Fast multipole method for the solution of electromagnetic scattering problems

The fast multipole method (FMM) is investigated in detail for the solution of electromagnetic scattering problems involving arbitrarily shaped three-dimensional conducting surfaces. This method is known to reduce the computational complexity and the memory requirement of the solution without sacrificing the accuracy. Therefore, it achieves the solution of large problems with less computational resources compared to the other traditional solution algorithms. However, the expected efficiency of the FMM may not be obtained unless the appropriate choices of the components are made. The types of the employed integral equation, iterative algorithm, and preconditioning technique directly affect the efficiency of the implementations. Performances of these components are also related to each other, and their simultaneous optimization creates a challenging task in the design of an efficient solver.