Wenbin Chen

Wenbin Chen, Max Gunzburger, Dong Sun et al.

We propose and study two second-order in time implicit-explicit (IMEX) methods for the coupled Stokes-Darcy system that governs flows in karst aquifers. The first is a combination of a second-order backward differentiation formula and the second-order Gear's extrapolation approach. The second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algorithms only require the solution of two decoupled problems at each time step, one Stokes and the other Darcy. Hence, these schemes are very efficient and can be easily implemented using legacy codes. We establish the unconditional and uniform in time stability for both schemes. The uniform in time stability leads to uniform in time control of the error which is highly desirable for modeling physical processes, e.g., contaminant sequestration and release, that occur over very long time scales. Error estimates for fully-discretized schemes using finite element spatial discretizations are derived. Numerical examples are provided that illustrate the accuracy, efficiency, and long-time stability of the two schemes.

Wenbin Chen, Wenqiang Feng, Yuan Liu et al.

We present a second-order-in-time finite difference scheme for the Cahn-Hilliard-Hele-Shaw equations. This numerical method is uniquely solvable and unconditionally energy stable. At each time step, this scheme leads to a system of nonlinear equations that can be efficiently solved by a nonlinear multigrid solver. Owing to the energy stability, we derive an $\ell^2 (0,T; H_h^3)$ stability of the numerical scheme. To overcome the difficulty associated with the convection term $\nabla \cdot (ϕ\boldsymbol{u})$, we perform an $\ell^\infty (0,T; H_h^1)$ error estimate instead of the classical $\ell^\infty (0,T; \ell^2)$ one to obtain the optimal rate convergence analysis. In addition, various numerical simulations are carried out, which demonstrate the accuracy and efficiency of the proposed numerical scheme.

Wenbin Chen, Fang Wang, Yanqiu Wang

A family of weak Galerkin finite element discretization is developed for solving the coupled Darcy-Stokes equation. The equation in consideration admits the Beaver-Joseph-Saffman condition on the interface. By using the weak Galerkin approach, in the discrete space we are able to impose the normal continuity of velocity explicitly. Or in other words, strong coupling is achieved in the discrete space. Different choices of weak Galerkin finite element spaces are discussed, and error estimates are given.

Wenbin Chen, Yanqiu Wang

We construct H(curl) and H(div) conforming finite elements on convex polygons and polyhedra with minimal possible degrees of freedom, i.e., the number of degrees of freedom is equal to the number of edges or faces of the polygon/polyhedron. The construction is based on generalized barycentric coordinates and the Whitney forms. In 3D, it currently requires the faces of the polyhedron be either triangles or parallelograms. Formula for computing basis functions are given. The finite elements satisfy discrete de Rham sequences in analogy to the well-known ones on simplices. Moreover, they reproduce existing H(curl)-H(div) elements on simplices, parallelograms, parallelepipeds, pyramids and triangular prisms. Approximation property of the constructed elements is also analyzed, by showing that the lowest-order simplicial Nedelec- Raviart-Thomas elements are subsets of the constructed elements on arbitrary polygons and certain polyhedra.

Wenbin Chen, Xuejun Xu, Shangyou Zhang

In this work, we solve a long-standing open problem: Is it true that the convergence rate of the Lions' Robin-Robin nonoverlapping domain decomposition(DD) method can be constant, independent of the mesh size $h$? We closed this twenty-year old problem with a positive answer. Our theory is also verified by numerical tests.

Wenbin Chen, Daozhi Han, Xiaoming Wang

We propose and analyze two novel decoupled numerical schemes for solving the Cahn-Hilliard-Stokes-Darcy (CHSD) model for two-phase flows in karstic geometry. In the first numerical scheme, we explore a fractional step method (operator splitting) to decouple the phase-field (Cahn-Hilliard equation) from the velocity field (Stokes-Darcy fluid equations). To further decouple the Stokes-Darcy system, we introduce a first order pressure stabilization term in the Darcy solver in the second numerical scheme so that the Stokes system is decoupled from the Darcy system and hence the CHSD system can be solved in a fully decoupled manner. We show that both decoupled numerical schemes are uniquely solvable, energy stable, and mass conservative. Ample numerical results are presented to demonstrate the accuracy and efficiency of our schemes.

Wenbin Chen, Cheng Wang, Xiaoming Wang et al.

We present and analyze finite difference numerical schemes for the Allen Cahn/Cahn-Hilliard equation with a logarithmic Flory Huggins energy potential. Both the first order and second order accurate temporal algorithms are considered. In the first order scheme, we treat the nonlinear logarithmic terms and the surface diffusion term implicitly, and update the linear expansive term and the mobility explicitly. We provide a theoretical justification that, this numerical algorithm has a unique solution such that the positivity is always preserved for the logarithmic arguments. In particular, our analysis reveals a subtle fact: the singular nature of the logarithmic term around the values of $-1$ and 1 prevents the numerical solution reaching these singular values, so that the numerical scheme is always well-defined as long as the numerical solution stays similarly bounded at the previous time step. Furthermore, an unconditional energy stability of the numerical scheme is derived, without any restriction for the time step size. The unique solvability and the positivity-preserving property for the second order scheme are proved using similar ideas, in which the singular nature of the logarithmic term plays an essential role. For both the first and second order accurate schemes, we are able to derive an optimal rate convergence analysis, which gives the full order error estimate. The case with a non-constant mobility is analyzed as well. We also describe a practical and efficient multigrid solver for the proposed numerical schemes, and present some numerical results, which demonstrate the robustness of the numerical schemes.

Chen Zhang, Heyan Zhu, Wenbin Chen

The ground state of Bose--Einstein condensates can be described as the minimizer of the Gross--Pitaevskii energy functional subject to a mass conservation constraint. In this paper, we study the corresponding discrete optimization problem in nonconforming finite element spaces and establish a priori error estimates for the discrete ground state energy, the discrete eigenvalue, and the discrete ground state. Specifically, we derive explicit convergence rates for the a priori error in the particular case of the $EQ_1^{\mathrm{rot}}$ finite element. Furthermore, we proof that within the $EQ_1^{\mathrm{rot}}$ finite element framework, the discrete ground state energy provides a lower bound estimation to the exact energy. Finally, numerical experiments are presented to validate the theoretical analysis.

Wenkang Li, Qi Ke, Wenbin Chen et al.

Visible-infrared cross-modality person re-identification (VI-ReID), whose aim is to match person images between visible and infrared modality, is a challenging cross-modality image retrieval task. Most existing works integrate batch normalization layers into their neural network, but we found out that batch normalization layers would lead to two types of distribution gap: 1) inter-mini-batch distribution gap -- the distribution gap of the same modality between each mini-batch; 2) intra-mini-batch modality distribution gap -- the distribution gap of different modality within the same mini-batch. To address these problems, we propose a new batch normalization layer called Modality Batch Normalization (MBN), which normalizes each modality sub-mini-batch respectively instead of the whole mini-batch, and can reduce these distribution gap significantly. Extensive experiments show that our MBN is able to boost the performance of VI-ReID models, even with different datasets, backbones and losses.

Wenkang Li, Ke Qi, Wenbin Chen et al.

Visible-Infrared cross-modality person re-identification (VI-ReID), whose aim is to match person images between visible and infrared modality, is a challenging cross-modality image retrieval task. Batch Hard Triplet loss is widely used in person re-identification tasks, but it does not perform well in the Visible-Infrared person re-identification task. Because it only optimizes the hardest triplet for each anchor image within the mini-batch, samples in the hardest triplet may all belong to the same modality, which will lead to the imbalance problem of modality optimization. To address this problem, we adopt the batch all triplet selection strategy, which selects all the possible triplets among samples to optimize instead of the hardest triplet. Furthermore, we introduce Unified Batch All Triplet loss and Cosine Softmax loss to collaboratively optimize the cosine distance between image vectors. Similarly, we rewrite the Hetero Center Triplet loss, which is proposed for VI-ReID task, into a batch all form to improve model performance. Extensive experiments indicate the effectiveness of the proposed methods, which outperform state-of-the-art methods by a wide margin.

Pablo Navarrete Michelini, Wenbin Chen, Hanwen Liu et al.

Multi-Grid Back-Projection (MGBP) is a fully-convolutional network architecture that can learn to restore images and videos with upscaling artifacts. Using the same strategy of multi-grid partial differential equation (PDE) solvers this multiscale architecture scales computational complexity efficiently with increasing output resolutions. The basic processing block is inspired in the iterative back-projection (IBP) algorithm and constitutes a type of cross-scale residual block with feedback from low resolution references. The architecture performs in par with state-of-the-arts alternatives for regression targets that aim to recover an exact copy of a high resolution image or video from which only a downscale image is known. A perceptual quality target aims to create more realistic outputs by introducing artificial changes that can be different from a high resolution original content as long as they are consistent with the low resolution input. For this target we propose a strategy using noise inputs in different resolution scales to control the amount of artificial details generated in the output. The noise input controls the amount of innovation that the network uses to create artificial realistic details. The effectiveness of this strategy is shown in benchmarks and it is explained as a particular strategy to traverse the perception-distortion plane.

Pablo Navarrete Michelini, Wenbin Chen, Hanwen Liu et al.

Here, we describe our solution for the AIM-2019 Extreme Super-Resolution Challenge, where we won the 1st place in terms of perceptual quality (MOS) similar to the ground truth and achieved the 5th place in terms of high-fidelity (PSNR). To tackle this challenge, we introduce the second generation of MultiGrid BackProjection networks (MGBPv2) whose major modifications make the system scalable and more general than its predecessor. It combines the scalability of the multigrid algorithm and the performance of iterative backprojections. In its original form, MGBP is limited to a small number of parameters due to a strongly recursive structure. In MGBPv2, we make full use of the multigrid recursion from the beginning of the network; we allow different parameters in every module of the network; we simplify the main modules; and finally, we allow adjustments of the number of network features based on the scale of operation. For inference tasks, we introduce an overlapping patch approach to further allow processing of very large images (e.g. 8K). Our training strategies make use of a multiscale loss, combining distortion and/or perception losses on the output as well as downscaled output images. The final system can balance between high quality and high performance.

Wenbin Chen, Zhenhua Chen, Jin Cheng et al.

This paper concerns new continuum phenomenological model for epitaxial thin film growth with three different forms of the Ehrlich-Schwoebel current. Two of these forms were first proposed by Politi and Villain [1996] and then studied by Evans, Thiel and Bartelt [2006]. The other one is completely new. Following the techniques used in Li and Liu [2003], we present rigorous analysis of the well-posedness, regularity and time stability for the new model. We also studied both the global and the local behavior of the surface roughness in the growth process. The new model differs from other known models in that it features a linear convex part and a nonlinear concave part, and thus by using a convex-concave time splitting scheme, one can naturally build unconditionally stable semi-implicit numerical discretizations with linear implicit parts, which is much easier to implement than conventional models requiring nonlinear implicit parts. Despite this fundamental difference in the model, numerical experiments show that the nonlinear morphological instability of the new model agrees well with results of other models published in Li and Liu [2003], which indicates that the new model correctly captures the essential morphological states in the thin film growth process.