# Finite element computation of absorbing boundary conditions for time-harmonic wave problems

## TL;DR

This paper introduces a versatile finite element-based method in the frequency domain for defining absorbing boundary conditions in 2D wave problems, requiring only the dynamic stiffness matrix of a single period, and demonstrates its accuracy through comparisons with known solutions.

## Contribution

It presents a novel, general approach to derive absorbing boundary conditions from discretized equations without extensive analytical knowledge, applicable to various orders of accuracy.

## Key findings

- Accurate boundary conditions obtained for different orders.
- Good agreement with analytical solutions confirms method effectiveness.
- Requires only the dynamic stiffness matrix of one period.

## Abstract

This paper proposes a new method, in the frequency domain, to define absorbing boundary conditions for general two-dimensional problems. The main feature of the method is that it can obtain boundary conditions from the discretized equations without much knowledge of the analytical behavior of the solutions and is thus very general. It is based on the computation of waves in periodic structures and needs the dynamic stiffness matrix of only one period in the medium which can be obtained by standard finite element software. Boundary conditions at various orders of accuracy can be obtained in a simple way. This is then applied to study some examples for which analytical or numerical results are available. Good agreements between the present results and analytical solutions allow to check the efficiency and the accuracy of the proposed method.