Particles and fields represent two major modeling paradigms in pure and applied science at all. In this paper a methodology and some of the results for three-dimensional (3D) simulations that include both field and particle abstractions are presented. Electromagnetic field calculations used here are based on the discrete differential form representation of the finite elements method, while the Monte Carlo method makes foundation of the particle part of the simulations. The first example is the simulation of the feature profile evolution during SiO₂ etching enhanced by Ar + /CF₄ non-equilibrium plasma based on the sparse field method for solving level set equations. Second example is devoted to the design of a spiral inflector which is one of the key devices of the axial injection system of the VINCY Cyclotron.