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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:401

Article

Modave, A.¹  Geuzaine, C.²  Antoine, X.³ 

[1] Inst Polytech Paris, Lab POEMS, ENSTA Paris, Inria,CNRS, F-91120 Palaiseau, France

[2] Univ Liege, Inst Montefiore B28, B-4000 Liege, Belgium

[3] Univ Lorraine, Inst Elie Cartan Lorraine, Inria Nancy Grand Est EPI SPHINX, F-54506 Vandoeuvre Les Nancy, France

关键词: Finite element method;    Helmholtz problems;    Nonreflecting boundary condition;    Corner treatment;    Wave propagation;    High-order methods;   

DOI  :  10.1016/j.jcp.2019.109029

来源: Elsevier

【 摘 要 】

This paper deals with the design and validation of accurate local absorbing boundary conditions set on convex polygonal and polyhedral 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 Pade-type HABCs at corners: first by using compatibility relations (derived for right angle corners) and second by regularizing the boundary at the corner. Exhaustive numerical results for two- and three-dimensional problems are reported in the paper. They show that using the compatibility relations is optimal for domains with right angles. For the other cases, the error still remains acceptable, but depends on the choice of the corner treatment according to the angle. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free