This work presents a hybrid method (called FEM+DM) for efficient numerical modeling of multiscale electromagnetic (EM) radiation problems that involve thin wire antennas placed near objects. The proposed hybrid method incorporates the Dipole Moment (DM) approach into the Finite Element Method (FEM) in order to circumvent the bottlenecks pertaining to certain computational issues, such as mesh refinement, ill-conditioning, memory overload and long CPU time. The use of dipole moments for handling fine features as well as for modeling mutual interactions, enables us to employ parallelization techniques to accelerate the computation. The hybrid method with GPU computing has been programmed in MATLAB. Numerical results generated by using the proposed technique are presented, and are compared to those obtained from a commercial EM solver.