Implementing Higher Order Absorbing Boundary Conditions in Vector Finite Element Methods

It is vital 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). Previously derived higher order ABCs had difficulties in implementation which lead either to destruction of sparsity and symmetry of the FEM matrix or reduction of accuracy. The ABC proposed in this paper is not only capable of producing credible numerical results but also can easily be formulated and implemented via introduction of a cement variable on the surface it is imposed. In addition it is possible theoretically to extend the ABC to higher orders in a hierarchical way by improving the quality of approximation employed

Introduction

It is vital 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). Previously derived higher order ABCs had difficulties in implementation which lead either to destruction of sparsity and symmetry of the FEM matrix or reduction of accuracy [3]. The ABC proposed in this paper is not only capable of producing credible numerical results but also can easily be formulated and implemented via introduction of a cement variable on the surface it is imposed. In addition it is possible theoretically to extend the ABC to higher orders in a hierarchical way by improving the quality of approximation employed.