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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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Error analysis of SAV finite element method to phase field crystal model

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arXiv 2019年

作者： Wang, Liupeng Huang, Yunqing Jiang, Kai School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan Hunan411105 China Key Laboratory of Ministry of Education for Intelligent Computing and Information Processing Xiangtan University Xiangtan Hunan411105 China

In this paper, we construct and analyze an energy stable scheme by combining the latest developed scalar auxiliary variable (SAV) approach and linear finite element method (FEM) for phase field crystal (PFC) model, and show rigorously that the scheme is first-order in time and second-order in space for the L2and H1 gradient ow equations. To reduce eficiently computational cost and capture accurately the phase interface, we give a simple adaptive strategy, equipped with a posteriori gradient estimator, i.e. L2norm of the recovered gradient. Extensive numerical experiments are presented to verify our theoretical results and to demonstrate the efiectiveness and accuracy of our proposed method. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Error Estimates for the Iterative Discontinuous Galerkin Method to the Nonlinear Poisson-Boltzmann Equation

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Communications in computational Physics 2018年第1期23卷 168-197页

作者： Peimeng Yin Yunqing Huang Hailiang Liu Mathematics Department Iowa State UniversityAmesIA 50011USA Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and EngineeringSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan411105P.R.China

This paper is devoted to the error estimate for the iterative discontinuous Galerkin(IDG)method introduced in[***,*** and ***.16:491-515,2014]to the nonlinear Poisson-Boltzmann *** total error includes both the iteration error and the discretization error of the direct DG method to linear elliptic *** the DDG method,the energy error is obtained by a constructive approach through an explicit global projection satisfying interface conditions dictated by the choice of numerical *** L^(2) error of order O(h^(m+1))for polynomials of degree m is further *** bounding constant is also shown to be independent of the iteration *** tests are given to validate the established convergence theory.

关键词： Poisson-Boltzmann equation DG methods global projection energy error estimates L^(2)error estimates

Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations

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Advances in Applied Mathematics and Mechanics 2018年第6期10卷 1440-1458页

作者： Xingfa Yang Yin Yang Yanping Chen Jie Liu State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body Hunan UniversityChangsha 410082HunanChina Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing&Information Processing of Ministry of EducationSchool of Mathematics and Computational ScienceXiangtan UniversityXiangtan 411105HunanChina School of Mathematical Sciences South China Normal UniversityGuangzhou 510631GuangdongChina Center for Research on Leading Technology of Special Equipment School of Mechanical and Electric EngineeringGuangzhou UniversityGuangzhou 510006GuangdongChina

In this paper,we study a class of nonlinear fractional integro-differential equations,the fractional derivative is described in the Caputo *** the properties of the Caputo derivative,we convert the fractional integro-differential equations into equivalent integral-differential equations of Volterra type with singular kernel,then we propose and analyze a spectral Jacobi-collocation approximation for nonlinear integro-differential equations of Volterra *** provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximate fractional derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-norm.

关键词： Spectral method nonlinear fractional derivative Volterra integro-differential equations Caputo derivative

Mesh Quality and More Detailed Error Estimates of Finite Element Method

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高等学校计算数学学报（英文版） 2017年第2期10卷 420-436页

作者： Yunqing Huang Liupeng Wang Nianyu Yi Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan 411105 China

In this paper,we study the role of mesh quality on the accuracy of linear finite element *** derive a more detailed error estimate,which shows explicitly how the shape and size of elements,and symmetry structure of mesh effect on the error of numerical *** computable parameters Ge and Gv are given to depict the cell geometry property and symmetry structure of the *** compare with the standard a priori error estimates,which only yield information on the asymptotic error behaviour in a global sense,our proposed error estimate considers the effect of local element geometry properties,and is thus more *** certain conditions,the traditional error estimates and supercovergence results can be derived from the proposed error ***,the estimators Ge and Gv are computable and thus can be used for predicting the variation of *** tests are presented to illustrate the performance of the proposed parameters Ge and Gv.

关键词： Finite element methods error estimation cell geometry mesh quality

SATURATION AND RELIABLE HIERARCHICAL A POSTERIORI MORLEY FINITE ELEMENT ERROR CONTROL

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Journal of computational Mathematics 2018年第6期36卷 833-844页

作者： Carsten Carstensen Dietmar Gallistl Yunqing Huang Humboldt-Universitat zu Berlin Institut fiir Mathematik Unter den Linden 6 10099 Berlin Germany Department of Applied Mathematics University of Twente P.O. Box 217 7500 AE Enschede Institute for Computational and Applied Mathematics and Hunan Key Laboratory for Computation & Simulation in Science & Engineering Xiangtan University Xiangtan 411105 China

This paper proves the saturation assumption for the nonconforming Morley finite ele- ment discretization of the biharmonic equation. This asserts that the error of the Morley approximation under uniform refinement is strictly reduced by a contraction factor smaller than one up to explicit higher-order data approximation terms. The refinement has at least to bisect any edge such as red refinement or 3-bisections on any triangle. This justifies a hierarchical error estimator for the Morley finite element method, which simply compares the discrete solutions of one mesh and its red-refinement. The related adaptive mesh-refining strategy performs optimally in numerical experiments. A remark for Crouzeix-Raviart nonconforming finite element error control is included.

关键词： Saturation Hierarchical error estimation Finite element Nonconforming Biharmonie Morley Kirchhoff plate Crouzeix-Raviart

A multigrid-reduction-in-time solver with a new two-level convergence for unsteady fractional Laplacian problems

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arXiv 2019年

作者： Yue, Xiaoqiang Pan, Kejia Zhou, Jie Weng, Zhifeng Shu, Shi Tang, Juan Key Laboratory of Intelligent Computing & 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 Xiangtan411105 China School of Mathematics and Statistics HNP-LAMA Central South University Changsha410083 China School of Mathematical Sciences Fujian Province University Key Laboratory of Computation Science Huaqiao University Quanzhou362021 China

The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to develop and analyze a MGRIT algorithm, using FCF-relaxation with time-dependent time-grid propagators, to seek the finite element approximations of unsteady fractional Laplacian problems. The multigrid with line smoother proposed in [L. Chen, R. H. Nochetto, et al., Math. Comp. 85 (2016) 2583–2607] is chosen to be the spatial solver. Motivated by [B. S. Southworth, SIAM J. Matrix Anal. Appl. 40 (2019) 564–608], we provide a new temporal eigenvalue approximation property and then deduce a generalized two-level convergence theory which removes the previous unitary diagonalization assumption on the fine and coarse time-grid propagators required in [X. Q. Yue, S. Shu, et al., Comput. Math. Appl. 78 (2019) 3471–3484]. Numerical computations are included to confirm the theoretical predictions and demonstrate the sharpness of the derived convergence upper bound. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

Adaptive-multilevel BDDC algorithm for three-dimensional plane wave Helmholtz systems

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arXiv 2019年

作者： Peng, Jie Shu, Shi Wang, Junxian Zhong, Liuqiang School of Mathematical Sciences South China Normal University Guangzhou510631 China School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

In this paper we are concerned with the weighted plane wave least-squares (PWLS) method for three-dimensional Helmholtz equations, and develop the multi-level adaptive BDDC algorithms for solving the resulting discrete system. In order to form the adaptive coarse components, the local generalized eigenvalue problems for each common face and each common edge are carefully designed. The condition number of the two-level adaptive BDDC preconditioned system is proved to be bounded above by a user-defined tolerance and a constant that is only dependent on the maximum number of faces and edges per subdomain and the number of subdomains sharing a common edge. The effectiveness of these algorithms is illustrated on benchmark problem. The numerical results show the robustness of our two-level adaptive BDDC algorithms with respect to the wave number, the number of subdomains and the mesh size, and appear that our multi-level adaptive BDDC algorithm can reduce the number of dofs at the coarse problem and can be used to solving large wave number problems efficiently. Copyright © 2019, The Authors. All rights reserved.

关键词： Elastic waves

A finite element method of the self-consistent field theory on general curved surfaces

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arXiv 2018年

作者： Wei, Huayi Xu, Ming Si, Wei Jiang, Kai School of Mathematics and Computational Science Xiangtan University Xiangtan Hunan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering

Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory (SCFT) has been proven to be a powerful tool for studying the equilibrium ordered structures. Many numerical methods have been developed to solve the SCFT model. However, most of these focus on the bulk systems, and little work on the confined systems, especially on general curved surfaces. In this work, we developed a linear surface finite element method, which has a rigorous mathematical theory to guarantee numerical precsion, to study the self-assembled phases of block copolymers on general curved surfaces based on the SCFT. Furthermore, to capture the consistent surface for a given self-assembled pattern, an adaptive approach to optimize the size of the general curved surface has been proposed. To demonstrate the power of this approach, we investigate the self-assembled patterns of diblock copolymers on several distinct curved surfaces, including five closed surfaces and an unclosed surface. Numerical results illustrate the efficiency of the proposed method. The obtained ordered structures are consistent with the previous results on standard surfaces, such as sphere and torus. Certainly, the proposed numerical framework has the capability of studying the phase behaviors on general surfaces precisely. Copyright © 2018, The Authors. All rights reserved.

关键词： Mean field theory