Fast Multipole Boundary Element Method for Three Dimensional Electromagnetic Scattering Problem

TL;DR

This paper introduces a fast boundary element method combined with the fast multipole technique to efficiently solve 3D electromagnetic scattering problems, demonstrating high accuracy and practical applications in plasmonics.

Contribution

The paper presents a novel boundary element method with fast multipole acceleration for 3D electromagnetic scattering, enabling efficient and accurate simulations of complex metallic and dielectric objects.

Findings

Successfully applied to dielectric, plasmonic, and metallic objects.

Demonstrated the method's accuracy with practical examples.

Showed the silver torus can trap small particles.

Abstract

We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a boundary element method. Nystrom's quadrature rule with a triangular grid is employed to linearize the integral equations, which are then solved by using a right-preconditioned iterative method. We apply the fast multipole technique to accelerate the matrix-vector multiplications in the iterations. We demonstrate the broad applications and accuracy of this method with practical examples including dielectric, plasmonic and metallic objects. We then apply the method to investigate the plasmonic properties of a silver torus and a silver split-ring resonator under the incidence of an electromagnetic plane wave. We show the silver torus can be used as a trapping tool to bind small dielectric or metallic particles.