A hybrid FEBI-MLFMM-UTD method for numerical solutions of electromagnetic problems including arbitrarily shaped and electrically large objects

Abstract

Numerical solutions of electromagnetic scattering and radiation problems including arbitrarily shaped objects are obtained by solving integral equations with the method of moments (MoM). Fast and efficient solution of the integral equation with low computation and memory complexity is provided by the multilevel fast multipole method (MLFMM). The presence of electrically large conducting objects leads to hybrid MoM techniques with high-frequency methods. For ray-based high-frequency methods no discretization of the electrically large objects is needed, resulting into a more efficient numerical treatment of the problem. However, in order to retain low computation and memory complexity, the high-frequency fields must be taken into account in the matrix-vector product computations in the various levels of the MLFMM. In this contribution, a ray-based hybridization of the MLFMM with the uniform geometrical theory of diffraction (UTD) is proposed within a hybrid finite element-boundary integral (FEBI) technique, using the combined field integral equation (CFIE), resulting into a hybrid FEBI-MLFMM-UTD method. The hybridization is performed at the translation procedure on the various levels of the MLFMM, using a far-field approximation of the appropriate translation operator to obtain the high-frequency incident fields at the critical points of the UTD. The formulation of this new hybrid technique is presented and numerical results are shown.