A Hybrid MLFMM–UTD Method for the Solution of Very Large 2-D Electromagnetic Problems

The multilevel fast multipole method (MLFMM) is combined with the uniform theory of diffraction (UTD) to model two-dimensional (2-D) scattering problems including very large scatterers. The discretization of the very large scatterers is avoided by using ray-based methods. Reflections are accounted for by image source theory, while for diffraction a new MLFMM translation matrix is introduced. The translation matrix elements are derived based on a technique that generalizes the use of UTD for arbitrary source configurations and that efficiently describes the field over extended regions of space. (9(n) scaling of the computational time and memory requirements is achieved for relevant structures, such as large antenna arrays in the presence of a wedge. The theory is validated by means of several illustrative numerical examples and is shown to remain accurate for non-line-of-sight (NLoS) scattering problems.