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

Modave, Axel; Geuzaine, Christophe; Antoine, Xavier

doi:10.1016/j.jcp.2019.109029

Cited by 41 publications

(53 citation statements)

References 70 publications

(129 reference statements)

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“…The development of corner conditions for high-order ABCs has been a topic of interest for many researchers. 8,38 This is true for the proposed boundary condition in this study. The development of corner conditions to combine the RFABC with natural boundary conditions and half-space boundary conditions must be studied to improve the applicability of the RFABC.…”

Section: F I G U R E 11supporting

confidence: 53%

“…It should also be noted that corner conditions must be considered when the developed RFABC is applied to wave propagation problems in a half‐space or a full‐space. The development of corner conditions for high‐order ABCs has been a topic of interest for many researchers 8,38 . This is true for the proposed boundary condition in this study.…”

Section: Numerical Examplementioning

confidence: 80%

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Root‐finding absorbing boundary condition for anisotropic scalar waves in infinite media

Lee

2020

Numerical Meth Engineering

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A root-finding absorbing boundary condition (RFABC) for scalar-wave propagation problems in infinite anisotropic media was developed. Although the phase velocity and the group velocity in isotropic media have the same sign, the sign of the latter can differ from that of the former in anisotropic media. Therefore, a RFABC for anisotropic scalar waves consistent with the group velocity of the considered media is developed, as the velocity is closely related to the direction of energy propagation. The developed boundary condition is shown to satisfy a criterion for an "enough accurate" boundary condition. The well-posedness of the boundary condition is proven at the continuous level. Its finite-element formulation, which ensures well-posedness at a discrete level, is derived, after which it is demonstrated that accurate and stable solutions to the problem of antiplane shear-wave propagation in an anisotropic elastic waveguide, an example of anisotropic scalar-wave propagation, can be obtained using the proposed numerical approach.

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Section: F I G U R E 11supporting

confidence: 53%

Section: Numerical Examplementioning

confidence: 80%

Root‐finding absorbing boundary condition for anisotropic scalar waves in infinite media

Lee

2020

Numerical Meth Engineering

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“…The cube with the reentrant corner is neither smooth nor convex. Novel high-order absorbing boundary conditions for polyhedral domains [31] could be used to improve this behavior: this is the subject of current work.…”

Section: Weak Bem-bem Couplingmentioning

confidence: 99%

Optimized weak coupling of boundary element and finite element methods for acoustic scattering

Caudron

Antoine

Geuzaine

2020

Journal of Computational Physics

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In this paper we present an optimized weak coupling of boundary element and finite element methods to solve acoustic scattering problems. This weak coupling is formulated as a nonoverlapping Schwarz domain decomposition method, where the transmission conditions are constructed through Padé localized approximations of the Dirichlet-to-Neumann map. The performance of the resulting formulations is analyzed on several three-dimensional examples, with both homogeneous and inhomogeneous scatterers.

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“…The basic impedance boundary condition is the simplest and cheapest approach, but it provides a rather poor accuracy. High‐order absorbing boundary conditions (e.g., References 2–8), infinite elements (e.g., References 9–11), and perfectly matched layers (e.g., References 12–16) constitute families of more accurate techniques. In particular, the perfectly matched layers (PMLs) are easy to use and accurate for a limited computational cost, which makes them attractive for large‐scale industrial simulations.…”

Section: Introductionmentioning

confidence: 99%

An automatic perfectly matched layer for acoustic finite element simulations in convex domains of general shape

Bériot

Modave

2020

Int J Numer Methods Eng

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This article addresses the efficient finite element solution of exterior acoustic problems with truncated computational domains surrounded by perfectly matched layers (PMLs). The PML is a popular nonreflecting technique that combines accuracy, computational efficiency, and geometric flexibility. Unfortunately, the effective implementation of the PML for convex domains of general shape is tricky because of the geometric parameters that are required to define the PML medium. In this work, a comprehensive implementation strategy is proposed. This approach, which we call the automatically matched layer (AML) implementation, is versatile and fully automatic for the end-user. With the AML approach, the mesh of the layer is extruded, the required geometric parameters are automatically obtained during the extrusion step, and the practical implementation relies on a simple modification of the Jacobian matrix in the elementwise integrals. The AML implementation is validated and compared with other implementation strategies using numerical benchmarks in two and three dimensions, considering computational domains with regular and nonregular boundaries. A three-dimensional application with a generally shaped domain generated using a convex hull is proposed to illustrate the interest of the AML approach for realistic industrial cases. K E Y W O R D S exterior acoustics, finite element method, Helmholtz equation, perfectly matched layer, wave propagation 1 INTRODUCTION Finite element methods (FEMs) are widely used in academia and industry to simulate acoustic wave propagation phenomena. With these methods, high-frequency oscillatory fields can be represented accurately in realistic settings with complicated geometries thanks to unstructured meshes, curved elements, high-order basis functions and hp-adaptivity. 1 Nevertheless, for many applications occurring in the free space, the computational domain must be truncated, and a specific nonreflecting technique must be used at the artificial boundary of the finite element mesh to represent the outward [Correction added on 6 January 2021, after first online publication: ζ symbols have been corrected to throughout the article.] This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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

Cited by 41 publications

References 70 publications

Root‐finding absorbing boundary condition for anisotropic scalar waves in infinite media

Root‐finding absorbing boundary condition for anisotropic scalar waves in infinite media

Optimized weak coupling of boundary element and finite element methods for acoustic scattering

An automatic perfectly matched layer for acoustic finite element simulations in convex domains of general shape

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