
Helmholtz scattering by random domains: firstorder sparse boundary elements approximation
We consider the numerical solution of timeharmonic acoustic scattering ...
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Inverse obstacle scattering for elastic waves in the time domain
This paper concerns an inverse elastic scattering problem which is to de...
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A parabolic equation on domains with random boundaries
A heat equation with uncertain domains is thoroughly investigated. Stati...
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A Shape calculus approach for time harmonic solidfluid interaction problem in stochastic domains
The present paper deals with the interior solidfluid interaction proble...
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A Neural Network Perturbation Theory Based on the Born Series
Deep Learning has become an attractive approach towards various databas...
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LowDimensional Spatial Embedding Method for Shape Uncertainty Quantification in Acoustic Scattering
This paper introduces a novel boundary integral approach of shape uncert...
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Discretized boundary surface reconstruction
Domain discretization is an essential part of the solution procedure in ...
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A higher order perturbation approach for electromagnetic scattering problems on random domains
We consider timeharmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the twopoint correlation of the domain boundary variations around a reference domain, we derive a perturbation analysis for the mean of the scattered field. Therefore, we compute the second shape derivative of the scattering problem for a single perturbation. Taking the mean, this leads to an at least third order accurate approximation with respect to the perturbation amplitude of the domain variations. To compute the required second order correction term, a tensor product equation on the domain boundary has to be solved. We discuss its discretization and efficient solution using boundary integral equations. Numerical experiments in three dimensions are presented.
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