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A DECOUPLING TWO-GRID METHOD FOR THE STEADY-STATE POISSON-NERNST-PLANCK EQUATIONS
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作者 Ying Yang Benzhuo Lu Yan Xie 《计算数学:英文版》 SCIE CSCD 2019年第4期556-578,共23页
Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poi... Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck equations by coarse grid finite element approximations. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid algorithms for solving Poisson-Nernst-Planck equations. 展开更多
关键词 Poisson-Nernst-Planck equations Two-grid finite element METHOD DECOUPLING METHOD Error analysis Gummel ITERATION
A mathematical aspect of Hohenberg-Kohn theorem
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作者 Aihui Zhou 《中国科学:数学英文版》 SCIE CSCD 2019年第1期63-68,共6页
The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become the most popular and powerful computational approach to study the electronic structure of matter.In this article, we s... The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become the most popular and powerful computational approach to study the electronic structure of matter.In this article, we study the Hohenberg-Kohn theorem for a class of external potentials based on a unique continuation principle. 展开更多
关键词 density functional theory electronic structure UNIQUE CONTINUATION PRINCIPLE Hohenberg-Kohn THEOREM
ALTERNATING DIRECTION IMPLICIT SCHEMES FOR THE TWO-DIMENSIONAL TIME FRACTIONAL NONLINEAR SUPER-DIFFUSION EQUATIONS
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作者 Jianfei Huang Yue Zhao +2 位作者 Sadia Arshad Kuangying Li Yifa Tang 《计算数学:英文版》 SCIE CSCD 2019年第3期297-315,共19页
As is known,there exist numerous alternating direction implicit(ADI)schemes for the two-dimensional linear time fractional partial differential equations(PDEs).However,if the ADI schemes for linear problems combined w... As is known,there exist numerous alternating direction implicit(ADI)schemes for the two-dimensional linear time fractional partial differential equations(PDEs).However,if the ADI schemes for linear problems combined with local linearization techniques are applied to solve nonlinear problems,the stability and convergence of the methods are often not clear.In this paper,two ADI schemes are developed for solving the two-dimensional time fractional nonlinear super-diffusion equations based on their equivalent partial integrodifferential equations.In these two schemes,the standard second-order central difference approximation is used for the spatial discretization,and the classical first-order approximation is applied to discretize the Riemann-Liouville fractional integral in time.The solvability,unconditional stability and L2 norm convergence of the proposed ADI schemes are proved rigorously.The convergence order of the schemes is 0(τ+hx^2+hy^2),where τ is the temporal mesh size,hx and hy are spatial mesh sizes in the x and y directions,respectively.Finally,numerical experiments are carried out to support the theoretical results and demonstrate the performances of two ADI schemes. 展开更多
关键词 Time FRACTIONAL super-diffusion equation NONLINEAR system ADI SCHEMES Stability CONVERGENCE
Domain Decomposition Preconditioners for Mixed Finite-Element Discretization of High-Contrast Elliptic Problems 预览
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作者 Hui Xie Xuejun Xu 《应用数学与计算数学学报(英文)》 2019年第1期141-165,共25页
In this paper,we design an efficient domain decomposition(DD)preconditioner for the saddle-point problem resulting from the mixed finite-element discretization of multiscale elliptic problems.By proper equivalent alge... In this paper,we design an efficient domain decomposition(DD)preconditioner for the saddle-point problem resulting from the mixed finite-element discretization of multiscale elliptic problems.By proper equivalent algebraic operations,the original saddle-point system can be transformed to another saddle-point system which can be preconditioned by a block-diagonel matrix efficiently.Actually,the first block of this block-diagonal matrix corresponds to a multiscale H(div)problem,and thus,the direct inverse of this block is unpractical and unstable for the large-scale problem.To remedy this issue,a two-level overlapping DD preconditioner is proposed for this//(div)problem.Our coarse space consists of some velocities obtained from mixed formulation of local eigenvalue problems on the coarse edge patches multiplied by the partition of unity functions and the trivial coarse basis(e.g.,Raviart-Thomas element)on the coarse grid.The condition number of our preconditioned DD method for this multiscale H(div)system is bounded by C(1+务)(1+log4(^)),where 6 denotes the width of overlapping region,and H,h are the typical sizes of the subdomain and fine mesh.Numerical examples are presented to confirm the validity and robustness of our DD preconditioner. 展开更多
关键词 High contrast.Mixed FEM DD PRECONDITIONER Spectral coarse space
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Efficient projected gradient methods for cardinality constrained optimization
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作者 Fengmin Xu Yuhong Dai +1 位作者 Zhihu Zhao Zongben Xu 《中国科学:数学英文版》 SCIE CSCD 2019年第2期245-268,共24页
Sparse optimization has attracted increasing attention in numerous areas such as compressed sensing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constra... Sparse optimization has attracted increasing attention in numerous areas such as compressed sensing, financial optimization and image processing. In this paper, we first consider a special class of cardinality constrained optimization problems, which involves box constraints and a singly linear constraint. An efficient approach is provided for calculating the projection over the feasibility set after a careful analysis on the projection subproblem. Then we present several types of projected gradient methods for a general class of cardinality constrained optimization problems. Global convergence of the methods is established under suitable assumptions. Finally, we illustrate some applications of the proposed methods for signal recovery and index tracking.Especially for index tracking, we propose a new model subject to an adaptive upper bound on the sparse portfolio weights. The computational results demonstrate that the proposed projected gradient methods are efficient in terms of solution quality. 展开更多
关键词 SPARSE APPROXIMATION projected GRADIENT method global CONVERGENCE signal recovery index tracking
A DISCONTINUOUS GALERKIN METHOD BY PATCH RECONSTRUCTION FOR BIHARMONIC PROBLEM
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作者 Ruo Li Pingbing Ming +2 位作者 Zhiyuan Sun Fanyi Yang Zhijian Yang 《计算数学:英文版》 SCIE CSCD 2019年第4期524-540,共17页
We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dime... We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes. 展开更多
关键词 LEAST-SQUARES PROBLEM Reconstructed basis function DISCONTINUOUS GALERKIN method BIHARMONIC PROBLEM
A Review on Stochastic Multi-symplectic Methods for Stochastic Maxwell Equations 预览
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作者 Liying Zhang Chuchu Chen +1 位作者 Jialin Hong Lihai Ji 《应用数学与计算数学学报(英文)》 2019年第3期467-501,共35页
Stochastic multi-symplectic methods are a class of numerical methods preserving the discrete stochastic multi-symplectic conservation law. These methods have the remarkable superiority to conventional numerical method... Stochastic multi-symplectic methods are a class of numerical methods preserving the discrete stochastic multi-symplectic conservation law. These methods have the remarkable superiority to conventional numerical methods when applied to stochastic Hamiltonian partial differential equations (PDEs), such as long-time behavior, geometric structure preserving, and physical properties preserving. Stochastic Maxwell equations driven by either additive noise or multiplicative noise are a system of stochastic Hamiltonian PDEs intrinsically, which play an important role in fields such as stochastic electromagnetism and statistical radiophysics. Thereby, the construction and the analysis of various numerical methods for stochastic Maxwell equations which inherit the stochastic multi-symplecticity, the evolution laws of energy and divergence of the original system are an important and promising subject. The first stochastic multi-symplectic method is designed and analyzed to stochastic Maxwell equations by Hong et al.(A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise. J. Comput. Phys. 268:255-268, 2014). Subsequently, there have been developed various stochastic multi-symplectic methods to solve stochastic Maxwell equations. In this paper, we make a review on these stochastic multi-symplectic methods for solving stochastic Maxwell equations driven by a stochastic process. Meanwhile, the theoretical results of well-posedness and conservation laws of the stochastic Maxwell equations are included. 展开更多
关键词 STOCHASTIC MULTI-SYMPLECTIC METHODS STOCHASTIC HAMILTONIAN partial differential EQUATIONS STOCHASTIC Maxwell EQUATIONS Structure-preserving METHODS
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Hexahedral constraint-free finite element method on meshes with hanging nodes
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作者 Xuying Zhao Zhong-Ci Shi 《中国科学:数学英文版》 SCIE CSCD 2019年第12期2591-2616,共26页
Nonconforming grids with hanging nodes are frequently used in adaptive finite element comput at ions.In all earlier works on such methods,proper cons train ts should be enforced on degrees of freedom on edges/faces wi... Nonconforming grids with hanging nodes are frequently used in adaptive finite element comput at ions.In all earlier works on such methods,proper cons train ts should be enforced on degrees of freedom on edges/faces with hanging nodes to keep continuity,which yield numerical computations much complicated.In 2014,Zhao et al.(2014)presented quadrilateral constraint-free finite element methods on quadrilateral grids with hanging nodes.This paper further develops a hexahedral constraint-free finite element method on hexahedral grids with hanging nodes,which is of greater challenge than the two-dimensional case.Residual-based a posteriori error reliability and efficiency are also established in this paper. 展开更多
关键词 adaptive finite element a posteriori error estimate hexahedral nonconforming element hangingnode
A GENERAL TWO-LEVEL SUBSPACE METHOD FOR NONLINEAR OPTIMIZATION
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作者 Cheng Chen Zaiwen Wen Yaxiang Yuan 《计算数学:英文版》 SCIE CSCD 2018年第6期881-902,共22页
一个新二水平的 subspace 方法为从无限维的优化问题解决一般非强迫的最小化明确的表达 discretized 被建议。在每次重复,算法也在当前的水平或粗糙的 subspace 修正步上执行直接的步。在粗糙的 subspace 修正步,我们由并列方向和坡... 一个新二水平的 subspace 方法为从无限维的优化问题解决一般非强迫的最小化明确的表达 discretized 被建议。在每次重复,算法也在当前的水平或粗糙的 subspace 修正步上执行直接的步。在粗糙的 subspace 修正步,我们由并列方向和坡度方向在当前的点跨越的二维的 subspace 扩充传统的粗糙的格子空间。全球集中被证明,集中率在 discretized 功能上在一些温和条件下面被学习。一些变化问题的初步的数字实验证明我们的二水平的 subspace 方法是有希望的。 展开更多
关键词 优化 非线性 温和条件 数字实验 最小化 无限维 粗糙 子空间
OPTIMAL QUADRATIC NITSCHE EXTENDED FINITE ELEMENT METHOD FOR INTERFACE PROBLEM OF DIFFUSION EQUATION
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作者 Fei Wang Shuo Zhang 《计算数学:英文版》 SCIE CSCD 2018年第5期693-717,共25页
在这份报纸,我们学习 Nitsche 为二个维的散开方程的接口问题的扩大有限元素方法(XFEM ) 。明确地,我们在格子的某形状常规的家庭上学习二次的 XFEM 计划并且关于网孔尺寸证明计划的最佳的集中率。主要努力被奉献到分类在元素和接口... 在这份报纸,我们学习 Nitsche 为二个维的散开方程的接口问题的扩大有限元素方法(XFEM ) 。明确地,我们在格子的某形状常规的家庭上学习二次的 XFEM 计划并且关于网孔尺寸证明计划的最佳的集中率。主要努力被奉献到分类在元素和接口之间的交叉的盒子上并且证明为扩大有限元素功能的加权的踪迹不平等需要,并且分析 XFEM 的一般框架那时能被实现。 展开更多
关键词 有限元素 接口 方程 网孔尺寸 集中率 学习 证明 盒子
AN AUGMENTED LAGRANGIAN TRUST REGION METHOD WITH A BI-OBJECT STRATEGY
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作者 Caixia Kou Zhongwen Chen +1 位作者 Yuhong Dai Haifei Han 《计算数学:英文版》 SCIE CSCD 2018年第3期331-350,共20页
有双性人目标策略的一个扩充 Lagrangian 信任区域方法被建议因为解决非线性的平等抑制了优化,它在惩罚类型方法和没有惩罚的之间掉落。在每次重复,试用步被在一个信任区域以内最小化一个二次的近似模型到扩充 Lagrangian 功能计算。... 有双性人目标策略的一个扩充 Lagrangian 信任区域方法被建议因为解决非线性的平等抑制了优化,它在惩罚类型方法和没有惩罚的之间掉落。在每次重复,试用步被在一个信任区域以内最小化一个二次的近似模型到扩充 Lagrangian 功能计算。模型是为非强迫的优化的标准信任区域 subproblem 并且能被许多存在方法高效地因此解决。选择惩罚参数,辅助信任区域 subproblem 与限制违背有关被介绍。结果,惩罚参数不必 monotonically 正在增加并且不趋于到无穷。双性人目标策略,与客观功能和限制违背的措施有关,被利用决定试用步是否将被接受。方法的全球集中在温和假设下面被建立。数字实验被做,它在各种各样的困难的状况上说明算法的效率。 展开更多
关键词 LAGRANGIAN 信任 LAGRANGIAN 近似模型 数字实验 罚参数 非线性 最小化
Coupled modified KdV equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property
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作者 Xiangke Chang Yi He +3 位作者 Xingbiao Hu Shihao Li Hon-wah Tam Yingnan Zhang 《中国科学:数学英文版》 SCIE CSCD 2018年第6期1063-1078,共16页
关键词 加速算法 KDV 多项式 性质 修改 方程 直角 数学结构
A NEW INTEGRAL EQUATION FORMULATION FOR SCATTERING BY PENETRABLE DIFFRACTION GRATINGS
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作者 Ruming Zhang Bo Zhang 《计算数学:英文版》 SCIE CSCD 2018年第1期110-127,共18页
Thin film dynamics in coating problems using Onsager principle
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作者 邸亚娜 许现民 +1 位作者 周嘉嘉 Masao Doi 《中国物理B:英文版》 SCIE EI CAS CSCD 2018年第2期51-55,共5页
关键词 Onsager 动力学 电影 涂层 度理论 可伸缩 侧面
Acoustic Based Crosshole Full Waveform Slowness Inversion in the Time Domain 预览
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作者 Wensheng Zhang Atish Kumar Joardar 《应用数学与应用物理(英文)》 2018年第5期1086-1110,共25页
We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the c... We develop a new full waveform inversion (FWI) method for slowness with the crosshole data based on the acoustic wave equation in the time domain. The method combines the total variation (TV) regularization with the constrained optimization together which can inverse the slowness effectively. One advantage of slowness inversion is that there is no further approximation in the gradient derivation. Moreover, a new algorithm named the skip method for solving the constrained optimization problem is proposed. The TV regularization has good ability to inverse slowness at its discontinuities while the constrained optimization can keep the inversion converging in the right direction. Numerical computations both for noise free data and noisy data show the robustness and effectiveness of our method and good inversion results are yielded. 展开更多
关键词 ACOUSTIC Wave Equation CROSSHOLE Full WAVEFORM INVERSION SLOWNESS Bound Constraints TV REGULARIZATION
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Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations
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作者 Ya-bing WEI Yan-min ZHAO +2 位作者 Zheng-guang SHI Fen-ling WANG Yi-fa TANG 《应用数学学报:英文版》 SCIE CSCD 2018年第4期828-841,共14页
关键词 空间方向 时间 女性 术语 方程 波浪 精确性 二维
频率域声波方程全波形反演
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作者 张文生 庄源 《数值计算与计算机应用》 2017年第3期167-196,共30页
全波形反演是一种利用地表或井中观测到的波场来推测地下物性参数的高精度成像方法.本文研究了频率域声波方程全波形反演的数值方法.正演用带PML边界条件的九点差分格式求解.反演是一个极小化模拟数据与观测数据之间残量的优化迭代... 全波形反演是一种利用地表或井中观测到的波场来推测地下物性参数的高精度成像方法.本文研究了频率域声波方程全波形反演的数值方法.正演用带PML边界条件的九点差分格式求解.反演是一个极小化模拟数据与观测数据之间残量的优化迭代过程,文中比较了多种数值优化方法,包括最速下降法、共轭梯度法、LBFGS方法、高斯牛顿法以及预条件方法.反演从低频到高频逐级进行,且前一个频率的反演结果作为下一个频率反演的初值,该策略有效克服了反演发散或收敛到局部极小值的情况.文中详细描述了正反演方法,并对一个简单模型和两个国际标准模型(即Marmousi模型和Overthrust模型)进行了MPI并行反演计算,结果表明牛顿方法和预条件方法能较精确地对复杂构造模型进行反演成像. 展开更多
关键词 波动方程 频率域 全波形反演 预条件 最速下降法 共轭梯度法 LBFGS方法 高斯牛顿法 MARMOUSI模型 Overthrust模型
The Minimal Measurement Number Problem in Phase Retrieval: A Review of Recent Developments
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作者 Zhiqiang XU 《数学研究及应用:英文版》 CSCD 2017年第1期40-46,共7页
Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number m so that one can recover d-... Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number m so that one can recover d-dimensional signals from m phaseless measurements. This problem attracts much attention of experts from different areas. In this paper, we review the recent development on the minimal measurement number and also raise many interesting open questions. 展开更多
关键词 相位测量 进展综述 检索 开放式问题 复信号
A CASCADIC MULTIGRID METHOD FOR EIGENVALUE PROBLEM
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作者 Xiaole Han Hehu Xie Fei Xu 《计算数学:英文版》 SCIE CSCD 2017年第1期74-90,共17页
一个 cascadic multigrid 方法基于 multilevel 修正计划为特征值问题被建议。与这个新计划,在最好的空间的一个特征值问题能被线性变光滑的步在一系列 multilevel 上解决在特殊最粗糙的空格的有限元素空格和非线性的改正步。一旦有限... 一个 cascadic multigrid 方法基于 multilevel 修正计划为特征值问题被建议。与这个新计划,在最好的空间的一个特征值问题能被线性变光滑的步在一系列 multilevel 上解决在特殊最粗糙的空格的有限元素空格和非线性的改正步。一旦有限元素空格的顺序和弄平步的数字适当地被选择,有最佳的计算工作的最佳的集中率能被获得。一些数字实验被介绍验证我们的理论分析。 展开更多
关键词 瀑布型多重网格法 特征值问题 有限元空间 非线性求解 校正方案 收敛速度 数值实验 多层次
Robustness properties of dimensionality reduction with Gaussian random matrices
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作者 HAN Bin XU ZhiQiang 《中国科学:数学英文版》 SCIE CSCD 2017年第10期1753-1778,共26页
In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the r... In this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property(RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure. 展开更多
关键词 随机矩阵 鲁棒性 高斯 降维 相位恢复 矩阵范数 下界估计 保持性
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