676 research outputs found
Looking back on inverse scattering theory
We present an essay on the mathematical development of inverse scattering theory for time-harmonic waves during the past fifty years together with some personal memories of our participation in these events
The linear sampling method for random sources
We present an extension of the linear sampling method for solving the
sound-soft inverse acoustic scattering problem with randomly distributed point
sources. The theoretical justification of our sampling method is based on the
Helmholtz--Kirchhoff identity, the cross-correlation between measurements, and
the volume and imaginary near-field operators, which we introduce and analyze.
Implementations in MATLAB using boundary elements, the SVD, Tikhonov
regularization, and Morozov's discrepancy principle are also discussed. We
demonstrate the robustness and accuracy of our algorithms with several
numerical experiments in two dimensions
Shape derivatives of boundary integral operators in electromagnetic scattering. Part II : Application to scattering by a homogeneous dielectric obstacle
We develop the shape derivative analysis of solutions to the problem of
scattering of time-harmonic electromagnetic waves by a bounded penetrable
obstacle. Since boundary integral equations are a classical tool to solve
electromagnetic scattering problems, we study the shape differentiability
properties of the standard electromagnetic boundary integral operators. The
latter are typically bounded on the space of tangential vector fields of mixed
regularity TH\sp{-1/2}(\Div_{\Gamma},\Gamma). Using Helmholtz decomposition,
we can base their analysis on the study of pseudo-differential integral
operators in standard Sobolev spaces, but we then have to study the G\^ateaux
differentiability of surface differential operators. We prove that the
electromagnetic boundary integral operators are infinitely differentiable
without loss of regularity. We also give a characterization of the first shape
derivative of the solution of the dielectric scattering problem as a solution
of a new electromagnetic scattering problem.Comment: arXiv admin note: substantial text overlap with arXiv:1002.154
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