On the canonical grid method for two-dimensional scattering problems

The banded matrix iterative approach with a canonical grid expansion (BMIA/CAG) has been shown by Tsang et al. (see ibid., vol.43, p.851-9, 1995) to be an efficient method for the calculation of scattering for near planar two-dimensional (2-D) geometries such as one-dimensional rough surfaces. However, in the article of Tsang et. al, only the first three terms in the canonical grid series for TE polarization above a perfectly conducting surface were discussed and methods for implementing only a portion of these terms were presented. In this paper, a general form for all terms in the canonical grid series is provided for both TE and TM polarizations above an impedance surface and an efficient algorithm for calculating their contributions is described. The relationship between the canonical grid and operator expansion methods is also discussed. A sample surface scattering problem is shown to illustrate the utility of higher order terms in the canonical grid method.