Corner treatment for high-order local absorbing boundary conditions in high-frequency acoustic scattering

Axel Modave, Christophe Geuzaine and Xavier Antoine
submitted
Publication type:
Paper in peer-reviewed journals
Abstract:
This paper deals with the design and validation of accurate local absorbing boundary conditions set on convex polygonal computational domains for the finite element solution of high-frequency acoustic scattering problems. While high-order absorbing boundary conditions (HABCs) are accurate for smooth fictitious boundaries, the precision of the solution drops in the presence of corners if no specific treatment is applied. We present and analyze two strategies to preserve the accuracy of Padé-type HABCs at corners: first by using compatibility relations (derived for right angle corners) and second by regularizing the boundary at the corner. We show that the former strategy is well-adapted to right corners and efficient for nearly-right corners, while the later is better for very obtuse corners. Numerical results are proposed to analyze and compare the approaches for two-and three-dimensional problems.
BibTeX:
@article{Mod-Geu-Ant-2200,
    author={Axel Modave and Christophe Geuzaine and Xavier Antoine },
    title={Corner treatment for high-order local absorbing boundary 
           conditions in high-frequency acoustic scattering },
    year={submitted },
}