Meshfree analysis of electromagnetic wave scattering from conducting targets: Formulation and computations

We propose a completely meshfree procedure aimed at the time-harmonic analysis of electromagnetic wave scattering from conducting targets. The problem is described by the vector wave equation with a divergence-free constraint. We propose a mixed formulation whose unknowns are the electric field vector and a Lagrange multiplier. We investigate the well-posedness of the variational problem and construct compatible meshfree function spaces able to describe solutions in any geometry, in two and three dimensions. The method does not depend on any kind of parameter tuning. We illustrate its performance in a number of solutions through experimentally derived convergence rates and comparisons with other techniques.