Fast spectral methods for the shape identification problem of a perfectly conducting obstacle

Frédérique Le Louër (1)

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

We are concerned with fast methods for the numerical implementation of the direct and inverse scattering problems for a perfectly conducting obstacle. The scattering problem is usually reduced to a single uniquely solvable modified combined-field integral equation (M-CFIE). For the numerical solution of the M-CFIE we propose a new high-order spectral algorithm by transporting this equation on the unit sphere via the Piola transform. The inverse problem is formulated as a nonlinear least squares problem for which the iteratively regularized Gauss-Newton method is applied to recover an approximate solution. Numerical experiments are presented in the special case of star-shaped obstacles.

Mots clés: regularized Newton method; Maxwell equations; perfectly conducting interface; boundary integral equation; spectral method; Fréchet derivative; regularized Newton method.

Domaines: Analyse numérique [math.NA]

Frédérique Le Louër. Fast spectral methods for the shape identification problem of a perfectly conducting obstacle. 2013. ⟨hal-00780379⟩