Transparent-Influx Boundary Conditions for FEM Based Modelling of 2D Helmholtz Problems in Optics

Abstract

A numerical method for the analysis of the 2D Helmholtz equation is presented, which incorporates Transparent-Influx Boundary Conditions into a variational formulation of the Helmholtz problem. For rectangular geometries, the non-locality of those boundaries can be efficiently handled by using Fourier decomposition. The Finite Element Method is used to discretise the interior and the nonlocal Dirichlet-to-Neumann operators arising from the formulation of Transparent-Influx Boundary Conditions