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| 1 | Cascadic multigrid methods for parabolic problems显示文摘In this paper,we consider the cascadic multigrid method for a parabolic type equation.Backward Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the smoother.Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter,these conditions are verified for a number of popular smoothers.Optimal error bound sare derived for both smooth and non-smooth data.Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented. | DU Qiang MING PingBing | 2008 | Science China Mathematics2008，51，8： | 7 |
| 2 | NONCONFORMING QUADRILATERAL ROTATED ELEMENT FOR REISSNER-MINDLIN PLATE显示文摘In this paper,we extend two rectangular elements for Reissner-Mindlin plate[9] to the quadrilateral case,Optimal H^1 and L^2 error bounds independent of the plate hickness are derived under a mild assumption on the mesh partition. | Jun Hu Pingbing Ming Zhongci Shi (Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China) | 2003 | Journal of Computational Mathematics2003，21，1： | 7 |
| 3 | QUADRILATERAL MESH显示文摘Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version (1+α)-Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples. | MING PINGBING SHI ZHONGCI | 2002 | Chinese Annals of Mathematics,Series B2002，23，2： | 6 |
| 4 | GHOST FORCE INFLUENCE OF A QUASICONTINUUM METHOD IN TWO DIMENSION显示文摘鬼力量引起的错误在二种尺寸与平面接口为一个 quasicontinuum 方法被学习。为一种特殊情况,我们导出错误的分析表情,它被利用证明鬼力量可以为答案的坡度导致一个有限尺寸错误。错误指数地为腐烂离开接口的错误代数学地腐烂离开接口的错误表演的 pointwise 估计,比 onedimensional 问题的慢得多,。 | Jingrun Chen Pingbing Ming | 2012 | Journal of Computational Mathematics2012，30，6： | 2 |
| 5 | Two nonconforming quadrilateral elements for the Reissner- Mindlin plate显示文摘 | MING PINGBING SHI ZHONGCI | 2005 | Mathematical Models and Methods in Applied Science2005，1510，： | 1 |
| 6 | Abinitio calculation of ideal strength and phonon instability of graphene under tension显示文摘 | LIU Fang MING Pingbing LI Ju | | 0，，： | 1 |
| 7 | THE QUADRATIC SPECHT TRIANGLE显示文摘We propose a class of 12 degrees of freedom triangular plate bending elements with quadratic rate of convergence.They may be viewed as the second order Specht triangle,while the Specht triangle is one of the best first order plate bending element.The conver gence result is proved under minimal smoothness assumption on the solution.Numerical results for both the smooth solution and nonsmmoth solution confirm the theoretical pre diction. | Hongliang Li Pingbing Ming Zhongci Shi | 2020 | Journal of Computational Mathematics2020，38，1： | 1 |
| 8 | Analysis of multiscale methods 显示文摘 | E Weinan Ming Pingbing | 2004 | Journal of Computational Mathematics (S0254-9409)2004，22，2： | 1 |
| 9 | Ab initio calculation of ideal strength and phonon instability of graphene under tension显示文摘 | Fang Liu Pingbing Ming Ju Li | 2007 | Physical Review B2007，76，06： | 1 |
| 10 | On the Effect of Ghost Force in the Quasicontinuum Method:Dynamic Problems in One Dimension显示文摘Numerical error caused by“ghost forces”in a quasicontinuum method is studied in the context of dynamic problems.The error in the discrete W^(1,∞)norm is analyzed for the time scale O(ε)and the time scale O(1)withεbeing the lattice spacing. | Xiantao Li Pingbing Ming | 2014 | Communications in Computational Physics2014，15，3： | 0 |
| 11 | An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids显示文摘We propose a multigrid method to solve the molecular mechanics model(molecular dynamics at zero temperature).The Cauchy-Born elasticity model is employed as the coarse grid operator and the elastically deformed state as the initial guess of the molecular mechanics model.The efficiency of the algorithm is demonstrated by three examples with homogeneous deformation,namely,one dimensional chain under tensile deformation and aluminum under tension and shear deformations.The method exhibits linear-scaling computational complexity,and is insensitive to parameters arising from iterative solvers.In addition,we study two examples with inhomogeneous deformation:vacancy and nanoindentation of aluminum.The results are still satisfactory while the linear-scaling property is lost for the latter example. | Jingrun Chen Pingbing Ming | 2011 | Communications in Computational Physics2011，10，6： | 0 |
| 12 | The efect of ghost forces for a quasicontinuum method in three dimension显示文摘We study the efect of'ghost forces'for a quasicontinuum method in three dimension with a planar interface.'Ghost forces'are the inconsistency of the quasicontinuum method across the interface between the atomistic region and the continuum region.Numerical results suggest that'ghost forces'may lead to a negilible error on the solution,while lead to a fnite size error on the gradient of the solution.The error has a layer-like profle,and the interfacial layer width is of O(ε).The error in certain component of the displacement gradient decays algebraically from O(1)to O(ε)away from the interface.A surrogate model is proposed and analyzed,which suggests the same scenario for the efect of'ghost forces'.Our analysis is based on the explicit solution of the surrogate model. | CUI Long MING PingBing | 2013 | Science China Mathematics2013，56，12： | 0 |
| 13 | A DISCONTINUOUS GALERKIN METHOD BY PATCH RECONSTRUCTION FOR BIHARMONIC PROBLEM显示文摘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. | Ruo Li Pingbing Ming Zhiyuan Sun Fanyi Yang Zhijian Yang | 2019 | Journal of Computational Mathematics2019，37，4： | 0 |
| 14 | Specht Triangle Approximation of Large Bending Isometries显示文摘We propose a Specht triangle discretization for a geometrically nonlinear Kirchhoff plate model with large bending isometry.A combination of an adaptive time-stepping gradient flow and a Newton’s method is employed to solve the ensuing nonlinear minimization problem.Γ−convergence of the Specht triangle discretization and the unconditional stability of the gradient flow algorithm are proved.We present several numerical examples to demonstrate that our approach significantly enhances both the computational efficiency and accuracy. | Xiang Li Pingbing Ming | 2023 | Annals of Applied Mathematics2023，39，4： | 0 |
| 15 | A Generalized Peierls-Nabarro Model for Curved Dislocations Using Discrete Fourier Transform显示文摘In this paper,we present a generalized Peierls-Nabarro model for curved dislocations using the discrete Fourier transform.In our model,the total energy is expressed in terms of the disregistry at the discrete lattice sites on the slip plane,and the elastic energy is obtained efficiently within the continuum framework using the discrete Fourier transform.Our model directly incorporates into the total energy both the Peierls energy for the motion of straight dislocations and the second Peierls energy for kink migration.The discreteness in both the elastic energy and the misfit energy,the full long-range elastic interaction for curved dislocations,and the changes of core and kink profiles with respect to the location of the dislocation or the kink are all included in our model.The model is presented for crystals with simple cubic lattice.Simulation results on the dislocation structure,Peierls energies and Peierls stresses of both straight and kinked dislocations are reported.These results qualitatively agree with those from experiments and atomistic simulations. | He Wei Yang Xiang Pingbing Ming | 2008 | Communications in Computational Physics2008，4，7： | 0 |
| 16 | A Family of Nonconforming Rectangular Elements for Strain Gradient Elasticity显示文摘We propose a family of nonconforming rectangular elements for the linear strain gradient elastic model.Optimal error estimates uniformly with respect to the small material parameter have been proved.Numerical results confirm the theoretical prediction. | Yulei Liao Pingbing Ming | 2019 | Advances in Applied Mathematics and Mechanics2019，11，6： | 0 |
| 17 | A Constrained Cauchy-Born Elasticity Accelerated Multigrid Method for Nanoindentation显示文摘We introduce a new multigrid method to study the lattice statics model arising from nanoindentation.A constrained Cauchy-Born elasticity model is used as the coarse-grid operator.This method accelerates the relaxation process and considerably reduces the computational cost.In particular,it saves quite a bit when dislocations nucleate and move,as demonstrated by the simulation results. | Jingrun Chen Pingbing Ming Jerry Zhijian Yang | 2014 | Communications in Computational Physics2014，15，2： | 0 |
| 18 | A New Function Space from Barron Class and Application to Neural Network Approximation显示文摘We introduce a new function space,dubbed as the Barron spectrum space,which arises from the target function space for the neural network approximation.We give a Bernstein type sufficient condition for functions in this space,and clarify the embedding among the Barron spectrum space,the Bessel potential space,the Besov space and the Sobolev space.Moreover,the unexpected smoothness and the decaying behavior of the radial functions in the Barron spectrum space have been investigated.As an application,we prove a dimension explicit L^(q) error bound for the two-layer neural network with the Barron spectrum space as the target function space,the rate is dimension independent. | Yan Meng Pingbing Ming | 2022 | Communications in Computational Physics2022，32，10： | 0 |
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