Search Results
Variational approach to scattering of plane elastic waves by diffraction gratings
2009, Elschner, Johannes, Hu, Guanghui
The scattering of a time-harmonic plane elastic wave by a two-dimensional periodic structure is studied. The grating profile is given by a Lipschitz curve on which the displacement vanishes. Using a variational formulation in a bounded periodic cell involving a nonlocal boundary operator, existence of solutions in quasi-periodic Sobolev spaces is investigated by establishing the Fredholmness of the operator generated by the corresponding sesquilinear form. Moreover, by a Rellich identity, uniqueness is proved under the assumption that the grating profile is given by a Lipschitz graph. The direct scattering problem for transmission gratings is also investigated. In this case, uniqueness is proved except for a discrete set of frequencies.
Variational approach in weighted Sobolev spaces to scattering by unbounded rough surface
2009, Chandler-Wilde, Simon N., Elschner, Johannes
[no abstract available]
Uniqueness in inverse elastic scattering with finitely many incident waves
2009, Elschner, Johannes, Yamamoto, Masahiro
We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation.
Uniqueness in determining polyhedral sound-hard obstacles with a single incoming wave
2008, Elschner, Johannes, Yamamoto, Masahiro
We consider the inverse acoustic scattering problem of determining a sound-hard obstacle by far field measurements. It is proved that a polyhedral scatterer in $R^n, nge 2$, consisting of finitely many solid polyhedra, is uniquely determined by a single incoming plane wave.
An optimisation method in inverse acoustic scattering by an elastic obstacle
2008, Elschner, Johannes, Hsiao, George C., Rathsfeld, Andreas
We consider the interaction between an elastic body and a compressible inviscid fluid, which occupies the unbounded exterior domain. The inverse problem of determining the shape of such an elastic scatterer from the measured far field pattern of the scattered fluid pressure field is of central importance in detecting and identifying submerged objects. Following a method proposed by Kirsch and Kress, we approximate the acoustic and elastodynamic wave by potentials over auxiliary surfaces, and we reformulate the inverse problem as an optimisation problem. The objective function to be minimised is the sum of three terms. The first is the deviation of the approximate far field pattern from the measured one, the second is a regularisation term, and the last a control term for the transmission condition. We prove that the optimisation problem has a solution and that, for the regularisation parameter tending to zero, the minimisers tend to a solution of the inverse problem. In contrast to a numerical method from a previous paper, the presented method does require neither a direct solution method nor an additional treatment of possible Jones modes.