Consequences of symmetry in the computation of characteristic modes for conducting bodies

When computing the characteristic modes of a symmetric conducting body, it is always advantageous and sometimes absolutely necessary to block diagonalize the matrix representation of the operator for the eigencurrents. This procedure reduces computation time and memory requirements. The formal theoretical approach to operator block diagonalization is developed using group theory. It is shown that the operator for the eigencurrents on a conducting body is invariant under the group of symmetry operations of the structure. The eigencurrents are shown to provide bases for the irreducible representations of the symmetry group. It is further proven that expansion of the current in terms of functions belonging to the irreducible representations of the symmetry group of the structure leads to block diagonalization of the matrix representation of the operator. Basis functions for bodies of revolution are discussed as an example.