Transformation electromagnetics eigen‐analysis of perfect electric conductor cavities

Abstract

An alternative variational modal analysis technique is contributed by this study. Although the weak form of the Maxwell equations is employed, instead of using the finite elements technique, the authors utilise entire/global domain vectorial basis functions. In such a case, to assist performance, the basis functions must comply with the boundary conditions. Since in general, this is a difficult task, they adopt the following strategy. They transform the initial convex cavity using coordinate transformation to a canonical one, where a known complete set of vectorial basis functions exist. Then, taking advantage of the form invariance property of the Maxwell equations, in the transformed domain, the authors solve the canonical variational problem and acquire the respective solution to the initial problem by the inverse electromagnetics transformation. Summarising, the contributing concept is to employ a coordinate transformation to a canonical shape employing ‘transformation electromagnetics’ approach as a pre-processing tool to enlarge the scope of a classical electomagnetics (EM) variational eigen-analysis using the canonical shape's vector modes.