Accurate H‐shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half‐space

Li, Huifang; Zhao, Mi; Du, Xiuli

doi:10.1002/nme.6424

Cited by 14 publications

(8 citation statements)

References 66 publications

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“…The finite element method discretizes a physical field into limited units and then establishes finite linear equations using the connections between these units to obtain the exact solutions of the physical field [17][18][19]. Therefore, the finite element method is more suitable for deriving an accurate solution of sound fields in complex ocean environments.…”

Section: Introductionmentioning

confidence: 99%

[Retracted] Analysis of VLF Wave Field Components and Characteristics Based on Finite Element Time‐Domain Method

et al. 2023

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Most traditional sound field calculation methods regard the seabed as the horizontal stratified liquid sea bottom and conduct simulation analysis based on the frequency domain. Hence, the generality of the above research methods is limited to varying degrees. To accurately clarify the propagation characteristics and mechanism of very low-frequency (VLF, ≤100 Hz) sound waves in the shallow sea, a numerical calculation model is established using the finite element time-domain method (FETD) based on the three-dimensional cylindrical coordinate system. Using this model, the effects of sea-bottom topographies and geoacoustic parameters on the composition and characteristics of VLF sound fields in the shallow sea and their corresponding mechanism are investigated through the comparative analysis of various numerical simulation examples. The simulation results demonstrate that the low-frequency sound field in the full waveguide of the shallow sea is composed of normal mode waves in the seawater layer, Scholte waves at the liquid-solid interface, and elastic waves at the sea bottom. Compared with the soft sea bottom, which has a more negligible elastic impedance, the hard sea bottom is more conducive to the long-distance propagation of normal mode waves and the excitation of Scholte waves. The Scholte waves on the hard sea bottom are significantly stronger than those on the soft sea bottom. Compared with the horizontal sea bottom, the uphill topography enhances the sound energy leakage to the sea bottom. It is more favorable to receive Scholte waves at shallow depths, whereas the influence laws of downhill topography are the opposite.

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Section: Introductionmentioning

confidence: 99%

[Retracted] Analysis of VLF Wave Field Components and Characteristics Based on Finite Element Time‐Domain Method

et al. 2023

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“…When analyzing the seismic response of a two-dimensional layered slope site with the aid of the FEM, the finite computational domain needs to be cut off from the infinite ground. Artificial boundaries are usually used to simulate waves scattered by target structures and the nonreflecting wave effect of truncated infinite domains (Du et al, 2006;Huang et al, 2016;Zhao et al, 2019;Li et al, 2020). The stable and accurate viscoelasticity artificial boundary developed by Du et al (2006) is adopted in this study.…”

Section: Governing Equationsmentioning

confidence: 99%

Seismic response analysis of slope sites exposed to obliquely incident P waves

et al. 2023

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This study proposes a seismic input method for layered slope sites exposed to obliquely-incident seismic waves which transforms the waves into equivalent nodal forces that act on the truncated boundary of a finite element model. The equivalent nodal forces at the left and right boundaries are obtained by combining the free field response of a one-dimensional layered model with a viscoelastic boundary. The equivalent nodal forces at the bottom boundary are obtained by combining the incident wave field with the viscoelastic boundary. This proposed seismic input method for slope sites exposed to obliquely incident seismic waves is implemented with the aid of MATLAB software; it is applied to the seismic response analysis of slope sites in the commercial finite element ABAQUS software. The calculation results are compared with the reference solutions obtained by using the extended model to verify the correctness of the established seismic input method. The proposed seismic input method is then employed to investigate the influencing factors of the seismic response of layered slope sites exposed to oblique incidence P waves. The results show that the angle of incidence, location of the interface between soft and hard rocks, and impedance ratio have significant effects on the seismic landslide.

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“…4 The perfectly matched layer (PML) and the absorbing boundary conditions (ABCs) are the most prominent ABMs, and development of new ABMs is still an ongoing topic of research. [5][6][7][8] Essentially, the idea of ABMs is to limit the computational domain to a region of interest called the near-field, while referring to the area outside that region as the far-field. Provided that appropriate (artificial) boundary conditions are imposed on the boundary of the near-field (referred to as the truncating boundary), the solution of an unbounded problem can be obtained within this region.…”

Section: Introductionmentioning

confidence: 99%

Dirichlet‐type absorbing boundary conditions for peridynamic scalar waves in two‐dimensional viscous media

Hermann

Shojaei

Seleson

et al. 2023

Numerical Meth Engineering

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Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave‐type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi‐analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane‐wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near‐field) with that of the exterior region (far‐field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two‐dimensional unbounded domains.

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Accurate H‐shaped absorbing boundary condition in frequency domain for scalar wave propagation in layered half‐space

Cited by 14 publications

References 66 publications

[Retracted] Analysis of VLF Wave Field Components and Characteristics Based on Finite Element Time‐Domain Method

[Retracted] Analysis of VLF Wave Field Components and Characteristics Based on Finite Element Time‐Domain Method

Seismic response analysis of slope sites exposed to obliquely incident P waves

Dirichlet‐type absorbing boundary conditions for peridynamic scalar waves in two‐dimensional viscous media

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