TY - JOUR

T1 - Wave scattering by randomly shaped objects

AU - Ditkowski, A.

AU - Harness, Y.

N1 - Funding Information:
✩ This research was supported by the Israel Science Foundation (grant No. 1364/04) and the United States–Israel Binational Science Foundation (grant No. 2004099). * Corresponding author. E-mail addresses: adid@post.tau.ac.il (A. Ditkowski), harness@post.tau.ac.il (Y. Harness).

PY - 2012/12

Y1 - 2012/12

N2 - We propose a new methodology for the evaluation of the scattered radiation by objects of uncertain shape. The uncertainties are handled by treating them as random fields. The analysis is not restricted to small geometric variations, such as in modeling of rough surfaces. Due to its efficiency and accuracy we employ the Stochastic Galerkin method. We combine this later method with a specially suited domain decomposition procedure, with which we obtain a spectrally global convergence rate. The key idea is to split the equation system with respect to the spatial position of the boundaries, and consider the interface fields as the unknown quantities. This approach preserves the governing equations, allowing us to obtain the projections of the classical integral representation of the solution. The original unbounded domain of interest is transformed to a bounded domain, while the far-field radiation condition is automatically satisfied. Discretization is accomplished by standard numerical integration, which coincides with a collocation scheme. We conclude by showing the inherent connection of the integral representation to the formulation of the problem in terms of boundary integrals.

AB - We propose a new methodology for the evaluation of the scattered radiation by objects of uncertain shape. The uncertainties are handled by treating them as random fields. The analysis is not restricted to small geometric variations, such as in modeling of rough surfaces. Due to its efficiency and accuracy we employ the Stochastic Galerkin method. We combine this later method with a specially suited domain decomposition procedure, with which we obtain a spectrally global convergence rate. The key idea is to split the equation system with respect to the spatial position of the boundaries, and consider the interface fields as the unknown quantities. This approach preserves the governing equations, allowing us to obtain the projections of the classical integral representation of the solution. The original unbounded domain of interest is transformed to a bounded domain, while the far-field radiation condition is automatically satisfied. Discretization is accomplished by standard numerical integration, which coincides with a collocation scheme. We conclude by showing the inherent connection of the integral representation to the formulation of the problem in terms of boundary integrals.

KW - Boundary Integral

KW - Domain decomposition

KW - Geometric uncertainty

KW - Maxwells Equations

KW - Polynomial Chaos expansion

KW - Uncertainty quantification

KW - Wave scattering

UR - http://www.scopus.com/inward/record.url?scp=84867097146&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2012.07.002

DO - 10.1016/j.apnum.2012.07.002

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AN - SCOPUS:84867097146

SN - 0168-9274

VL - 62

SP - 1819

EP - 1836

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 12

ER -