Abstract. An analytical approach to analyze the diffraction of an arbitrarily directed complex-source beam (CSB) by an acoustically soft or hard semi-infinite circular cone is presented. The beam is generated by assigning a complexvalued location to a point source; its waist and direction are defined by the real and imaginary parts of the source coordinate, respectively. The corresponding scalar boundary-value problem is solved by a spherical-multipole analysis. The solution requires the calculation of associated Legendre functions of the first kind for complex-valued arguments which turns out to be a non-trivial task. Beside a numerical analysis of the corresponding algorithms we present numerical results for the total near-and scattered far-fields.

This paper proposes a compression of far field matrices in the fast multipole method and its multilevel extension for electromagnetic problems. The compression is based on a spherical harmonic representation of radiation patterns in conjunction with a radiating mode expression of the surface current. The method is applied to study near field effects and the far field of an antenna placed on a ship surface. Furthermore, the electromagnetic scattering of an electrically large plate is investigated. It is demonstrated, that the proposed technique leads to a significant memory saving, making multipole algorithms even more efficient without compromising the accuracy.