Abstract. This paper adresses the construction and study of a Crank-Nicolson-type discretization of the two-dimensional linear Schrödinger equation in a bounded domain Ω with artificial boundary conditions set on the arbitrarily shaped boundary of Ω. These conditions present the features of being differential in space and nonlocal in time since their definition involves some time fractional operators. After having proved the well-posedness of the continuous truncated initial boundary value problem, a semi-discrete Crank-Nicolson-type scheme for the bounded problem is introduced and its stability is provided. Next, the full discretization is realized by way of a standard finite-element method to preserve the stability of the scheme. Some numerical simulations are given to illustrate the effectiveness and flexibility of the method.

Abstract. We consider non-absorbing inhomogeneous media represented by some refraction index. We have developed a method to reconstruct, from far-field measurements, the shape of the areas where the actual index differs from a reference index. Following the principle of the Factorization Method, we present a fast reconstruction algorithm relying on far field measurements and near field values, easily computed from the reference index. Our reconstruction result is illustrated by several numerical test cases.

Abstract-Aim of this paper is to present an efficient scheme of domain decomposition to study, in the time domain, multiple scattering by separated obstacles and sources with any composition and geometry, in an homogeneous media. A method of decomposition into disjointed sub-domains is proposed, resting onto an homogeneous and adaptable approximation of coupling terms and leading to a natural parallelized and hybrid numerical schema. It permits to significantly lower the cumulative error of dissipation and/or dispersion introduced by classical scheme. It also leads to a suitable answer for a wide class of problems involving large scattering scenes limiting for classical time domain methods. Numerical examples are given to illustrate it. 42Mouysset, Mazet, and Borderies

A bi-static short-range elastic backscatter micro-lidar, named Colibri, has been developed for quantitative aerosol profiling with high range and temporal resolution within the first hundred meters. The geometric (i.e., overlap) and radiometric (i.e., lidar constant) calibrations were performed along with dark current and background noise characterizations. Results of a measurement campaign have demonstrated the capability of our system to characterize aerosol plumes with high range-resolution (<10 cm) in the short-range close to their emission sources (from 10 m). To this aim, fog-oil aerosol plumes were generated in a tunnel and characterized by using an optical particle counter. A forward inverse method without boundary conditions is presented for inverting short-range lidar profiles when no reference molecular zone is available. Lastly, we report the different retrieved lidar products, namely the distribution of aerosol layers, radiative properties (i.e., backscatter profiles), and the microphysical properties (i.e., number concentration profiles). For the validation of the proposed methodology, the lidar products were compared with measurements from the optical particle counter. Lastly, the impact of calibration errors on the lidar products is discussed through an uncertainty analysis.