Analytical study of the effect of wave number on the performance of local absorbing boundary conditions for acoustic scattering

Harari, Isaac; Djellouli, Rabïa

doi:10.1016/j.apnum.2003.11.007

Cited by 28 publications

(40 citation statements)

References 42 publications

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“…For ka = 0.01 there is several orders of magnitude difference in the error. In three dimensions the approximation to DtN and the BGT boundary conditions are identical [20].…”

Section: Resultsmentioning

confidence: 99%

“…Thompson and Pinsky [19] and later Harari and Djellouli [20] have shown that through second order these are identical to the BGT far field boundary conditions (30).…”

Section: Two-dimensional Scatteringmentioning

confidence: 91%

“…We compare three ways of calculating the new solution: First the Padé based on an expansion in u as presented in Reference [7]. Second use of the recursion formula (20) and finally a Padé based directly on solving Equation (12) for v. In Table II, we show in parenthesis the order of the numerator and denominator of the Padé expansion. Thus, using transformation (20) improves the accuracy compared with the original method.…”

Section: Bands Of Kmentioning

confidence: 99%

“…Second use of the recursion formula (20) and finally a Padé based directly on solving Equation (12) for v. In Table II, we show in parenthesis the order of the numerator and denominator of the Padé expansion. Thus, using transformation (20) improves the accuracy compared with the original method. This improvement occurs only if the mesh is fine enough so that the higher derivatives have some accuracy.…”

Section: Bands Of Kmentioning

confidence: 99%

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Improved accuracy for the Helmholtz equation in unbounded domains

Turkel

Farhat

Hetmaniuk

2004

Numerical Meth Engineering

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SUMMARYBased on properties of the Helmholtz equation, we derive a new equation for an auxiliary variable. This reduces much of the oscillations of the solution leading to more accurate numerical approximations to the original unknown. Computations confirm the improved accuracy of the new models in both two and three dimensions. This also improves the accuracy when one wants the solution at neighbouring wavenumbers by using an expansion in k. We examine the accuracy for both waveguide and scattering problems as a function of k, h and the forcing mode l. The use of local absorbing boundary conditions is also examined as well as the location of the outer surface as functions of k. Connections with parabolic approximations are analysed.

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“…For ka = 0.01 there is several orders of magnitude difference in the error. In three dimensions the approximation to DtN and the BGT boundary conditions are identical [20].…”

Section: Resultsmentioning

confidence: 99%

“…Thompson and Pinsky [19] and later Harari and Djellouli [20] have shown that through second order these are identical to the BGT far field boundary conditions (30).…”

Section: Two-dimensional Scatteringmentioning

confidence: 91%

Section: Bands Of Kmentioning

confidence: 99%

Section: Bands Of Kmentioning

confidence: 99%

See 2 more Smart Citations

Improved accuracy for the Helmholtz equation in unbounded domains

Turkel

Farhat

Hetmaniuk

2004

Numerical Meth Engineering

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“…Hence, this result provides practitioners with the needed confidence to employ the proposed boundary condition on artificial boundaries that are "close" to the considered scatterer's boundary, leading therefore to small computational domains. Note that the situation is not the same in the case of the standard DtN2/BGT2 boundary conditions (recall that in 3D, the standard DtN2 and BGT2 conditions coincide [11]). More specifically, in the high-frequency regime, the high-order spurious modes (whether they are propagating, evanescent, or grazing modes) created by the standard BGT2/DtN2 boundary condition do not decay, as observed in [2], requiring therefore to place the artificial boundary very far from the obstacle to avoid the deterioration of the accuracy level due to the possible contamination of these non physical modes.…”

Section: Introductionmentioning

confidence: 88%

Exponential Decay of High-Order Spurious Prolate Spheroidal Modes Induced by a Local Approximate DTN Exterior Boundary Condition

Barucq¹,

Djellouli²,

Saint-Guirons³

2012

PIER B

Self Cite

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Abstract-We investigate analytically the asymptotic behavior of high-order spurious prolate spheroidal modes induced by a second-order local approximate DtN absorbing boundary condition (DtN2) when employed for solving high-frequency acoustic scattering problems. We prove that these reflected modes decay exponentially in the high frequency regime. This theoretical result demonstrates the great potential of the considered absorbing boundary condition for solving efficiently exterior high-frequency Helmholtz problems. In addition, this exponential decay proves the superiority of DtN2 over the widely used Bayliss-Gunsburger-Turkel absorbing boundary condition.

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Fluid Finite Elements

2015

Fluid‐Structure Interaction

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Analytical study of the effect of wave number on the performance of local absorbing boundary conditions for acoustic scattering

Cited by 28 publications

References 42 publications

Improved accuracy for the Helmholtz equation in unbounded domains

Improved accuracy for the Helmholtz equation in unbounded domains

Exponential Decay of High-Order Spurious Prolate Spheroidal Modes Induced by a Local Approximate DTN Exterior Boundary Condition

Fluid Finite Elements

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