相关论文: A robust inversion method for quantitative 3D shap…

The stability of annular electromagnetic pumps (EMPs) is investigated through 3D direct numerical simulations. When induction effects dominate dissipative processes, linear induction EMPs become unstable and lead to non-axisymmetric states…

We address the estimation of seismic wavefields by means of Multidimensional Deconvolution (MDD) for various redatuming applications. While offering more accuracy than conventional correlation-based redatuming methods, MDD faces challenges…

We have recently seen great progress in 3D scene reconstruction through explicit point-based 3D Gaussian Splatting (3DGS), notable for its high quality and fast rendering speed. However, reconstructing dynamic scenes such as complex human…

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

The reconstruction of electrical current densities from magnetic field measurements is an important technique with applications in materials science, circuit design, quality control, plasma physics, and biology. Analytic reconstruction…

To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…

Mathematical methods of step-by-step and combined shifts are proposed for experimental data processing to reconstruct the measuring system impulse response distorted by shift-invariant blur. Proposed methods base on direct non-blind…

In-line digital holography is a valuable tool for sizing, locating and tracking micro- or nano-objects in a volume. When a parametric imaging model is available, Inverse Problems approaches provide a straightforward estimate of the object…

Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…

Traditional 1D system thermal hydraulic analysis has been widely applied in nuclear industry for licensing purposes due to its numerical efficiency. However, such codes are inherently deficient for modeling of multiscale multidimensional…

We discuss a new approach to three-dimensional electrical impedance imaging based on a reduction of the information to be demanded from a reconstruction algorithm. Images are obtained from a single measurement by suitably simplifying the…

We introduce a method for high-quality 3D reconstruction from multi-view images. Our method uses a new point-based representation, the regularized dipole sum, which generalizes the winding number to allow for interpolation of per-point…

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…

We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…

The issue of justifying the eddy current approximation of Maxwell's equations is re-considered in the time-dependent setting. Convergence of the solution operators is shown in the sense of strong operator limits.

Working within the class of piecewise constant conductivities, the inverse problem of electrical impedance tomography can be recast as a shape optimization problem where the discontinuity interface is the unknown. Using Gr\"oger's…

We present a highly accurate numerical method based on a boundary integral formulation and the leaky dielectric model to study the dynamics of surfactant-covered drops in the presence of an applied electric field. The method can simulate…

We present the development of extended diffraction tomography, a new approach to the solution of the linear seismic waveform inversion problem. This method has several appealing features, such as the use of arbitrary depth-dependent…

We introduce a continuous (downscaling) data assimilation algorithm for the 2D B\'enard convection problem using vorticity or local circulation measurements only. In this algorithm, a nudging term is added to the vorticity equation to…

This paper puts forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model. These models, which…