An automatic approach for the acoustic analysis of three-dimensional bounded and unbounded domains by scaled boundary finite element method

Liu, Lei; Zhang, Junqi; Song, Chongmin; Birk, Carolin; Gao, Wei

doi:10.1016/j.ijmecsci.2018.12.018

Cited by 56 publications

(21 citation statements)

References 109 publications

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“…Since the boundaries at y ¼ 0; 1 are assumed to be perfectly rigid, the normal derivative of the acoustic pressure vanishes on these boundaries. The exact solution of problem (31) with ABC is given as [71] where k x ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi k 2 À ðcπÞ 2 q and the coefficients A 1 and A 2 are obtained from…”

Section: Waveguide Problemmentioning

confidence: 99%

“…Finally, let us remark that another way to use both the FEM and BEM is to combine these two methods through FEM-BEM coupling strategies. Another method that shares the advantages of both the FEM and the BEM is the scaled boundary finite element method (SBFEM) [30,31]. Like the FEM, it does not require any fundamental solution and like the BEM, only the boundary is discretized.…”

Section: Introductionmentioning

confidence: 99%

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Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions

Dsouza

Khajah

Antoine

et al. 2021

Mathematical and Computer Modelling of Dynamical Systems

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The paper aims to evaluate the performance of the Lagrange-based finite element method and the non-uniform rational B-splines isogeometric analysis of time-harmonic acoustic exterior scattering problems using high-order local absorbing boundary conditions, in particular based on the Karp's and Wilcox's far-field expansions. The analysis of accuracy and convergence of both methods is achieved by observing the effect of the order of the approximating polynomial, the number of degrees of freedom, the wave number, and the absorbing boundary conditions tuning parameters. It is concluded that, regardless of the polynomial order, IGA provides a higher accuracy per degree of freedom compared to the traditional Lagrange-based finite element method.

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Section: Waveguide Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions

Dsouza

Khajah

Antoine

et al. 2021

Mathematical and Computer Modelling of Dynamical Systems

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“…The scaled boundary finite element method (SBFEM) is a semi-analytical technique that was introduced in the late 1990's to model problems of unbounded media (Wolf & Song, 2000). Since its inception, the SBFEM has been further developed for applications in many different fields in engineering including fracture propagation (He et al, 2021), heat conduction problems (Yu et al, 2021), electrostatic problems (Liu & Lin, 2012), acoustic analysis (Liu et al, 2019), dispersion analysis (Gravenkamp et al, 2012) and seepage flow (Johari & Heydari, 2018). A salient feature of SBFEM is that it requires only a simple scaling condition during the discretisation of a domain into a computational mesh and hence enables its formulation on any arbitrary polygon (Ooi et al, 2018) or quadtree of scales varying from small to large (K. .…”

Section: Introductionmentioning

confidence: 99%

Development of the scaled boundary finite element method for image-based slope stability analysis

Wijesinghe

Dyson

You

et al. 2022

Computers and Geotechnics

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“…1c. This approach has been applied to solve problems related to acoustics [37] and fracture [52]. However, this concept may be considered somewhat inelegant and unsatisfactory as the triangular elements require additional degrees of freedom and are intrinsically less accurate compared to quadrilateral elements.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional image-based modeling by combining SBFEM and transfinite element shape functions

2020

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The scaled boundary finite element method (SBFEM) has recently been employed as an efficient tool to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree decomposition of the computational domain is deployed, and each cubic cell is treated as an SBFE subdomain. The surfaces of each subdomain are discretized in the finite element sense. We improve on this idea by combining the semi-analytical concept of the SBFEM with a particular class of transition elements on the subdomains’ surfaces. Thus, a triangulation of these surfaces as executed in previous works is avoided, and consequently, the number of surface elements and degrees of freedom is reduced. In addition, these discretizations allow coupling elements of arbitrary order such that local p-refinement can be achieved straightforwardly.

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An automatic approach for the acoustic analysis of three-dimensional bounded and unbounded domains by scaled boundary finite element method

Cited by 56 publications

References 109 publications

Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions

Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions

Development of the scaled boundary finite element method for image-based slope stability analysis

Three-dimensional image-based modeling by combining SBFEM and transfinite element shape functions

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