Boundary Relaxation Method for the Analysis of Terminations in Ducts

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Abstract
A hybrid combination of modal/ray-tracing and numerical techniques is developed for treating inhomogeneous or arbitrarily shaped terminations in ducts. The problem-domain, usually electrically large, is divided into two regions: one region is homogeneous and some distance away from the termination; the other one which includes the termination is (in general) inhomogeneous. A modal or ray-tracing solution is developed to solve the incoming wave in the first region, while the solution for the termination region is obtained numerically (finite differences) with an initial estimate of the boundary condition on the interface between the two regions. Then, an iterative technique, Boundary Relaxation Method (BRM), is utilized to implement the correct boundary condition. In this paper, some 2-D waveguide termination problems are analyzed to illustrate the BRM. Examples include the study of loaded waveguide cavities.

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