Application of the generalized finite difference method to three-dimensional transient electromagnetic problems

We apply the generalized finite difference method (GFDM), a relatively new domain-type meshless method, for the numerical solution of three-dimensional (3D) transient electromagnetic problems. The method combines Taylor series expansions and the weighted moving least-squares method. The main idea here is to inherit the high-accuracy advantage of the former and the stability and meshless attributes of the latter. This makes the method particularly attractive for problems defined in 3D complex geometries. Three benchmark 3D problems governed by the Maxwell's equations with both smooth and piecewise smooth geometries have been analyzed. The convergence, accuracy and stability of the method with respect to increasing the number of scattered nodes inside the domain are studied.