A uniform implementation of fast multipole method for different integral operators encountered in electromagnetic scattering calculations

A uniform formulation is presented for using the multilevel fast multipole algorithm (MLFMA) to solve a set of simultaneous integral equations for electromagnetic wave scattering. The formulation is based on two operators that apply to the aggregation and disaggregation matrices. With these two operators, we can easily extend the MLFMA that is developed for PEC scatterers to include material coatings (bulk dielectrics as well as approximate boundary conditions). The introduction of the P and Q operators (two operators that modify the matrices, based on the integral operators of the integral equations) does not cause an increase in computation time and memory. A numerical example is presented to illustrate the application of the uniform formulation.