In this paper, a new particle interaction method based on Coulomb's force law has been developed and computationally implemented for performing meshless spatial discretization. The new methodology, which is named Coulomb's Law Discretization Method (CLDM), employs an adapted version of the Coulomb's 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.

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An auxiliary‐differential equation perfectly matched layer formulation is developed for the first time for truncating radial point interpolation method meshless domains. Absorption parameters are optimized, producing maximum relative reflection error of −84.14 dB when 10 layers are used. The developed formulation is also validated by calculating the radar cross section of a metallic cylindrical scatterer, which has a known analytical solution.

An improved meshless discretization methodology, based on the Coulomb's law discretization method, is introduced. With the presented improvement, it is possible to naturally and controllably increase the density of nodes around edges and corners of scatterers immersed in analysis space. This is achieved by gradually modifying node's charges across space according to Gaussian functions. It is observed that higher concentration of nodes in the neighborhood of media interfaces substantially improves the precision of numerical solutions of Maxwell's equations obtained with the radial point interpolation method. This improvement is justified by refined calculation of intense spatial field variations near the boundaries. Several other relevant benefits resulting from the new technique are observed and highlighted.