arXiv subjects

Tiantian Huang

Publications and source records attributed to Tiantian Huang.

3 recordsLinked to original sources

arXiv2026

Weighted $H^2$ regularity of fluid-structure interaction when the interface intersects the boundary

This paper analyzes the regularity of solutions to a fluid-structure interaction (FSI) problem involving a Stokesian fluid and a linear elastic solid in a two-dimensional polygonal domain, seperated by an interface which intersects the boundary of the domain. The main challenges arise from the limited solution regularity caused by geometric singularities at the domain corners. To address this, we introduce tailored weighted Sobolev spaces, denoted by $\mathbf{H}^{k,l}_{\boldsymbolβ}$, and a novel solution operator framework on these spaces. This framework provides the key insight for decoupling the coupled FSI system into tractable fluid and elastic solid subproblems in the regularity analysis. As our main result, we prove the existence and uniqueness of a solution in the weighted Sobolev space $\mathbf{H}^{2,2}_{\boldsymbolβ}$.

math.AP↗

arXiv2026

A convergent finite element method with minimal deformation rate for mean curvature flow

We propose and analyze a fully discrete parametric finite element method with minimal deformation rate (MDR) for simulating the mean curvature flow of general closed surfaces in three dimensions. The method is formulated from a coupled system that enforces the mean curvature flow law for the normal velocity while introducing an artificial tangential velocity that minimizes the deformation-rate energy, thereby preserving mesh quality without requiring remeshing or reparametrization. An $L^{2}$-projected averaged normal vector is used in the scheme to facilitate a rigorous convergence analysis. Within the projected--distance framework, we establish the first complete convergence proof for a parametric finite element method that incorporates the MDR tangential motion without relying on evolution equations for the mean curvature or the normal vector, achieving optimal-order error estimates for finite elements of degree $k \ge 3$. Numerical experiments corroborate the theoretical results and demonstrate that the proposed MDR method maintains mesh quality comparable to the Barrett--Garcke--Nürnberg method, for which convergence has not yet been established.

math.NA↗

arXiv2020

Residual-CycleGAN based Camera Adaptation for Robust Diabetic Retinopathy Screening

There are extensive researches focusing on automated diabetic reti-nopathy (DR) detection from fundus images. However, the accuracy drop is ob-served when applying these models in real-world DR screening, where the fun-dus camera brands are different from the ones used to capture the training im-ages. How can we train a classification model on labeled fundus images ac-quired from only one camera brand, yet still achieves good performance on im-ages taken by other brands of cameras? In this paper, we quantitatively verify the impact of fundus camera brands related domain shift on the performance of DR classification models, from an experimental perspective. Further, we pro-pose camera-oriented residual-CycleGAN to mitigate the camera brand differ-ence by domain adaptation and achieve increased classification performance on target camera images. Extensive ablation experiments on both the EyePACS da-taset and a private dataset show that the camera brand difference can signifi-cantly impact the classification performance and prove that our proposed meth-od can effectively improve the model performance on the target domain. We have inferred and labeled the camera brand for each image in the EyePACS da-taset and will publicize the camera brand labels for further research on domain adaptation.

eess.IV↗