A plane wave discontinuous Galerkin method with a Dirichlet-to-Neumann boundary condition for the scattering problem in acoustics

Kapita, Shelvean; Monk, Peter

doi:10.1016/j.cam.2017.06.011

Cited by 8 publications

(5 citation statements)

References 28 publications

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“…The FEM is a general method for solving mathematical and physical equations. However, the FEM is difficult in dealing with the infinite domain problems and needs several additional technologies [8][9][10]. The BEM is a boundary-type numerical algorithm after the FEM.…”

Section: Introductionmentioning

confidence: 99%

A Modified Formulation of Singular Boundary Method for Exterior Acoustics

Wu¹,

Fu²,

Min³

2023

Computer Modeling in Engineering &Amp; Sciences

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This paper proposes a modified formulation of the singular boundary method (SBM) by introducing the combined Helmholtz integral equation formulation (CHIEF) and the self-regularization technique to exterior acoustics. In the SBM, the concept of the origin intensity factor (OIF) is introduced to avoid the singularities of the fundamental solutions. The SBM belongs to the meshless boundary collocation methods. The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently. Consequently, by using the SBM coupled with the CHIEF scheme and the self-regularization technique, the accuracy of the numerical solution can be improved, especially near the corresponding internal characteristic frequencies. Several numerical examples of two-dimensional and threedimensional benchmark examples about exterior acoustics are used to verify the effectiveness and accuracy of the proposed method. The proposed numerical results are compared with the analytical solutions and the solutions obtained by the other numerical methods.

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Section: Introductionmentioning

confidence: 99%

A Modified Formulation of Singular Boundary Method for Exterior Acoustics

Wu¹,

Fu²,

Min³

2023

Computer Modeling in Engineering &Amp; Sciences

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“…Among them, finite element method (FEM) (Brenner et al, 2018) and boundary element method (BEM) (Venas and Kvamsdal, 2020) are the two commonly used methods. The BEM inherently satisfies the Sommerfeld radiation condition for the exterior acoustic problems, whereas some special mathematical treatments need to be incorporated with the FEM to model the infinite exterior acoustic domain, such as perfectly matched layer (PML) (Bunting et al, 2018), infinite elements (Wu and Xiang, 2019), absorbing boundary condition (Jeon, 2018), and Dirichlet to Neumann mapping (Kapita and Monk, 2018). However, the system matrices yielded in the FEM are sparse and symmetric, which can significantly reduce the computation cost and storage requirement.…”

Section: Introductionmentioning

confidence: 99%

Effects of concentrated elements on vibro-acoustic characteristics of a circular ring considering both external and internal fluids

Niu

Huang

et al. 2020

Journal of Vibration and Control

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This study focuses on the vibro-acoustic characteristics of submerged structures with concentrated elements and filled with fluid. A weak formulation is developed based on the modified variational principle. The accurate energy expressions for both structural and acoustic domains are incorporated into the coupled vibro-acoustic model. With introduced Lagrangian multipliers, a domain partitioning technique is developed to divide the whole acoustic domain into several subdomains. The continuity conditions between adjacent subdomains are further guaranteed by the least square weighted residual method working on the common interfaces. To satisfy the Sommerfeld radiation condition, an artificial boundary with the local absorbing boundary condition is adopted to truncate the infinite external acoustic domain. A water-submerged and air-filled bidimensional circular ring with concentrated elements is used as the research object to validate the accuracy of the proposed approach. The concentrated elements are considered as lumped masses with elastic boundary conditions. The structural displacements and acoustic pressures are expanded by the Fourier series and Chebyshev orthogonal polynomials. Furthermore, the effects of the concentrated elements on the coupled vibro-acoustic responses are carefully investigated, as considering different distribution patterns.

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“…To our knowledge, this is the best result by far for the preasymptotic error estimate of higher-order FEM. Numerous approaches have emerged over the past two decades to reduce the pollution errors, including hp-FEM [9,40,50,51], CIP-FEM [22,46,47,55,59], discontinuous Galerkin method (DG) [23,24,32,49,58], Trefftz methods [30,31,[34][35][36][37][38]42], and multiscale methods [8,29,52]. In this paper, we would like to introduce the higher-order CIP-FEM which offers significant advantages in reducing pollution errors.…”

Section: Introductionmentioning

confidence: 99%

FEM and CIP-FEM for Helmholtz Equation with High Wave Number and Perfectly Matched Layer Truncation

Li¹,

Wu²

2019

SIAM J. Numer. Anal.

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The Helmholtz scattering problem with high wave number is truncated by the perfectly matched layer (PML) technique and then discretized by the linear continuous interior penalty finite element method (CIP-FEM). It is proved that the truncated PML problem satisfies the inf-sup condition with inf-sup constant of order O(k −1 ). Stability and convergence of the truncated PML problem are discussed. In particular, the convergence rate is twice of the previous result. The preasymptotic error estimates in the energy norm of the linear CIP-FEM as well as FEM are proved to be C1kh + C2k 3 h 2 under the mesh condition that k 3 h 2 is sufficiently small. Numerical tests are provided to illustrate the preasymptotic error estimates and show that the penalty parameter in the CIP-FEM may be tuned to reduce greatly the pollution error. R 0 J n (kt)f n (t)tdt.(2.24)Note that from [49, 10.21(i)], the zeros of J ν (z) are all real for ν ≥ −1. SinceR is not real and J −n = (−1) n J n for integer n, we have J n (kR) = 0, n ∈ Z.

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A plane wave discontinuous Galerkin method with a Dirichlet-to-Neumann boundary condition for the scattering problem in acoustics

Cited by 8 publications

References 28 publications

A Modified Formulation of Singular Boundary Method for Exterior Acoustics

A Modified Formulation of Singular Boundary Method for Exterior Acoustics

Effects of concentrated elements on vibro-acoustic characteristics of a circular ring considering both external and internal fluids

FEM and CIP-FEM for Helmholtz Equation with High Wave Number and Perfectly Matched Layer Truncation

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