arXiv subjects

Xiaopeng Zhu

Publications and source records attributed to Xiaopeng Zhu.

4 recordsLinked to original sources

arXiv2026

The direct-line method for forward and inverse linear elasticity problems of composite materials in general domains with multiple singularities

In this work, a combined strategy of domain decomposition and the direct-line method is implemented to solve the forward and inverse linear elasticity problems of composite materials in general domains with multiple singularities. Domain decomposition technology treats the general domain as the union of some star-shaped subdomains, which can be handled using the direct-line method. The direct-line method demonstrates rapid convergence of the semi-discrete eigenvalues towards the exact eigenvalues of the elliptic operator, thereby naturally capturing the singularities. We also establish optimal error estimates for the proposed method. Especially, our method can handle multiple singular point problems in general regions, which are difficult to deal with by most methods. On the other hand, the inverse elasticity problem is constructed as a energy functional minimization problem with total variational regularization, we use the aforementioned method as a forward solver to reconstruct the lamé coefficient of multiple singular points in general regions. Our method can simultaneously deduce heterogeneous $μ$ and $λ$ between different materials. Through numerical experiments on three forward and inverse problems, we systematically verified the accuracy and reliability of this method to solve forward and inverse elastic problems in general domains with multiple singularities.

math.NA↗

arXiv2025

Heterogeneous and anisotropic elastic parameter estimation using a novel semi-analytical forward solver

An efficient procedure using a novel semi-analytical forward solver for identifying heterogeneous and anisotropic elastic parameters from only one full-field measurement is proposed and explored. We formulate the inverse problem as an special energy functional minimization with total variation(TV) regularization. The minimization problem is solved by Adam algorithm, which only requires solving one forward problem and no adjoint problem in each iteration. In order to deal with the irregularity of the elastic regions, the anisotropy and heterogeneity of parameters and potential singularities in forward-modeled issues, a novel semi-analytical forward solver named the direct method of lines is proposed, which discretizes angular variable while preserving analytical solutions along remaining coordinates. To validate the efficacy of our procedure, a series of numerical experiments are implemented subsequently, achieving reliable performance in both forward modeling and the six elastic arguments reconstruction scenarios.

math.NA↗

arXiv2024

Effectiveness Assessment of Recent Large Vision-Language Models

The advent of large vision-language models (LVLMs) represents a remarkable advance in the quest for artificial general intelligence. However, the model's effectiveness in both specialized and general tasks warrants further investigation. This paper endeavors to evaluate the competency of popular LVLMs in specialized and general tasks, respectively, aiming to offer a comprehensive understanding of these novel models. To gauge their effectiveness in specialized tasks, we employ six challenging tasks in three different application scenarios: natural, healthcare, and industrial. These six tasks include salient/camouflaged/transparent object detection, as well as polyp detection, skin lesion detection, and industrial anomaly detection. We examine the performance of three recent open-source LVLMs, including MiniGPT-v2, LLaVA-1.5, and Shikra, on both visual recognition and localization in these tasks. Moreover, we conduct empirical investigations utilizing the aforementioned LVLMs together with GPT-4V, assessing their multi-modal understanding capabilities in general tasks including object counting, absurd question answering, affordance reasoning, attribute recognition, and spatial relation reasoning. Our investigations reveal that these LVLMs demonstrate limited proficiency not only in specialized tasks but also in general tasks. We delve deep into this inadequacy and uncover several potential factors, including limited cognition in specialized tasks, object hallucination, text-to-image interference, and decreased robustness in complex problems. We hope that this study can provide useful insights for the future development of LVLMs, helping researchers improve LVLMs for both general and specialized applications.

cs.CV↗

arXiv2023

Helmholtz decomposition based windowed Green function methods for elastic scattering problems on a half-space

This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz decomposition is applied to separate the pressure and shear waves, which satisfy the Helmholtz and Helmholtz/Maxwell equations, respectively, and the corresponding boundary integral equations of type $(\mathbb{I}+\mathbb{T})\bsϕ=\bs f$, that couple these two waves on the unbounded surface, are derived based on the free-space fundamental solution of Helmholtz equation. This approach avoids the treatment of the complex elastic displacement tensor and traction operator that involved in the classical integral equation method for elastic problems. Then a smooth ``slow-rise'' windowing function is introduced to truncate the boundary integral equations and a ``correction'' strategy is proposed to ensure the uniformly fast convergence for all incident angles of plane incidence. Numerical experiments for both two and three dimensional problems are presented to demonstrate the accuracy and efficiency of the proposed method.

physics.comp-ph↗