Applicability and Optimization of the Alternating-Direction-Implicit Iterative Method for the 2-D Finite-Difference Frequency-Domain Solution of Scattering Problems

The applicability of the alternating-direction-implicit (ADI) iterative method for the 2-D finite-difference frequency-domain (FDFD) solution of electromagnetic problems is studied, evaluated, and optimized. The ADI is used as an iterative solver of the system of linear equations resulting from the FDFD formulation. The physical limitations of applying the ADI method with a single acceleration parameter are examined in terms of its convergence behavior. In order to overcome these limitations, multiple acceleration parameters are necessary. An optimization procedure based on the simulated annealing algorithm is presented in order to obtain the optimum or near-optimum acceleration parameters. The approach is applied on the scattering problem by a dielectric cylinder as a test. The optimized acceleration parameters are compared with the ones suggested by Hadley. The acceleration parameters depend on the type of transparency conditions used to treat open-boundary problems. A simple absorbing layer (ABL), the stretched-coordinated perfectly matched layer (SC-PML), and the uniaxial PML are tested for both TE and TM polarizations. The SC-PML absorbing condition seems to be the best solution for the ADI iterative implementation of FDFD. Finally, empirical acceleration parameters are proposed for arbitrary scatterers for ABL and SC-PML absorbing conditions.