Search results for "35R30"
showing 2 items of 42 documents
Shape identification in inverse medium scattering problems with a single far-field pattern
2016
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset {\mathbb R}^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be Holder continuous near the corners. If $D\subset {\mathbb R}^2$ is a convex polygon, we prove that its shape and location can be uniquely determined by the far-field pattern incited by a single incident wave at a fixed frequency. In dimensions $N \geq 3$, the uniqueness applies to penetrable scatterers of rectangular type with additional assumptions on the smoothness of the contrast. Our arguments are motivated by recent studies on the absence of nonscattering waven…
Numerical Recovery of Source Singularities via the Radiative Transfer Equation with Partial Data
2013
The inverse source problem for the radiative transfer equation is considered, with partial data. Here we demonstrate numerical computation of the normal operator $X_{V}^{*}X_{V}$ where $X_{V}$ is the partial data solution operator to the radiative transfer equation. The numerical scheme is based in part on a forward solver designed by F. Monard and G. Bal. We will see that one can detect quite well the visible singularities of an internal optical source $f$ for generic anisotropic $k$ and $\sigma$, with or without noise added to the accessible data $X_{V}f$. In particular, we use a truncated Neumann series to estimate $X_{V}$ and $X_{V}^{*}$, which provides a good approximation of $X_{V}^{*…