A Path Integral Representation Model to Extend the Analytical Capability of the Nonstandard Finite-difference Time-domain Method

The nonstandard finite-difference time- domain (NS-FDTD) method is a powerful tool for solving Maxwell's equations in their differential form on orthogonal grids. Nonetheless, to precisely treat arbitrarily shaped objects, very fine lattices should be employed, which often lead to unduly computational requirements. Evidently, such an issue hinders the applicability of the technique in realistic problems. For its alleviation, a new path integral (PI) representation model, equivalent to the NS-FDTD concept, is introduced. The proposed model uses a pair of basic and complementary path integrals for the H-nodes. To guarantee the same accuracy and stability as the NS-FDTD method, the two path integrals are combined via optimization parameters, derived from the corresponding NS-FDTD formulae. Since in the PI model, E-field computations on the complementary path are not necessary, the complexity is greatly reduced. Numerical results from various real-world problems prove that the proposed method improves notably the efficiency of the NS-FDTD scheme, even on coarse orthogonal meshes.