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**Additional info for Finite Element and Finite Difference Methods in Electromagnetic Scattering**

**Example text**

1. 3 F4 PA\ • -F7. — • -P7J The finite element solution thus comes down to inverting a matrix. As was the case for the finite difference example, the global array is mostly filled with zeros. This is in contrast to integral equation methods, which produce full matrix structures. A sparse matrix allows highly economical inversion, for even very large matrix order, by any of a number of different algorithms [15]. In addition, by properly ordering the nodes, as was done here, the matrix can often be made to have a block structure.

As developed in the unimoment method, the exterior region fields are represented by a functional expansion in one of the separable co ordinate systems for the vector Helmholtz equation [14: sect. 1]. The spatial interface for coupling the interior numerical solution to the unbounded exterior region is thus a constant coordinate surface of the separable system employed in the outside expansion. Spherical interfaces were utilized in [16] and [22-26] due to the relative ease of generation of exterior region spherical harmonic field expansions.

Such a phenomenon is related to the classical "Rayleigh hypothesis" [31]. As a result, we may not be able to obtain as a good match between the numerical solution at SB and the original truncated analytical expan sion, as we were able to do on the spherical surface for the unimoment method. To evaluate the expansion coefficients for the boundary field in the FEBI, we can use a system of two combined field integral equations, as employed in the EBCM [30]. These integral equations are vector field 3-D versions of that in (63); they relate the tangential fields just inside of the boundary SB to that just outside, without making use of a knowledge of the material structure inside of SB · The FEBI method has been shown to work well for scattering cal culations involving moderately elongated lossy dielectric objects.