Global boundary flattening transforms for acoustic propagation under rough sea surfaces

Oba, Roger M.

doi:10.1121/1.3445783

Cited by 4 publications

(7 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The example here revisits the problem of [17]: acoustic scattering from an undulating surface ensonified by an acoustic beam. A single frequency line source at range 0 m uses a Gaussian beam source…”

Section: The Acoustical Problemmentioning

confidence: 99%

See 1 more Smart Citation

Minimal Sparse Sampling for Fourier-Polynomial Chaos in Acoustic Scattering

Oba

2015

Int. J. UncertaintyQuantification

Self Cite

View full text Add to dashboard Cite

Single frequency acoustic scattering from an uncertain surface (with sinusoidal components) admits an efficient Fourier-polynomial chaos (FPC) expansion of the acoustic field. The expansion coefficients are computed nonintrusively, i.e., by functional sampling from existing acoustic models. The structure of the acoustic decomposition permits sparse selection of FPC orders within the framework of the Smolyak construction. The main result shows a minimal, sparse sampling required to exactly reconstruct FPC expansions of Smolyak form. To this end, this paper defines two concepts: exactly discretizable orthonormal, function systems (EDO); and nested systems created by decimation or "fledging." An EDO generalizes the Nyquist-Shannon sampling conditions (exact recovery of "bandlimited" functions given sufficient sampling) to multidimensional FPC expansions. EDO criteria replace the concept of polynomially exact quadrature. Fledging parallels the idea of sub-sampling for sub-bands, from higher to lower level. The FPC Smolyak construction is an EDO fledged from a full grid EDO. An EDO results exactly when the sampled FPC expansion can be inverted to find its coefficients. EDO fledging requires that the lower level (1) has grid points and expansion orders nested in the higher level, and (2) derives its map from the samples to the coefficients from the higher level map. The theory begins with a single dimension fledged EDO, since a tensor product of fledged EDOs yields a fledged tensor EDO. A sequence of nested EDO levels fledge recursively from the largest EDO. The Smolyak construction uses telescoping sums of tensor products up to a maximum level to develop nested EDO systems for sparse grids and orders. The Smolyak construction transform gives exactly the inverse of the weighted evaluation map, and that inverse has a condition number that expresses the numerical limitations of the Smolyak construction.

show abstract

Section: The Acoustical Problemmentioning

confidence: 99%

“…The beam is directed so that it impinges in the middle of variable height surface of 750 m horizontal extent. Other details of the acoustic propagation model (including surface flattening via conformal mapping) appear in [17].…”

Section: The Acoustical Problemmentioning

confidence: 99%

Minimal Sparse Sampling for Fourier-Polynomial Chaos in Acoustic Scattering

Oba

2015

Int. J. UncertaintyQuantification

Self Cite

View full text Add to dashboard Cite

show abstract

“…This conformal mapping has already been used in the literature, for instance in [4,6,7], for boundaries that can be described by a real function under the form…”

Section: Conformal Mappingsmentioning

confidence: 99%

“…As a result, a very large literature exists on the subject, including several books which deal with this topic (for instance [1][2][3]). Introduced by Nevière & Cadilhac [4], and then used by other authors (for instance [5][6][7]), one approach consists in using a conformal mapping. Despite being an old mathematical tool, conformal mappings still remain the object of recent and active research works [8][9][10] and are now used in different domains of physics.…”

Section: Introductionmentioning

confidence: 99%

Multimodal method and conformal mapping for the scattering by a rough surface

Favraud

Pagneux

2015

Proc. R. Soc. A.

View full text Add to dashboard Cite

The scattering of a wave from a periodic rough surface in two dimensions is considered. The proposed method is based on the use of a conformal mapping and of the multimodal admittance method. The use of the conformal mappings induces a spatially varying refractive index and transforms the boundary condition on the rough surface into a boundary condition on a flat surface. Then, the multimodal admittance method reduces this problem to a Riccati equation for the modal admittance matrix, which is solved numerically with a MagnusMöbius scheme. The method is shown to converge exponentially with the number of Fourier modes. The method also allows to find geometries having trapped modes, or quasi-trapped modes, at a given frequency, by looking at singularities, or quasisingularities, of this Riccati equation. Besides, a simple perturbation expansion, based on a small roughness approximation, is developed.

show abstract

“…from physical stresses, manufacturing deficiencies, and uncertainty in measurements of a fixed geometry. Specific applications are found in transport in tubes with rough boundaries [28], aerodynamic studies in the design of wind turbines [10], heat diffusion across irregular and fractal-like surfaces [6,7], structural analysis studies [26], acoustic scattering on rough surfaces [27,30], seismology and oil reservoir management [4], various civil and nuclear engineering studies [3], chemical transport in rough domains [9], and electromechanical studies for nanostructures [1]. This paper focuses on two key issues that arise in such problems:• Since the geometric properties of the domain has a strong effect on solution behavior and smoothness, significant variation in solution behavior for different realizations of the domain is to be expected.…”

mentioning

confidence: 99%

Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries

Chaudhry¹,

Burch²,

Estep³

2018

SIAM/ASA J. Uncertainty Quantification

View full text Add to dashboard Cite

We study the problem of uncertainty quantification for the numerical solution of elliptic partial differential equation boundary value problems posed on domains with stochastically varying boundaries. We also use the uncertainty quantification results to tackle the efficient solution of such problems. We introduce simple transformations that map a family of domains with stochastic boundaries to a fixed reference domain. We exploit the transformations to carry out a prior and a posteriori error analyses and to derive an efficient Monte Carlo sampling procedure. IntroductionIn this paper, we study uncertainty quantification and efficient solution of boundary value problems for elliptic partial differential equations (PDEs) posed on domains with stochastically perturbed boundaries. The problem of stochastic boundaries occurs for a variety of reasons, e.g. from physical stresses, manufacturing deficiencies, and uncertainty in measurements of a fixed geometry. Specific applications are found in transport in tubes with rough boundaries [28], aerodynamic studies in the design of wind turbines [10], heat diffusion across irregular and fractal-like surfaces [6,7], structural analysis studies [26], acoustic scattering on rough surfaces [27,30], seismology and oil reservoir management [4], various civil and nuclear engineering studies [3], chemical transport in rough domains [9], and electromechanical studies for nanostructures [1]. This paper focuses on two key issues that arise in such problems:• Since the geometric properties of the domain has a strong effect on solution behavior and smoothness, significant variation in solution behavior for different realizations of the domain is to be expected. Correspondingly, significant variation in the error arising from discretization and sampling is also to be expected;

show abstract

Global boundary flattening transforms for acoustic propagation under rough sea surfaces

Cited by 4 publications

References 23 publications

Minimal Sparse Sampling for Fourier-Polynomial Chaos in Acoustic Scattering

Minimal Sparse Sampling for Fourier-Polynomial Chaos in Acoustic Scattering

Multimodal method and conformal mapping for the scattering by a rough surface

Efficient Distribution Estimation and Uncertainty Quantification for Elliptic Problems on Domains with Stochastic Boundaries

Contact Info

Product

Resources

About