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

Denis Duhamel (1) , Tien-Minh Nguyen (2)

1 Dynamique des structures et identification
2 navier umr 8205 - Laboratoire Navier

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.

Mots clés: Absorbing boundary conditions; waveguide; finite element; periodic medium

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Denis Duhamel, Tien-Minh Nguyen. Finite element computation of absorbing boundary conditions for time-harmonic wave problems. Computer Methods in Applied Mechanics and Engineering, 2009, 198 (37-40), pp.3006-3019. ⟨10.1016/j.cma.2009.05.002⟩. ⟨hal-00425197⟩