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A two-dimensional GeSe/SnSe heterostructure for high performance thin-film solar cells

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Journal of Materials Chemistry A 2019年第18期7卷 11265-11271页

作者： Yuliang Mao Congsheng Xu Jianmei Yuan Hongquan Zhao Hunan Key Laboratory for Micro-Nano Energy Materials and Devices School of Physics and Optoelectronics Xiangtan University Hunan 411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan 411105 China Chongqing Institute of Green and Intelligent Technology Chinese Academy of Sciences Chongqing 401120 China

Based on the first-principles calculations, we demonstrated that a GeSe/SnSe heterostructure has type-II band alignment and a direct band gap, which can effectively prevent the recombination of photogenerated electron–hole pairs. Moreover, the GeSe/SnSe heterostructure also exhibits strong optical absorption intensity, which can reach the order of 10⁵ cm⁻¹. Our predicted photoelectric conversion efficiency (PCE) for the GeSe/SnSe heterostructure reaches 21.47%. We also found that the hole carrier mobility of the GeSe/SnSe heterostructure along the x direction has been significantly improved to 6.42 × 10⁴ cm² V⁻¹ s⁻¹, which is higher than that of black phosphorus (1 × 10⁴ cm² V⁻¹ s⁻¹). By applying a vertical external electric field, we found that the band gap and band offset of the GeSe/SnSe heterojunction can be effectively tuned. The revealed type-II band alignment, strong optical absorption, superior PCE and superior hole carrier mobility of the GeSe/SnSe heterostructure imply that this new proposed material has broad application prospects in solar cells.

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A PRIORI AND A POSTERIORI ERROR ESTIMATES OF A REALLY PRESSURE-ROBUST VIRTUAL ELEMENT METHOD FOR THE INCOMPRESSIBLE BRINKMAN PROBLEM

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arXiv 2024年

作者： Xiong, Yu Chen, Yanping School of Science Nanjing University of Posts and Telecommunications Nanjing210023 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

This paper presents both a priori and a posteriori error analyses for a really pressure-robust virtual element method to approximate the incompressible Brinkman problem. We construct a divergence-preserving reconstruction operator using the Raviart–Thomas element for the discretization on the right-hand side. The optimal priori error estimates are carried out, which imply the velocity error in the energy norm is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method’s ability to handle more general polygonal meshes, we implement effective mesh refinement strategies and develop a residual-type a posteriori error estimator. This estimator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method. Copyright © 2024, The Authors. All rights reserved.

关键词： Mesh generation

The grad-div conforming virtual element method for the quad-div problem in three dimensions

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arXiv 2024年

作者： Dong, Xiaojing Han, Yibing Huang, Yunqing Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Er huan Road Hunan Xiangtan411105 China

We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the H(grad-div)-conforming virtual element method of arbitrary approximation orders on polyhedral meshes. Three families of H(grad-div)conforming virtual elements are constructed based on the structure of a de Rham sub-complex with enhanced smoothness, resulting in an exact discrete virtual element complex. In the lowest-order case, the simplest element has only one degree of freedom at each vertex and face, respectively. We rigorously prove the interpolation error estimates, the stability of discrete bilinear forms, the well-posedness of discrete formulation and the optimal error estimates. Some numerical examples are shown to verify the theoretical results. © 2024, CC BY-NC-ND.

关键词： Mesh generation

Low-rank generalized alternating direction implicit iteration method for solving matrix equations

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arXiv 2024年

作者： Zhang, Juan Xun, Wenlu Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China

This paper presents an effective low-rank generalized alternating direction implicit iteration (R-GADI) method for solving large-scale sparse and stable Lyapunov matrix equations and continuous-time algebraic Riccati matrix equations. The method is based on generalized alternating direction implicit iteration (GADI), which exploits the low-rank property of matrices and utilizes the Cholesky factorization approach for solving. The advantage of the new algorithm lies in its direct and efficient low-rank formulation, which is a variant of the Cholesky decomposition in the Lyapunov GADI method, saving storage space and making it computationally effective. When solving the continuous-time algebraic Riccati matrix equation, the Riccati equation is first simplified to a Lyapunov equation using the Newton method, and then the R-GADI method is employed for computation. Additionally, we analyze the convergence of the R-GADI method and prove its consistency with the convergence of the GADI method. Finally, the effectiveness of the new algorithm is demonstrated through corresponding numerical experiments. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

Diffeomorphic image registration with an optimal control relaxation and its implementation

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arXiv 2021年

作者： Zhang, Jianping Li, Yanyan School of Mathematics and Computational Science Hunan National Center for Applied Mathematics Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Image registration has played an important role in image processing problems, especially in medical imaging applications. It is well known that when the deformation is large, many variational models cannot ensure diffeomorphism. In this paper, we propose a new registration model based on an optimal control relaxation constraint for large deformation images, which can theoretically guarantee that the registration mapping is diffeomorphic. We present an analysis of optimal control relaxation for indirectly seeking the diffeomorphic transformation of Jacobian determinant equation and its registration applications, including the construction of diffeomorphic transformation as a special space. We also provide an existence result for the control increment optimization problem in the proposed diffeomorphic image registration model with an optimal control relaxation. Furthermore, a fast iterative scheme based on the augmented Lagrangian multipliers method (ALMM) is analyzed to solve the control increment optimization problem, and a convergence analysis is followed. Finally, a grid unfolding indicator is given, and a robust solving algorithm for using the deformation correction and backtrack strategy is proposed to guarantee that the solution is diffeomorphic. Numerical experiments show that the registration model we proposed can not only get a diffeomorphic mapping when the deformation is large, but also achieves the state-of-the-art performance in quantitative evaluations in comparing with other classical models. Copyright © 2021, The Authors. All rights reserved.

关键词： Dynamical systems

A general alternating direction implicit iteration method for solving complex symmetric linear systems

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arXiv 2024年

作者： Zhang, Juan Xun, Wenlu Key Laboratory of Intelligent Computing and Information Processing Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China

We have introduced the generalized alternating direction implicit iteration (GADI) method for solving large sparse complex symmetric linear systems and proved its convergence properties. Additionally, some numerical results have demonstrated the effectiveness of this algorithm. Furthermore, as an application of the GADI method in solving complex symmetric linear systems, we utilized the flattening operator and Kronecker product properties to solve Lyapunov and Riccati equations with complex coefficients using the GADI method. In solving the Riccati equation, we combined inner and outer iterations, first simplifying the Riccati equation into a Lyapunov equation using the Newton method, and then applying the GADI method for solution. Finally, we provided convergence analysis of the method and corresponding numerical results. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

Low-rank alternating direction doubling algorithm for solving large-scale continuous time algebraic Riccati equations

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arXiv 2024年

This paper proposes an effective low-rank alternating direction doubling algorithm (R-ADDA) for computing numerical low-rank solutions to large-scale sparse continuous-time algebraic Riccati matrix equations. The method is based on the alternating direction doubling algorithm (ADDA), utilizing the low-rank property of matrices and employing Cholesky factorization for solving. The advantage of the new algorithm lies in computing only the 2k-th approximation during the iterative process, instead of every approximation. Its efficient low-rank formula saves storage space and is highly effective from a computational perspective. Finally, the effectiveness of the new algorithm is demonstrated through theoretical analysis and numerical experiments. Copyright © 2024, The Authors. All rights reserved.

关键词： Matrix algebra

Optimization methods for solving matrix equations

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arXiv 2024年

作者： Zhang, Juan Luo, Xiao Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China

In this paper, we focus on using optimization methods to solve matrix equations by transforming the problem of solving the Sylvester matrix equation or continuous algebraic Riccati equation into an optimization problem. Initially, we use a constrained convex optimization method (CCOM) to solve the Sylvester matrix equation with 2,1-norm, where we provide a convergence analysis and numerical examples of CCOM;however, the results show that the algorithm is not efficient. To address this issue, we employ classical quasi-Newton methods such as DFP and BFGS algorithms to solve the Sylvester matrix equation and present the convergence and numerical results of the algorithm. Additionally, we compare these algorithms with the CG algorithm and AR algorithm, and our results demonstrate that the presented algorithms are effective. Furthermore, we propose a unified framework of the alternating direction multiplier method (ADMM) for directly solving the continuous algebraic Riccati equation (CARE), and we provide the convergence and numerical results of ADMM. Our experimental results indicate that ADMM is an effective optimization algorithm for solving CARE. Finally, to improve the effectiveness of the optimization method for solving Riccati equation, we propose the Newton-ADMM algorithm framework, where the outer iteration of this method is the classical Newton method, and the inner iteration involves using ADMM to solve Lyapunov matrix equations inexactly. We also provide the convergence and numerical results of this algorithm, which our results demonstrate are more efficient than ADMM for solving CARE. Copyright © 2024, The Authors. All rights reserved.

关键词： Newton-Raphson method

Efficient numerical methods for computing the stationary states of phase field crystal models

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arXiv 2020年

作者： Jiang, Kai Si, Wei Chen, Chang Bao, Chenglong School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan Hunan411105 China Yau Mathematical Sciences Center Tsinghua University Beijing100084 China

Finding the stationary states of a free energy functional is an important problem in phase field crystal (PFC) models. Many efforts have been devoted for designing numerical schemes with energy dissipation and mass conservation properties. However, most existing approaches are time-consuming due to the requirement of small effective time steps. In this paper, we discretize the energy functional and propose efficient numerical algorithms for solving the constrained non-convex minimization problem. A class of first order approaches, which is the so-called adaptive accelerated Bregman proximal gradient (AA-BPG) methods, is proposed and the convergence property is established without the global Lipschitz constant requirements. Moreover, we design a hybrid approach that applies an inexact Newton method to further accelerate the local convergence. One key feature of our algorithm is that the energy dissipation and mass conservation properties hold during the iteration process. Extensive numerical experiments, including two three dimensional periodic crystals in Landau-Brazovskii (LB) model and a two dimensional quasicrystal in Lifshitz-Petrich (LP) model, demonstrate that our approaches have adaptive time steps which lead to a significant acceleration over many existing methods when computing complex structures. Copyright © 2020, The Authors. All rights reserved.

关键词： Quasicrystals