On the well-posedness of integral equations associated with cavity Green’s functions around resonant frequencies

In this paper, a theoretical analysis is presented for the numerical scheme in [Lu, 20007]. It is shown that the numerical difficulties associated with cavity Greenpsilas functions around resonances originate from the non-unique solutions within fully-enclosed lossless cavities. As a result, conventional integral equations are not well-posed around cavitiespsila resonant frequencies, and modified integral equations need to be formulated. The numerical scheme in [Lu, 2007] straightforwardly follows from the modified integral equations constructed in this paper. Moreover, in this paper the modified integral equations are theoretically proven well-posed at cavitiespsila resonant frequencies.