The BEM and surface plasmons

Abstract

Abstract The boundary element method (BEM) can be used to advantage for solving differential equations in a region occupied by more than one material. Here the integral equations are formulated for each subregion, and the matrices obtained on discretization of the contour integrals are put together in a manner analogous to overlaying element matrices in the finite element method (FEM). In this chapter, we begin by solving Laplace’s equation for a physical domain having two rectangular regions with dielectric constants EJ and EIJ in a constant electric field. The example makes use of the calculations of Section 16.6, where the solution at the boundary is given in terms of the linear interpolation between nodal values of the potential, and also the normal derivatives of the potential, at the extremities of a boundary element. We then discuss the issues in using Hermite interpolation polynomials in a multiregion BEM. We note here that when the physical region has a large aspect ratio and is elongated in one direction the boundary integrals will be nearly equal for destination points along the shorter side with source points at the farther end. This leads to ill-conditioning qf the final matrices. The problem can be alleviated by breaking up the region into sub regions, each with its own boundary integral. Again, a multiregion BEM can be employed.