arXiv subjects

Shenwen Yu

Publications and source records attributed to Shenwen Yu.

4 recordsLinked to original sources

arXiv2026

Reconstruction methods for inverse scattering problems with phaseless data

We investigate phaseless inverse scattering problem for the Schr\"odinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total field and the far-field scattered field. For phaseless total-field data, we extend the IBS framework and analyze its radius of convergence. In the far-field setting, we propose a Fourier-based reconstruction method that exploits the scattering reciprocity between incident and observation directions to recover Fourier coefficients of the scattering potential. For phaseless scattered-field data, we employ a polarization-based approach to recover phase information and enable IBS reconstruction. Numerical experiments are conducted to validate the proposed methods.

math-ph↗

arXiv2026

Inverse Scattering for Dirac Equations Arising in Waveguide Arrays

We investigate inverse scattering problems for Dirac equations that arise as continuum models of waveguide arrays. We first establish the well-posedness of the forward models. For the associated inverse problems, we develop the inverse Born series and the reduced inverse Born series, providing analysis of convergence and rigorous error estimates. Numerical experiments are presented to validate the proposed algorithms and demonstrate their effectiveness.

math.NA↗

arXiv2025

Optimal-Transport Stability of Inverse Point-Source Problems for Elliptic and Parabolic Equations

We establish quantitative global stability estimates, formulated in terms of optimal transport (OT) cost, for inverse point-source problems governed by elliptic and parabolic equations with spatially varying coefficients. The key idea is that the Kantorovich dual potential can be represented as a boundary functional of suitable adjoint solutions, thereby linking OT geometry with boundary observations. In the elliptic case, we construct complex geometric optics solutions that enforce prescribed pointwise constraints, whereas in the parabolic case we employ controllable adjoint solutions that transfer interior information to the boundary. Under mild regularity and separation assumptions, we obtain estimates of the form \[ \mathcal{T}_c(\mu,\nu) \le C\,\|u_1 - u_2\|_{L^2(\partial\Omega)} \quad \text{and} \quad \mathcal{T}_c(\mu,\nu) \le C\,\|u_1 - u_2\|_{L^2(\partial\Omega\times[0,T])}, \] where $\mu$ and $\nu$ are admissible point-source measures. These results provide a unified analytical framework connecting inverse source problems and optimal transport, and establish OT-based stability theory for inverse source problems governed by partial differential equations with spatially varying coefficients.

math.NA↗

arXiv2023

Traceability of Water Pollution: An Inversion Scheme Via Dynamic Complex Geometrical Optics Solutions

We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex geometrical optics (CGO) solutions, a variational formulation of the inverse source problem is analyzed, leading to a proof of uniqueness result. Our proposed two-step reconstruction algorithm first determines the point source locations and subsequently reconstructs the Fourier components of the emission concentration functions. Numerical experiments on simulated data are conducted. The results demonstrate that the proposed two-step reconstruction algorithm can reliably reconstruct multiple point sources and accurately reconstruct the emission concentration functions. Additionally, by partitioning the algorithm into online and offline computations, and concentrating computational demand offline, real-time pollutant traceability becomes feasible. This method, applicable in various fields - especially those related to water pollution, can identify the source of a contaminant in the environment, thus serving as a valuable tool in environmental protection.

math.NA↗