Wave scattering by randomly shaped objects

Ditkowski, Adi; Harness, Yuval

doi:10.1016/j.apnum.2012.07.002

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…where r = r(σ, θ) = r(σ; θ) · (cos θ, sin θ). Note, that the change of variables in (59) effectively maps each triangular subdomain of integration R q (57) onto the 1]. Accordingly, we propose the following repeated Gauss-Legendre quadrature rules, for the approximation of (59):…”

Section: Numerical Examplementioning

confidence: 99%

“…The expansion of the scattered field in 3D is of the form (1) n (κr)Y m n (θ, ϕ) , The expressions are, however, technically more complicated to work with. The usage of automatic integration as well as optimization methods for obtaining the spatial grid may prove to be a necessity.…”

Section: Future Studymentioning

confidence: 99%

“…Their applicability range is, however, more limited. The null-field reconstruction technique [1,18] is inherently stable, admits a-priori error evaluation, and facilitates the extraction of features of interest without prior estimation of the entire solution. The method enables us to perform analysis from a purely geometric point of view, which avoids the additional complications associated with integration of weakly singular kernels.…”

Section: Introductionmentioning

confidence: 99%

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Low-Dimensional Spatial Embedding Method for Shape Uncertainty Quantification in Acoustic Scattering by 2D Star Shaped Obstacles

Harness

2018

J Sci Comput

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This paper introduces a novel boundary integral approach of shape uncertainty quantification for the Helmholtz scattering problem in the framework of the so-called parametric method. The key idea is to construct an integration grid whose associated weight function encompasses the irregularities and nonsmoothness imposed by the random boundary. Thus, the solution can be evaluated accurately with relatively low number of grid points. The integration grid is obtained by employing a low-dimensional spatial embedding using the coarea formula. The proposed method can handle large variation as well as non-smoothness of the random boundary. For the ease of presentation the theory is restricted to star-shaped obstacles in low-dimensional setting. Higher spatial and parametric dimensional cases are discussed, though, not extensively explored in the current study.

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Section: Numerical Examplementioning

confidence: 99%

Section: Future Studymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Low-Dimensional Spatial Embedding Method for Shape Uncertainty Quantification in Acoustic Scattering by 2D Star Shaped Obstacles

Harness

2018

J Sci Comput

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On applying the perturbation theory for the evaluation of near zone scattering properties of a perturbed PEMC cylinder

Masood

Fiaz

Ashraf

2021

Optik

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A High Performance Computing and Sensitivity Analysis Algorithm for Stochastic Many-Particle Wave Scattering

Ganesh¹,

Hawkins²

2015

SIAM J. Sci. Comput.

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We present a high performance computing framework for quantifying uncertainties in the propagation of acoustic waves through a stochastic media comprising a large number of three-dimensional particles. We subsequently describe an efficient postprocessing approach using our framework to statistically quantify the sensitivity of the uncertainties with respect to input parameters that govern the stochasticity in the model. The stochasticity arises through the random positions and orientations of the component particles in the media. Simulation even for a single deterministic three-dimensional configuration is inherently difficult because of the large number of particles; the stochasticity leads to a larger dimensional model involving three spatial variables and additional stochastic variables, and accounting for uncertainty in key parameters of the input probability distributions leads to prohibitive computational complexity. In the first part of our paper we describe a high performance computing framework for uncertainty quantification with fixed input parameters. In the second part of our paper we describe and analyze an efficient offline/online approach that allows characterization of the quantity of interest with respect to the variance of the input stochastic variables. Our approach provides a framework for high performance computing implementation to compute statistical moments for the three-dimensional model and can be used in conjunction with any method to simulate a single-particle deterministic model. We demonstrate the efficiency of our high performance computing implementation with Monte Carlo (MC) and quasi-Monte Carlo (QMC) realization numerical results for more than one thousand stochastic dimensions describing stochastic media comprising hundreds to thousands of nonconvex particles. Our demonstration of the efficient sensitivity analysis algorithm includes over a million MC samples of the backscattered cross section and thousands of generalized polynomial chaos-based realizations of the three-dimensional model with parallelization in both spatial and stochastic variables. Introduction.Computational uncertainty quantification techniques are a crucial tool for understanding wave scattering by large configurations of particles with uncertain geometry. Innovative approaches are required to overcome the significant computational challenges that are inherent due to both the large stochastic dimension and the large dimension due to spatial discretization of the underlying three-dimensional partial differential equation (PDE) model. In addition, a key component for quantification of uncertainties in stochastic configurations is to perform sensitivity analysis on the output quantity of interest (QoI) with respect to various sources of uncertainties in the random input data that determine the stochastic configurations.In this article we are interested in (i) developing iterative computational tools for

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Wave scattering by randomly shaped objects

Cited by 3 publications

References 19 publications

Low-Dimensional Spatial Embedding Method for Shape Uncertainty Quantification in Acoustic Scattering by 2D Star Shaped Obstacles

Low-Dimensional Spatial Embedding Method for Shape Uncertainty Quantification in Acoustic Scattering by 2D Star Shaped Obstacles

On applying the perturbation theory for the evaluation of near zone scattering properties of a perturbed PEMC cylinder

A High Performance Computing and Sensitivity Analysis Algorithm for Stochastic Many-Particle Wave Scattering

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