Single layer regularized meshless method for three dimensional exterior acoustic problem

Liu, Lin

doi:10.1016/j.enganabound.2017.02.001

Cited by 25 publications

(9 citation statements)

References 27 publications

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“…These methods still avoid integration, particularly singular integration and can also be used on the modal problem. There are several reports of implementations of these methods [144,145,[338][339][340][341].…”

Section: Meshless Methodsmentioning

confidence: 99%

The Boundary Element Method in Acoustics: A Survey

Kirkup

2019

Applied Sciences

106

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The boundary element method (BEM) in the context of acoustics or Helmholtz problems is reviewed in this paper. The basis of the BEM is initially developed for Laplace’s equation. The boundary integral equation formulations for the standard interior and exterior acoustic problems are stated and the boundary element methods are derived through collocation. It is shown how interior modal analysis can be carried out via the boundary element method. Further extensions in the BEM in acoustics are also reviewed, including half-space problems and modelling the acoustic field surrounding thin screens. Current research in linking the boundary element method to other methods in order to solve coupled vibro-acoustic and aero-acoustic problems and methods for solving inverse problems via the BEM are surveyed. Applications of the BEM in each area of acoustics are referenced. The computational complexity of the problem is considered and methods for improving its general efficiency are reviewed. The significant maintenance issues of the standard exterior acoustic solution are considered, in particular the weighting parameter in combined formulations such as Burton and Miller’s equation. The commonality of the integral operators across formulations and hence the potential for development of a software library approach is emphasised.

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Section: Meshless Methodsmentioning

confidence: 99%

The Boundary Element Method in Acoustics: A Survey

Kirkup

2019

Applied Sciences

106

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“…Thus, a regularisation technique should be adopted to overcome these singularities. Young and his colleagues [16] firstly proposed the regularised meshless method (RMM) and Liu [17] further developed it by proposing the double layer potential as the fundamental solution on the basis of the null-field boundary integral equation. Other techniques propose to replace the concentrated source with circular distributed sources [18,19].…”

Section: Introductionmentioning

confidence: 99%

“…For Neumann boundary conditions, it can be derived by using a subtracting and adding-back technique [22]. It is worth noting that in most original SBM formulations, single layer potential is employed to overcome those singularities [17]. The original SBM has been reformulated in various works to be adapted to particular cases.…”

Section: Introductionmentioning

confidence: 99%

A 2.5D coupled FEM–SBM methodology for soil–structure dynamic interaction problems

Liravi

Villamarín

Clot

et al. 2022

Engineering Structures

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In this paper, a novel numerical methodology to deal with longitudinally invariant soil-structure interaction problems is proposed. The methodology uses the finite element method to model the structure and the singular boundary method to model the wave propagation in the soil, both formulated in the wavenumberfrequency domain. The versatility presented by the finite element method combined with the simplicity and computational efficiency of the singular boundary method results in a friendly, robust and accurate novel methodology to address the soil-structure interaction problems. The accuracy of the proposed method is assessed by comparing it against 2.5D FEM-MFS and 2.5D FEM-BEM approaches for two cases: a thin cylindrical shell and a star-like beam structure, both embedded in a full-space medium. Moreover, the computational efficiency of the proposed method is evaluated against 2.5D FEM-MFS and 2.5D FEM-BEM methods. In the final step, the applicability of the proposed method is studied through an example of a railway tunnel embedded in a layered half-space. The results presented in this work exhibit the advantages of the novel approach in modelling simplicity, numerical efficiency and robustness with respect to previous methodologies.

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“…Unfortunately, the BEM and the BCM encounter the singularity and hyper singularity difficulties [20][21][22] due to the application of the fundamental solutions. In recent years, many useful techniques are proposed to bypass this limitation, such as the logarithmic quadrature formulation [23], the rigid body motion method [24], the subtraction and adding-back technique (SAB) [25][26][27], the integration by parts [28], the analytical integration approach [29] and the contour method [30].…”

Section: Introductionmentioning

confidence: 99%