Implementation of Higher Order Absorbing Boundary Conditions in Vector Finite Element Methods

It is important to use appropriate mesh truncation schemes and accurate absorbing boundary conditions (ABC) on the truncation surfaces to achieve reliable computational results while solving electromagnetic radiation and scattering problems in unbounded regions with the finite element method (FEM). In this paper, a new family of hierarchical higher order absorbing boundary conditions is derived and a second order ABC is implemented by use of a set of cement variables on the boundary

I. Introduction

Many problems of interest, including electromagnetic scattering and radiation problems require the solution of Maxwell's Equations in an infinite domain. However, due to the finite amount of computational resources, it is impossible to inherit the infinite nature of these problems directly into the numerical solution. Absorbing Boundary Conditions (ABC) is one of the methods used to overcome this difficulty when solving open region problems with the Finite Element Method (FEM).