作者：
Huajie ChenXingao GongLianhua HeAihui ZhouLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China Department of Physics
Fudan UniversityShanghai 200433China
In this paper,we study an adaptive finite element method for a class of nonlinear eigenvalue problems resulting from quantum physics that may have a nonconvex energy *** prove the convergence of adaptive finite elemen...
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In this paper,we study an adaptive finite element method for a class of nonlinear eigenvalue problems resulting from quantum physics that may have a nonconvex energy *** prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.
作者：
Dier ZhangAihui ZhouXin-Gao GongDepartment of Physics
Fudan UniversityShanghai 200433China LSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China
The finite element method is a promising method for electronic structure *** this paper,a new parallelmesh refinementmethod for electronic structure calculations is *** properties of the method are investigated to mak...
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The finite element method is a promising method for electronic structure *** this paper,a new parallelmesh refinementmethod for electronic structure calculations is *** properties of the method are investigated to make itmore efficient andmore convenient for *** practical issues such as distributed memory parallel computation,less tetrahedra prototypes,and the assignment of the mesh elements carried out independently in each sub-domain will be *** numerical experiments on the periodic system,cluster and nano-tube are presented to demonstrate the effectiveness of the proposed method.
作者：
DU QiangMING PingBingDepartment of Mathematics
Pennsylvania State UniversityUniversity ParkPA 16802USA LSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesBeijing 100190China
In this paper,we consider the cascadic multigrid method for a parabolic type *** Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some c...
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In this paper,we consider the cascadic multigrid method for a parabolic type *** Euler approximation in time and linear finite element approximation in space are employed.A stability result is established under some conditions on the *** 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 *** error bound sare derived for both smooth and non-smooth *** strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.
作者：
Abdullah ShahHong GuoLi YuanLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100080China Department of Mathematics
COMSATS Institute of Information TechnologyIslamabadPakistan
This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear *** artificial compressibility approach is used,which ...
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This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear *** artificial compressibility approach is used,which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be *** convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting,and the viscous terms are approximated by a fourth-order central compact *** solution algorithm used is the Beam-Warming approximate factorization *** solutions to benchmark problems of the steady plane Couette-Poiseuille flow,the liddriven cavity flow,and the constricting channel flow with varying geometry are *** computed results are found in good agreement with established analytical and numerical *** third-order accuracy of the scheme is verified on uniform rectangular meshes.
The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produ...
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The compressible Navier-Stokes equations discretized with a fourth order accurate compact finite difference scheme with group velocity control are used to simulate the Richtmyer-Meshkov (R-M) instability problem produced by cylindrical shock-cylindrical material interface with shock Mach number Ms=1.2 and density ratio 1:20 (interior density/outer density). Effect of shock refraction, reflection, interaction of the reflected shock with the material interface, and effect of initial perturbation modes on R-M instability are investigated numerically. It is noted that the shock refraction is a main physical mechanism of the initial phase changing of the material surface. The multiple interactions of the reflected shock from the origin with the interface and the R-M instability near the material interface are the reason for formation of the spike-bubble structures. Different viscosities lead to different spike-bubble structure characteristics. The vortex pairing phenomenon is found in the initial double mode simulation. The mode interaction is the main factor of small structures production near the interface.
作者：
Ying YangBenzhuo LuDepartment of Computational Science and Mathematics
Guilin University of Electronic TechnologyGuilin 541004GuangxiChina LSEC
Institute of Computational Mathematics and Scientific/Engineering Computingthe National Center for Mathematics and Interdisciplinary SciencesAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China
Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources,which de...
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Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources,which describe the electrodiffusion of ions in a solvated biomolecular *** this paper,some error bounds for a piecewise finite element approximation to this problem are *** numerical examples including biomolecular problems are shown to support our analysis.
In this paper we are concerned with the construction of a preconditioner for the Steklov-Poincaré operator arising from a non-overlapping domain decomposition method for second-order elliptic problems in three-di...
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ISBN:
(纸本)9783540751984
In this paper we are concerned with the construction of a preconditioner for the Steklov-Poincaré operator arising from a non-overlapping domain decomposition method for second-order elliptic problems in three-dimensional domains. We first propose a new kind of multilevel decomposition of the finite element space on the interface associated with a general quasi-uniform triangulation. Then, we construct a multilevel preconditioner for the underlying Steklov-Poincaré operator. The new multilevel preconditioner enjoys optimal computational complexity, and almost optimal convergence rate.
Abstract This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are give...
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Abstract This paper presents a restarted conjugate gradient iterative algorithm for solving ill-posed problems. The damped Morozov's discrepancy principle is used as a stopping rule. Numerical experiments are given to illustrate the efficiency of the method.
The solution of the biharmonic equation using Adini nonconforming finite elements are considered and results for the multi-parameter asymptotic expansions and extrapolation are reported. The Adini nonconforming finite...
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The solution of the biharmonic equation using Adini nonconforming finite elements are considered and results for the multi-parameter asymptotic expansions and extrapolation are reported. The Adini nonconforming finite element solution of the biharmonic equation is shown and it have a multi-parameter asymptotic error expansion and extrapolation. This expansion and a multi-parameter extrapolation technique are used to develop an accurate approximation parallel algorithm for the biharmonic equation. Finally, numerical results have verified the extrapolation theory.
In this paper, we propose a new trust region affine scaling method for nonlinear programming with simple bounds. Our new method is an interior-point trust region method with a new scaling technique. The scaling matrix...
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