
The Interior Inverse Electromagnetic Scattering for an Inhomogeneous Cavity
In this paper we consider the inverse electromagnetic scattering for a c...
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A spectrally accurate method for the dielectric obstacle scattering problem and applications to the inverse problem
We analyze the inverse problem to reconstruct the shape of a three dimen...
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Spacetime shape uncertainties in the forward and inverse problem of electrocardiography
In electrocardiography, the "classic" inverse problem consists of findin...
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Inverse scattering by a random periodic structure
This paper develops an efficient numerical method for the inverse scatte...
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Inverse scattering reconstruction of a three dimensional soundsoft axissymmetric impenetrable object
In this work, we consider the problem of reconstructing the shape of a t...
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Asymptotics for metamaterial cavities and their effect on scattering
It is wellknown that optical cavities can exhibit localized phenomena r...
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Local onsurface radiation condition for multiple scattering of waves from convex obstacles
We propose a novel onsurface radiation condition to approximate the out...
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Isogeometric multilevel quadrature for forward and inverse random acoustic scattering
We study the numerical solution of forward and inverse acoustic scattering problems by randomly shaped obstacles in threedimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations of the random scatterer can efficiently be computed by simply updating the NURBS mappings which represent the scatterer. This way, we end up with a random deformation field. In particular, we show that the knowledge of the deformation field's expectation and covariance at the surface of the scatterer are already sufficient to compute the surface KarhunenLoève expansion. Leveraging on the isogeometric framework, we utilize multilevel quadrature methods for the efficient approximation of quantities of interest, such as the scattered wave's expectation and variance. Computing the wave's Cauchy data at an artificial, fixed interface enclosing the random obstacle, we can also directly infer quantities of interest in free space. Adopting the Bayesian paradigm, we finally compute the expected shape and the variance of the scatterer from noisy measurements of the scattered wave at the artificial interface. Numerical results for the forward and inverse problem are given to demonstrate the feasibility of the proposed approach.
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