Space-domain finite-difference and time-domain moment method for electromagnetic simulation

A hybrid time-domain numerical method based on finite-difference technique and moment method is proposed. Starting from Maxwell's differential equations, our method uses Yee's finite difference scheme in the space domain, but does not utilize the customary explicit leap-frog time scheme. Instead, in the time domain, the fields are expanded in a series of basis functions and treated by a moment method procedure. By choosing appropriate basis functions and testing functions, the conventional finite-difference time-domain (FDTD) formulation and the order-marching unconditionally stable FDTD scheme can be derived from our method as two special cases. Finally, we use triangle basis functions and Galerkin's testing procedure to get an implicit formulation. To verify the accuracy and efficiency of the new formulation, we compare the results with the FDTD method. Our method improves computational efficiency notably, especially for multiscale problems with fine geometric structures, which is restricted by stability constrain in the FDTD method.