The lagrange padé parabolic equation (LP-PE) for the prediction of long range sound propagation in the atmosphere

Sack, R. A.; West, M.

doi:10.1016/0003-682x(95)00064-g

Cited by 3 publications

(6 citation statements)

References 4 publications

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“…In [2] the authors have given a specimen list of coefficients p, in (20) for M ranging from 1 to 4 and for M0 ranging from 2 to 1/32. The case M = I is equivalent to the standard WA-PE; the only coefficient in (20) has the value p, = -0t5 -11,, / 41rh.…”

Section: Application Of the Lp Pe For Realistic Atmospheric Propagati...mentioning

confidence: 99%

“…The authors prefer an alternative approach where W is factorized into an exponential "carrier" W0 and a slowly varying "modulator" (p, leading to [2] w =exP(ik.,r)¢; [of +2ik. D.+k q ¢ =0,…”

Section: Introductionmentioning

confidence: 99%

“…where q and kn have the same meanings as in (2). This approach generates the NA and WA PE s by an iterative process; but it can be used even when the terms in brackets depend explicitly on x.…”

Section: Introductionmentioning

confidence: 99%

“…Taylor's theorem can be written symbolically \P(x + h, z) = exp(h DI) I (x, z); (4) hence this error cannot be reduced by taking smaller step lengths. For this reason Collins [3] uses higher order Padé approximants of the square root in (2). However, this solves only part of the problem as the main interest lies not in D, itself, but in its exponential according to (4X As the operator q involves D, and thus, numerically, a tridiagonal or even more complicated matrix, an expansion for exp(h D) directly is preferable.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A New Fast Parabolic Equation (Pe) Based on a Lagrange Pade (Lp) Expansion of Implicit Functions for 2d Sound Propagation

SACK,

WEST

2024

Noise Control - The Next 25 Years

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Section: Application Of the Lp Pe For Realistic Atmospheric Propagati...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Fast Parabolic Equation (Pe) Based on a Lagrange Pade (Lp) Expansion of Implicit Functions for 2d Sound Propagation

SACK,

WEST

2024

Noise Control - The Next 25 Years

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“…8. This MIE method has proved effective and accurate and been applied to solving engineering problems at higher frequencies with an acceptable mesh density and data storage.…”

Section: Introductionmentioning

confidence: 98%

A Modified Infinite Element Method for Acoustic Radiation

Sun²,

Sakamoto³

2002

J. Comp. Acous.

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An infinite element method is proposed to help solve practical problems in engineering and extend the applicability of infinite element. Based on the Helmholtz's equation, a novel governing equation is derived in terms of the modified sound pressure. The relative boundary conditions are established and the system matrices in using the combination of conventional finite element and new infinite element are subsequently formed. As a result, the use of coarser finite element meshes is permitted for a given frequency. The effectiveness and accuracy of this method are demonstrated in application to two typical examples.

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Efficient prediction of acoustic pulses accounting for fractional travel time

Vecherin

Albert

2018

The Journal of the Acoustical Society of America

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Predicting a full waveform of an acoustic broadband signal propagating over different impedance surfaces is a stringent test of both the method used in the modeling of propagation and the surface impedance models. It has been shown that predicted waveforms might be sensitive to the fractional travel time, when the propagation time of the pulse does not equal an integer number of computational time steps. A method overcoming this issue is developed and demonstrated for different propagation conditions: a pulse propagating over a snow layer, frozen ground, and their combinations along the propagating path with homogeneous and vertically stratified atmosphere for a range of 60 m. For the numerical simulations, a conventional one-way parabolic equation with the Crank-Nicholson numerical algorithm is modified to improve computational efficiency and insure that the experimental time of arrival and spatial location of the receiver are matched exactly to the digital grids used in the simulations. The results are in a good agreement with experimental measurements and prior knowledge, and confirm that physical properties of a snow layer, sublayer ground, atmospheric conditions, and the order of range dependent ground properties affect the pulse waveforms.

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The lagrange padé parabolic equation (LP-PE) for the prediction of long range sound propagation in the atmosphere

Cited by 3 publications

References 4 publications

A New Fast Parabolic Equation (Pe) Based on a Lagrange Pade (Lp) Expansion of Implicit Functions for 2d Sound Propagation

A New Fast Parabolic Equation (Pe) Based on a Lagrange Pade (Lp) Expansion of Implicit Functions for 2d Sound Propagation

A Modified Infinite Element Method for Acoustic Radiation

Efficient prediction of acoustic pulses accounting for fractional travel time

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