High-order finite elements for the solution of Helmholtz problems

Christodoulou, Konstantinos; Laghrouche, Omar; Mohamed, M. Shadi; Trevelyan, J.

doi:10.1016/j.compstruc.2017.06.010

Cited by 36 publications

(22 citation statements)

References 40 publications

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“…However, the error increases quickly if for a given problem we increase the wavenumber and retain the discretization level of ten. This behaviour is well documented in the literature and is referred to as the pollution error [26][27][28].…”

Section: Introductionmentioning

confidence: 75%

Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation

Jiang

Mohamed

Seaı̈d

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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Section: Introductionmentioning

confidence: 75%

Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation

Jiang

Mohamed

Seaı̈d

et al. 2018

Computer Methods in Applied Mechanics and Engineering

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“…As a numerical method with such potential, acoustic numerical methods based on the Partition of Unity FEM [29] (PUFEM) have been formulated and examined in some studies [30][31][32][33][34][35][36][37][38][39][40]. Two papers [36,37] present demonstrations of PUFEM on 2D car interior analyses at high frequencies including porous absorbing materials modeled respectively using an equivalent fluid model [41][42][43][44] and poroelastic material model [45].…”

Section: Partition Of Unity Finite Element Methods For Acoustic Problemsmentioning

confidence: 99%

Potential of Room Acoustic Solver with Plane-Wave Enriched Finite Element Method

2020

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Predicting room acoustics using wave-based numerical methods has attracted great attention in recent years. Nevertheless, wave-based predictions are generally computationally expensive for room acoustics simulations because of the large dimensions of architectural spaces, the wide audible frequency ranges, the complex boundary conditions, and inherent error properties of numerical methods. Therefore, development of an efficient wave-based room acoustic solver with smaller computational resources is extremely important for practical applications. This paper describes a preliminary study aimed at that development. We discuss the potential of the Partition of Unity Finite Element Method (PUFEM) as a room acoustic solver through the examination with 2D real-scale room acoustic problems. Low-order finite elements enriched by plane waves propagating in various directions are used herein. We examine the PUFEM performance against a standard FEM via two-room acoustic problems in a single room and a coupled room, respectively, including frequency-dependent complex impedance boundaries of Helmholtz resonator type sound absorbers and porous sound absorbers. Results demonstrated that the PUFEM can predict wideband frequency responses accurately under a single coarse mesh with much fewer degrees of freedom than the standard FEM. The reduction reaches O ( 10 − 2 ) at least, suggesting great potential of PUFEM for use as an efficient room acoustic solver.

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“…where D m is a set of the so-called supporting nodes of node m, which is a group of nodes belonging to the elements that shares the node m. N I (x) is the shape function of node I, and p I is the nodal acoustic pressure. By substituting equation (7) into equation (6), the smoothed gradient of pressure can be written as follows:…”

Section: Briefing Of Ns-fem and Fs-femmentioning

confidence: 99%

“…However, it is well known that the accuracy of the FEM tends to deteriorate with increasing wave number [2,3]. Many efforts are currently spent on improving performance of the wavebased solution with high wave numbers [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Smoothed Finite Element Method for Predicting the Sound Field in the Enclosure with High Wave Numbers

Wang

Zeng

2019

Shock and Vibration

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Wave-based methods for acoustic simulations within enclosures suffer the numerical dispersion and then usually have evident dispersion error for problems with high wave numbers. To improve the upper limit of calculating frequency for 3D problems, a hybrid smoothed finite element method (hybrid SFEM) is proposed in this paper. This method employs the smoothing technique to realize the reduction of the numerical dispersion. By constructing a type of mixed smoothing domain, the traditional node-based and face-based smoothing techniques are mixed in the hybrid SFEM to give a more accurate stiffness matrix, which is widely believed to be the ultimate cause for the numerical dispersion error. The numerical examples demonstrate that the hybrid SFEM has better accuracy than the standard FEM and traditional smoothed FEMs under the condition of the same basic elements. Moreover, the hybrid SFEM also has good performance on the computational efficiency. A convergence experiment shows that it costs less time than other comparison methods to achieve the same computational accuracy.

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High-order finite elements for the solution of Helmholtz problems

Cited by 36 publications

References 40 publications

Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation

Identifying the wavenumber for the inverse Helmholtz problem using an enriched finite element formulation

Potential of Room Acoustic Solver with Plane-Wave Enriched Finite Element Method

A Hybrid Smoothed Finite Element Method for Predicting the Sound Field in the Enclosure with High Wave Numbers

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