A hybrid PSTD/ADI-CFDTD method for mixed-scale electromagnetic problems

We propose a hybrid technique combining the pseudospectral time-domain (PSTD) method with the alternating-direction implicit conformal finite-difference time-domain (ADI-CFDTD) method to solve 3-D mixed-scale problems in computational electromagnetics. A mixed-scale problem contains both electrically large and relatively homogeneous regions and electrically small fine details, thus poses a significant computational challenge to any single computational method if it is utilized alone. In particular, the ADI-CFDTD method is an unconditionally stable time-domain method with second-order spatial accuracy, and allows the time step to be increased beyond the Courant-Friedrichs-Levy limit; it is suitable for electrically small problem (structure details much smaller than a wavelength) but is inefficient and suffers from large numerical errors for electrically large-scale regions. The PSTD method, on the other hand, is accurate and efficient for regions with large, relatively homogeneous materials, but loses its efficiency for electrically small structures. The hybrid PSTD/ADI-CFDTD method overcomes these disadvantages and is potentially more useful than the individual solvers. The implementation details and numerical accuracy of this hybrid method are examined. Numerical examples demonstrate the advantages of the hybrid PSTD/ADI-CFDTD method.