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A Newton method for solving the inverse scattering problem for a sound-hard obstacle

Lars Mönch

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We present a Newton method for solving the ill-posed and nonlinear inverse scattering problem. For its foundation we establish the Fréchet differentiability of the far-field operator with respect to the boundary and show that the Fréchet derivative can be obtained as the solution of a hypersingular integral equation. In order to derive the right-hand sides of this integral equation we use a quadrature method. We describe the numerical solution method and give some numerical results.


PACS

02.30.Zz Inverse problems

02.30.Rz Integral equations

02.60.Lj Ordinary and partial differential equations; boundary value problems

02.60.Cb Numerical simulation; solution of equations

MSC

65Rxx Integral equations, integral transforms

65N21 Inverse problems

35R30 Inverse problems (undetermined coefficients, etc.) for PDE

78A46 Inverse scattering problems

47J06 Nonlinear ill-posed problems

Subjects

Mathematical physics

Computational physics

Dates

Issue 3 (June 1996)

Received 18 January 1996



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