Electromagnetic calculations for large bodies of translation

Abstract

Summary form only. A canonical geometry of great interest is the body of translation. A body of translation is defined as a geometry that has a constant cross-sectional shape and is translated over a finite distance. A computer program named GODOT has been written which evaluates the electromagnetic properties of a general dielectric body of translation using moment-method techniques. General geometries in the presence of the body of translation may also be solved. General geometries are modeled with the Rao triangular basis functions, while the body of translation is modeled with a rectangular generalization of these basis functions. The rectangular basis function conveniently segments the body of translation into a set of identical cells along the translation of the body. New algorithms evaluate the impedance matrix by converting all surface integrals over the basis functions into line integrals. These methods have been implemented for both the electric and magnetic fields from the triangular and rectangular basis functions. These algorithms are highly accurate and as speedy as previous techniques. The impedance matrix, which is in general block Toeplitz, is inverted using a novel and highly efficient block Toeplitz matrix solver. This new algorithm is compared to previous methods such as the Levinson recursion and the preconditioned biconjugate gradient techniques. A number of examples are presented showing the capability of this new computer program. The timing requirements for this algorithm is also discussed.