In this paper we refer to the computational issues in solving Maxwell’ s curl equations without using any connectivity among the points in which the problem domain is discretized. The adopted procedure is able to approximate the electric and magnetic vector fields making use of the derivatives of a kernel function at points arranged in the computational domain. In order to improve the numerical accuracy, dealing with irregular data distribution or data located near the boundary, a suitable strategy is considered. The computational core of the overall process requires elementary linear algebra operations. In the paper the method is presented and the discussion is revolved to the computational issues. Moreover, some numerical simulations are presented to validate the numerical process.