arXiv subjects

Huong T. T. Vu

Publications and source records attributed to Huong T. T. Vu.

2 recordsLinked to original sources

arXiv2024

A global approach for the inverse scattering problem using a Carleman contraction map

This paper addresses the inverse scattering problem in the domain Omega. The input data, measured outside Omega, involve the waves generated by the interaction of plane waves with various directions and unknown scatterers fully occluded inside Omega. The output of this problem is the spatially dielectric constant of these scatterers. Our approach to solving this problem consists of two primary stages. Initially, we eliminate the unknown dielectric constant from the governing equation, resulting in a system of partial differential equations. Subsequently, we develop the Carleman contraction mapping method to effectively tackle this system. It is noteworthy to highlight this method's robustness. It does not request a precise initial guess of the true solution, and its computational cost is not expensive. Some numerical examples are presented.

math.NA↗

arXiv2024

Determining initial conditions for nonlinear hyperbolic equations with time dimensional reduction and the Carleman contraction

This paper aims to determine the initial conditions for quasi-linear hyperbolic equations that include nonlocal elements. We suggest a method where we approximate the solution of the hyperbolic equation by truncating its Fourier series in the time domain with a polynomial-exponential basis. This truncation effectively removes the time variable, transforming the problem into a system of quasi-linear elliptic equations. We refer to this technique as the "time dimensional reduction method." To numerically solve this system comprehensively without the need for an accurate initial estimate, we used the newly developed Carleman contraction principle. We show the efficiency of our method through various numerical examples. The time dimensional reduction method stands out not only for its precise solutions but also for its remarkable speed in computation.

math.NA↗