The coefficients which appear in the representation of the far-field scattered by a twodimensional, perfectly electrically conducting obstacle, depend on the normal derivative of the scattered field on the obstacle boundary, $\partial_N v |_{\Gamma}$. A family of functions, W, deduced from the minimization of a boundary defect, is shown to be linearly independent and complete. As a consequence the approximation of @Nv|gamma results from a well posed algebraic problem. The approximation error is estimated from an a priori bound on the equation error in terms of the eigenvalues of a boundary integral operator. Rayleigh's hypothesis is nowhere required of the obstacle. These results justify some obstacle inversion methods which originated from heuristic arguments

Crosta, G. (2008). Approximating the scattering coefficients for a non-Rayleigh obstacle by boundary defect minimization. In The 24th International Review of Progress in Applied Computational Electromagnetics (ACES 2008) Proceedings. University, MS : Elsherbeni, A.

### Approximating the scattering coefficients for a non-Rayleigh obstacle by boundary defect minimization

#### Abstract

The coefficients which appear in the representation of the far-field scattered by a twodimensional, perfectly electrically conducting obstacle, depend on the normal derivative of the scattered field on the obstacle boundary, $\partial_N v |_{\Gamma}$. A family of functions, W, deduced from the minimization of a boundary defect, is shown to be linearly independent and complete. As a consequence the approximation of @Nv|gamma results from a well posed algebraic problem. The approximation error is estimated from an a priori bound on the equation error in terms of the eigenvalues of a boundary integral operator. Rayleigh's hypothesis is nowhere required of the obstacle. These results justify some obstacle inversion methods which originated from heuristic arguments
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Helmholtz equation; boundary integral equations; complete families; linear independence; analytic continuation; error bounds; interior eigenvalues
English
The 24th International Review of Progress in Applied Computational Electromagnetics (ACES 2008)
26-mar-2008
Crosta, G. (2008). Approximating the scattering coefficients for a non-Rayleigh obstacle by boundary defect minimization. In The 24th International Review of Progress in Applied Computational Electromagnetics (ACES 2008) Proceedings. University, MS : Elsherbeni, A.
Crosta, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/6017