A new algorithm for the modal analysis of 3-D arbitrarily shaped resonant cavities

A new algorithm, constituting a modified version of the Boundary Element Method (BEM), is used to find the resonant frequencies and the modal fields of arbitrarily shaped cavity resonators filled with a lossless, isotropic and homogeneous medium. Differently from the standard BEM, the unknown current flowing on the cavity wall is considered inside a spherical volume bounded by an electric wall, rather than in free-space. The electric field is expressed using the Green´s function of the spherical resonator, which can be approximated by a rational function of the frequency. Thank to that, the discretized problem results into a matrix linear eigenvalue problem, whose eigenvalues and eigenvectors yield the resonant frequencies and the associated modal currents. Since no frequency-by-frequency recalculation of the system matrices is required, CPU times are much shorter than in the standard BEM, especially when many resonances must be found. The cavity shape is modelled using triangular patches generated by a commercial mechanical CAD package.