The use of numerical methods for the solution of large electromagnetic (EM) problems is nowadays a common practice. Among the several available techniques, the Finite Difference Time Domain (FDTD) is one of the most frequently adopted algorithms, thanks to its versatility and its ability to deal with complex structures. Unfortunately, the method requires a huge computational effort, so that the study of large simulation domains and the investigation of many practical EM aspects cannot be afforded by using traditional computers. Also, the needs of high accuracy when the simulation domain is modeled, implies small mesh size, with a non-negligible impact on the memory requirement if a uniform mesh scheme is adopted. The proposed variable mesh FDTD (VM-FDTD) algorithm allows a natural and efficient parallel implementation, guaranteeing the possibility of managing large memory requirements. Results on relevant topics such as the antennas characterization and the interaction between humans and EM sources are investigated, demonstrating its ability to deal with complex EM problems.