The fast multipole method in electromagnetics applied to the simulation of metamaterials

In this paper the reader is introduced to an algorithm that revolutionized the complexity of problems that could be handled in electromagnetics in the past decennium. The algorithm, called fast multipole method, has allowed the solution of problems with many millions of degrees of freedom with reasonable computer resources. The method is explained on different levels of abstraction. It is illustrated by means of a wire scattering problem that is applied for the exact simulation of a piece of metamaterial with a negative index of refraction. It is the first time that an exact numerical verification of the lens effect in a negative index metamaterial is performed.