), employs an adapted version of the Coulombs vector force equation for obtaining a balanced distribution of nodes in space (equilibrium state), in such a way to achieve high discretization quality of space and complex structures. For this aim, a new quality metrics is introduced. The radial point interpolation method (RPIM) and the uniaxial perfectly matched layers (UPML) are used for solving Maxwell´s equations in time domain for 2D problems. The CLDM/RPIM methods are applied to electromagnetic scattering problems and for designing hybrid photonic band-gap filters, based on circular and triangular metallic cylinders. The obtained results are in accordance with analytical solutions.