Dirichlet-to-Neumann Maps for Unbounded Wave Guides

Harari, Isaac; Patlashenko, Igor; Givoli, Dan

doi:10.1006/jcph.1998.5960

Cited by 63 publications

(49 citation statements)

References 53 publications

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“…This is done easily by deriving an exact Dirichlet-to-Neumann boundary condition for u ε on Σ ε (see (2.22)) from the general form (2.39) of the solution inside the slot [21]. Proceeding this way, one easily shows that the restriction of u ε to Ω is characterized as the unique solution of the boundary value problem:…”

Section: Lemma 42 When ε → 0 One Has the Following Resultsmentioning

confidence: 99%

Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots

Joly¹,

Tordeux

2006

ESAIM: M2AN

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Section: Lemma 42 When ε → 0 One Has the Following Resultsmentioning

confidence: 99%

Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots

Joly¹,

Tordeux

2006

ESAIM: M2AN

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“…In order to validate the method, a full finite element model is used. Radiation conditions at both ends of the duct have been implemented using the DtN map [7]. In Fig.…”

Section: Results and Concluding Remarksmentioning

confidence: 99%

An efficient FEM-BEM procedure for the multi-frequency acoustical analysis of lined ducts containing passive components

Maréchal

Perrey‐Debain

Ville

et al. 2010

Boundary Elements and Other Mesh Reduction Methods XXXII

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This paper deals with strategies for computing efficiently the propagation of sound waves in ducts with acoustic lining at its walls. Although efficient, these treatments seem to have reached their limit and there is still a need for considering other passive techniques to reduce further the sound radiation at the duct exit. In most cases of practical interest, these added acoustics components can be modeled as acoustic cavities, which are connected to the duct and can be either purely reactive or dissipative. The assessment of the efficiency of such a system requires a precise knowledge of the acoustic field in the duct. Although standard Finite Element (FE) software could, in principle, be used for this purpose, a full FE model would be extremely demanding, particularly in the mid-frequency range and this can have a negative impact when, for instance, some efficient optimizations are needed. In the present work, we present a new numerical procedure that judiciously exploits the benefit of the FEM and the BEM approach. Firstly, a set of FE eigenmodes are computed in the cavity to produce a numerical impedance matrix connecting the pressure and the acoustic velocity on the duct wall interface. Then an integral representation for the acoustic pressure in the main duct is used. The presence of acoustic liners on the walls of the duct is taken into account via an appropriate modal decomposition of the Green's function. Typical applications involving Helmholtz resonators and Herschel-Quincke tubes are presented. We show that our algorithm allows a very fast and accurate computation of the scattering matrix of such a system with a numerical complexity that grows very mildly with the frequency.

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“…Several strategies have been reported to eliminate this di culty in the past [1; 2; 4; 6]. Recently, Harari et al [6] presented a derivation and the analysis of DtN formulations for unbounded wave guides in two and three dimensions. In virtue of this fact, the DtN operator is expressed in the form of inÿnite series.…”

Section: An Exact Gauss Filter For Helmholtz Equation In Unbounded Domentioning

confidence: 98%

“…The papers by Givoli [1] and Moore et al [2] provide good summaries of much of the work that has been done in this direction. Several nonlocal procedure has been developed in the last 10 years, such as the DtN method proposed by Givoli [3] and Giou and Keller [4] and developed by Harari and Hughes [5] and Harari et al [6]. The DtN boundary condition is exact and non-re ecting at the continuum medium, but it is dependent of the operator and the dimensional space where this is deÿned, then, when you apply this boundary condition do you need to know the fundamental solutions in question.…”

Section: Introductionmentioning

confidence: 99%

Non-reflective planar boundary condition based on Gauss filter

Bonet

Nigro

Storti

et al. 2000

Int. J. Numer. Meth. Engng.

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SUMMARYA non-re ecting boundary condition based on the Gauss ÿlter is employed for the determination of scattered potential governed by the Helmholtz equation. A ÿltering layer is used for closing inÿnite domain calculations. An expression for the re ection coe cient is derived and an optimal ÿltering layer is designed. Numerical results validate the performance of this method for unbounded wave guide problems.

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Dirichlet-to-Neumann Maps for Unbounded Wave Guides

Cited by 63 publications

References 53 publications

Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots

Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots

An efficient FEM-BEM procedure for the multi-frequency acoustical analysis of lined ducts containing passive components

Non-reflective planar boundary condition based on Gauss filter

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