Corrective meshless particle formulations for time domain Maxwell’s equations

Abstract

In this paper a meshless approximation of electromagnetic (EM) field functions and relative differential operators based on particle formulation is proposed. The idea is to obtain numerical solutions for EM problems by passing up the mesh generation usually required to compute derivatives, and by employing a set of particles arbitrarily placed in the problem domain. The meshless Smoothed Particle Hydrodynamics method has been reformulated for solving the time domain Maxwell’s curl equations. The consistency of the discretized model is investigated and improvements in the approximation are obtained by modifying the numerical process. Corrective algorithms preserving meshless consistency are presented and successfully used. Test problems, dealing with even and uneven particles distribution, are simulated to validate the proposed methodology, also by introducing a comparison with analytical solution.