A three-dimensional acoustics model using the method of fundamental solutions

António, Julieta; Tadeu, A.; Godinho, L.

doi:10.1016/j.enganabound.2007.10.008

Cited by 33 publications

(12 citation statements)

References 19 publications

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“…The MFS is a simple and efficient scheme and has been widely applied to various engineering and science problems, such as heat conduction [17][18][19], acoustics [20,21], diffusion-reaction [22,23], axisymmetric elasticity [24], stokes problem [25][26][27][28], and free vibration [29][30][31], just to mention a few. Furthermore, Smyrlis and Karageorghis [32][33][34][35][36], Drombosky [37], Marin [38], and Lin et al [39] presented some fundamental theoretical analysis about the MFS.…”

Section: The Methods Of Fundamental Solutionsmentioning

confidence: 99%

Boundary-Type RBF Collocation Methods

Chen

2013

Recent Advances in Radial Basis Function Collocation Methods

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The mesh generation in the standard BEM is still not trivial as one may imagine, especially for high-dimensional moving boundary problems. To overcome this difficulty, the boundary-type RBF collocation methods have been proposed and endured a fast development in the recent decade thanks to being integration-free, spectral convergence, easy-to-use, and inherently truly meshless. First, this chapter introduces the basic concepts of the method of fundamental solutions (MFS). Then a few recent boundary-type RBF collocation schemes are presented to tackle the issue of the fictitious boundary in the MFS, such as boundary knot method (BKM), regularized meshless method, and singular boundary method. Following this, an improved multiple reciprocity method (MRM), the recursive composite MRM (RC-MRM), is introduced to establish a boundary-only discretization of nonhomogeneous problems. Finally, numerical demonstrations show the convergence rate and stability of these boundary-type RBF collocation methods for several benchmark examples.Keywords Meshless Á Integration-free Á Collocation Á Fundamental solutions Á Singularity Á Method of fundamental solutions Á Boundary knot method Á Regularized meshless method Á Singular boundary method Á Boundary particle method During the past two decades we have witnessed a research boom on the boundarytype meshless techniques since the construction of a mesh in the standard BEM is not trivial. Among the typical techniques are the boundary node method, the local boundary integral equation method, the boundary cloud method, the boundary point method, the boundary point interpolation method (BPIM), and the method of fundamental solutions (MFS). The essence of all these techniques, excluding the MFS and BPIM, is basically a combination of the moving least square (MLS) technique with various boundary element schemes, whereas the MFS is a boundary-type RBF collocation scheme.Such MLS-based methods involve singular integration and are mathematically complicated, and their low-order approximations also depress computational efficiency. The numerical integration requires a background mesh, and thus the

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Section: The Methods Of Fundamental Solutionsmentioning

confidence: 99%

Boundary-Type RBF Collocation Methods

Chen

2013

Recent Advances in Radial Basis Function Collocation Methods

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“…The work by António et al (2008) revealed that the accuracy of the response computed using a 3D MFS model will significantly depend on the position of the virtual sources, used to simulate the pressure field. For this reason, a preliminary study will be performed, verifying the behaviour of the method against a reference solution known for a simple geometric configuration, with the purpose of defining an adequate position for those sources and to ensure that meaningful results will be obtained.…”

Section: Model Verificationmentioning

confidence: 99%

“…In one of the few published works, António et al (2008) simulated the propagation of sound within a closed space, using a MFS formulation. In that work, the authors used a single-domain formulation and concluded that the accuracy of the method depends on the number and location of the virtual sources.…”

Section: Introductionmentioning

confidence: 99%

3D Multi-Domain MFS Analysis of Sound Pressure Level Reduction Between Connected Enclosures

Godinho¹,

Branco²,

Amado-Mendes³

2011

Archives of Acoustics

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In this paper, the authors study the 3D propagation of sound waves between two closed spaces. The separation element between the two rooms is considered to include either a small opening or a homogeneous lightweight panel, coupling the two spaces. A numerical study of this configuration is performed, trying to understand the influence of the position and geometry of this opening in the sound pressure level reduction curve at low and midfrequencies. Additionally, the coupling effect between the two acoustic spaces is analyzed, in order to better understand its importance when determining the sound pressure level reduction. Different boundary conditions are ascribed to the walls of these rooms, simulating both the completely reflecting and partially absorbing surfaces.The numerical modelling was performed using a multi-domain formulation of the Method of Fundamental Solutions (MFS). The system is composed of two coupled rooms, limited by rigid or by absorbing walls, and separated by a thin wall (tending to null thickness) with a small opening. An experimental validation of the proposed model is presented, comparing its results with those found experimentally for a reduced-scale model. It is important to note that, for such a configuration, a traditional single-domain approach using methods like the MFS or the BEM would lead to undetermined equation systems, and thus the proposed model makes use of a domain decomposition technique.

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“…Some interesting applications of the MFS are the boundary singularity problem, 41 the eigenvalue problem, 42 room acoustics, 43,44 and underwater acoustics. 45,46 …”

Section: S Leementioning

confidence: 99%

Review: The Use of Equivalent Source Method in Computational Acoustics

Lee

2017

J. Comp. Acous.

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This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequencydomain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.

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A three-dimensional acoustics model using the method of fundamental solutions

Cited by 33 publications

References 19 publications

Boundary-Type RBF Collocation Methods

Boundary-Type RBF Collocation Methods

3D Multi-Domain MFS Analysis of Sound Pressure Level Reduction Between Connected Enclosures

Review: The Use of Equivalent Source Method in Computational Acoustics

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