Browsing by Author "Kirsch, Andreas"
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- ItemDirect and inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hu, Guanghui; Kirsch, AndreasConsider a time-harmonic acoustic plane wave incident onto a doubly periodic (biperiodic) surface from above. The medium above the surface is supposed to be filled with homogeneous compressible inviscid fluid with a constant mass density, whereas the region below is occupied by an isotropic and linearly elastic solid body characterized by the Lamé constants. This paper is concerned with direct (or forward) and inverse fluid-solid interaction (FSI) problems with unbounded bi-periodic interfaces between acoustic and elastic waves. We present a variational approach to the forward interaction problem with Lipschitz interfaces. Existence of quasi-periodic solutions in Sobolev spaces is established at arbitrary frequency of incidence, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. Concerning the inverse problem, we show that the factorization method by Kirsch (1998) is applicable to the FSI problem in periodic structures. A computational criterion and a uniqueness result are justified for precisely characterizing the elastic body by utilizing the scattered acoustic near field measured in the fluid.
- ItemInverse Problems for Partial Differential Equations(Zürich : EMS Publ. House, 2012) Kirsch, Andreas; Rundell, William; Lassas, MattiThis workshop brought together mathematicians engaged in different aspects of inverse problems for partial differential equations. Classical topics such as the inverse problems of impedance tomography and scattering theory as well as new developments such as interior transmission eigenvalues were discussed.
- ItemInverse Problems in Wave Scattering(Zürich : EMS Publ. House, 2007) Kirsch, Andreas; Rundell, WilliamThe workshop treated inverse problems for partial differential equations, especially inverse scattering problems, and their applications in technology. While special attention was paid to sampling methods, decomposition methods, Newton methods and questions of unique determination were also investigated.
- ItemInverse Problems in Wave Scattering and Impedance Tomography(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2003) Kirsch, Andreas; Rundell, William[no abstract available]
- ItemSome inverse problems arising from elastic scattering by rigid obstacles(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Kirsch, Andreas; Sini, MouradIn the first part, it is proved that a C2-regular rigid scatterer in R3 can be uniquely identified by the shear part (i.e. S-part) of the far-field pattern corresponding to all incident shear waves at any fixed frequency. The proof is short and it is based on a kind of decoupling of the S-part of scattered wave from its pressure part (i.e. P-part) on the boundary of the scatterer. Moreover, uniqueness using the S-part of the far-field pattern corresponding to only one incident plane shear wave holds for a ball or a convex Lipschitz polyhedron. In the second part, we adapt the factorization method to recover the shape of a rigid body from the scattered S-waves (resp. P-waves) corresponding to all incident plane shear (resp. pressure) waves. Numerical examples illustrate the accuracy of our reconstruction in R2. In particular, the factorization method also leads to some uniqueness results for all frequencies excluding possibly a discrete set.
- ItemTheory and Numerics of Inverse Scattering Problems(Zürich : EMS Publ. House, 2016) Hanke-Bourgeois, Martin; Kirsch, Andreas; Rundell, WilliamThis workshop addressed specific inverse problems for the time-harmonic Maxwell’s equations, resp. special cases of these, such as the Helmholtz equation or quasistatic approximations like in impedance tomography. The inverse problems considered include the reconstruction of obstacles and/or their material properties in a known background, given various kinds of data, such as near or far field measurements in the scattering context and boundary measurements in the quasistatic case.