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We developed a fast numerical algorithm for solving the three dimensionalvectorial Helmholtz equation that arises in electromagnetic scatteringproblems. The algorithm is based on electric field integral equations and isessentially a boundary element method. Nystrom's quadrature rule with atriangular grid is employed to linearize the integral equations, which are thensolved by using a right-preconditioned iterative method. We apply the fastmultipole technique to accelerate the matrix-vector multiplications in theiterations. We demonstrate the broad applications and accuracy of this methodwith practical examples including dielectric, plasmonic and metallic objects.We then apply the method to investigate the plasmonic properties of a silvertorus and a silver split-ring resonator under the incidence of anelectromagnetic plane wave. We show the silver torus can be used as a trappingtool to bind small dielectric or metallic particles.

Fast Multipole Boundary Element Method for Three Dimensional Electromagnetic Scattering Problem