Method for determining statistical mean and variance of electromagnetic energy transmission between coupled cavities

In this paper a statistical approach is employed to solve high frequency electromagnetism problems of coupled cavities at a reduced computational cost. The case of interest is a system of two reverberant cavities that have random or uncertain properties coupled by an aperture. If a conventional numerical approach is employed for this problem then very significant computational effort is required since Maxwell´s equations need to be solved for both the cavity and the system. The key aspect of the proposed approach is to avoid solving Maxwell´s equations inside the cavity by employing a relation known as the diffuse field reciprocity principle, which leads directly to the ensemble mean response of the system and its variance; all that is required is the impedance matrix of the coupling element associated with radiation into infinite space. Theoretical developments leading to the mean and variance are presented. This technique is then applied to a numerical example.