Finite Element Analysis of Electromagnetic Scattering Using $p$ -Adaption and an Iterative Absorbing Boundary Condition

Solving scattering problems using the finite element method (FEM) introduces two sources of error: from the discretization and from the truncation boundary. Here both errors are addressed in an iterative, balanced way. For the discretization error, p-adaption is used. An a posteriori error indicator automatically determines which elements should be increased in order to reduce and equi-distribute the discretization error. For the boundary error, an iterative absorbing boundary condition is applied. The overall scheme starts with low order polynomials and a first order absorbing boundary condition and progressively improves the quality of the solution by a combination of p-adaption and updating the boundary condition, so that both the discretization and the boundary errors are similar at each stage. Results are presented to show the reduction of computation time when p-adaption is used as opposed to an earlier approach of uniformly increasing the element orders.