arXiv subjects

Wenchao Zheng

Publications and source records attributed to Wenchao Zheng.

4 recordsLinked to original sources

arXiv2023

Uniform convergence of optimal order of a local discontinuous Galerkin method on a Shishkin mesh under a balanced norm

This article investigates a local discontinuous Galerkin (LDG) method for one-dimensional and two-dimensional singularly perturbed reaction-diffusion problems on a Shishkin mesh. During this process, due to the inability of the energy norm to fully capture the behavior of the boundary layers appearing in the solutions, a balanced norm is introduced. By designing novel numerical fluxes and constructing special interpolations, optimal convergences under the balanced norm are achieved in both 1D and 2D cases. Numerical experiments support the main theoretical conclusions.

math.NA↗

arXiv2023

Supercloseness of the LDG method for a two-dimensional singularly perturbed convection-diffusion problem on Bakhvalov-type mesh

In this paper, we focus on analyzing the supercloseness property of a two-dimensional singularly perturbed convection-diffusion problem with exponential boundary layers. The local discontinuous Galerkin (LDG) method with piecewise tensor-product polynomials of degree k is applied to Bakhvalov-type mesh. By developing special two-dimensional local Gauss-Radau projections and establishing a novel interpolation, supercloseness of an optimal order k+1 can be achieved on Bakhvalov-type mesh. It is crucial to highlight that this supercloseness result is independent of the singular perturbation parameter.

math.NA↗

arXiv2022

Uniform convergence of optimal order under a balanced norm of a local discontinuous Galerkin method on a Shishkin mesh

For singularly perturbed reaction-diffusion problems in 1D and 2D, we study a local discontinuous Galerkin (LDG) method on a Shishkin mesh. In these cases, the standard energy norm is too weak to capture adequately the behavior of the boundary layers that appear in the solutions. To deal with this deficiency, we introduce a balanced norm stronger than the energy norm. In order to achieve optimal convergence under the balanced norm in one-dimensional case, we design novel numerical fluxes and propose a special interpolation that consists of a Gauss-Radau projection and a local $L^2$ projection. Moreover, we generalize the numerical fluxes and interpolation, and extend convergence analysis of optimal order from 1D to 2D. Finally, numerical experiments are presented to confirm the theoretical results.

math.NA↗

arXiv2016

Object Boundary Guided Semantic Segmentation

Semantic segmentation is critical to image content understanding and object localization. Recent development in fully-convolutional neural network (FCN) has enabled accurate pixel-level labeling. One issue in previous works is that the FCN based method does not exploit the object boundary information to delineate segmentation details since the object boundary label is ignored in the network training. To tackle this problem, we introduce a double branch fully convolutional neural network, which separates the learning of the desirable semantic class labeling with mask-level object proposals guided by relabeled boundaries. This network, called object boundary guided FCN (OBG-FCN), is able to integrate the distinct properties of object shape and class features elegantly in a fully convolutional way with a designed masking architecture. We conduct experiments on the PASCAL VOC segmentation benchmark, and show that the end-to-end trainable OBG-FCN system offers great improvement in optimizing the target semantic segmentation quality.

cs.CV↗