Incorporating the multilevel fast multipole method into the characteristic basis function method to solve large scattering and radiation problems

This communication focuses on the problem of reducing the computational cost of generating the reduced matrix in the context of CBFM for very large scatterers using two different approaches: (i) MLFMM to compute the far-field interactions between distant functions; and (ii) stabilized bi-conjugated gradient method (BiCGM) to solve the reduced matrix equation iteratively. Additionally, the CBFM is combined with a geometrical description of the objects using non-uniform rational B-splines (NURBS) defined over a parametric domain, which is well suited for setting up an adaptive mesh without the need of external software tools (C. Delgado et al., 2006). A class of rooftop functions-located on the parametric domain-together with razor-blades serve as the low-level basis and testing functions, respectively, employed to construct the CBFs and subsequently used to generate the reduced matrix.