In this paper, we propose the component-consistent pressure correction projection method for the numerical solution of the incompressible Navier-Stokes equations. This projection preserves a discrete form of the compo...
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In this paper, we propose the component-consistent pressure correction projection method for the numerical solution of the incompressible Navier-Stokes equations. This projection preserves a discrete form of the component-consistent condition between components of the solution at every time step. We also propose, in particular, the CNMT2 + CCPC method and the RKMT + CCPC method, both involving one pressure Poisson solution per time step. We show that they are both of O(Delta t(2)) for the Velocity and O(Delta t) for the pressure on fixed meshes and finite time intervals. Numerical tests on flow simulation support our claim that the component-consistent pressure correction projection method solves the deviation problem encountered sometimes by the original pressure correction projection method.
A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the s...
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A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
In this paper,we consider the problem of computing the smallest enclosing ball(SEB)of a set of m balls in Rn,where the product mn is *** first approximate the non-differentiable SEB problem by its log-exponential agg...
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In this paper,we consider the problem of computing the smallest enclosing ball(SEB)of a set of m balls in Rn,where the product mn is *** first approximate the non-differentiable SEB problem by its log-exponential aggregation function and then propose a computationally efficient inexact Newton-CG algorithm for the smoothing approximation problem by exploiting its special(approximate)sparsity *** key difference between the proposed inexact Newton-CG algorithm and the classical Newton-CG algorithm is that the gradient and the Hessian-vector product are inexactly computed in the proposed algorithm,which makes it capable of solving the large-scale SEB *** give an adaptive criterion of inexactly computing the gradient/Hessian and establish global convergence of the proposed *** illustrate the efficiency of the proposed algorithm by using the classical Newton-CG algorithm as well as the algorithm from Zhou et al.(Comput Optim Appl 30:147–160,2005)as benchmarks.
作者：
Aihui ZhouLSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences
University of Chinese Academy of Sciences
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 *** this article, we study t...
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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 *** this article, we study the Hohenberg-Kohn theorem for a class of external potentials based on a unique continuation principle.
In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained...
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In this paper, we investigate the quadratic approximation methods. After studying the basic idea of simplex methods, we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces. And the quadratic model is solved in the new subspaces. The motivation is to use the information disclosed by the former steps to construct more promising directions. For most tested problems, the number of functions evaluations have been reduced obviously through our algorithms.
In this paper we generalize the method of constructing sympl ctic schemes by generating function in the case of autonomous Hamiltonian system to that of nonautonomous system.
In this paper we generalize the method of constructing sympl ctic schemes by generating function in the case of autonomous Hamiltonian system to that of nonautonomous system.
In the field of molecular modeling and simulation, molecular surface meshes are necessary for many problems, such as molecular structure visualization and analysis, docking problem and implicit solvent modeling and si...
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In the field of molecular modeling and simulation, molecular surface meshes are necessary for many problems, such as molecular structure visualization and analysis, docking problem and implicit solvent modeling and simulation. Recently, with the developments of advanced mathematical modeling in the field of implicit solvent modeling and simulation, providing surface meshes with good qualities efficiently for large real biomolecular systems becomes an urgent issue beyond its traditional purposes for visualization and geometry analyses for molecular structure. In this review, we summarize recent works on this issue. First, various definitions of molecular surfaces and corresponding meshing methods are introduced. Second, our recent meshing tool, TMSmesh, and its performances are presented. Finally, we show the applications of the molecular surface mesh in implicit solvent modeling and simulations using boundary element method (BEM) and finite element method (FEM).
作者：
Ying YangBenzhuo LuYan XieSchool of Mathematics and Computing Science
Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation Guilin University of Electronic Technology Guilin 541004 China LSEC
Institute of Computational Mathematics and Scientific/Engineering Computing the National Center for Mathematics and Interdisciplinary Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China LSEC
Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China
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...
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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.
Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification(UQ)*** for leastsquares regularization,compressive sampling recovery,and interpolatory reconstruction...
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Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification(UQ)*** for leastsquares regularization,compressive sampling recovery,and interpolatory reconstruction are becoming standard tools used in a variety of *** of a collocation mesh is frequently a challenge,but methods that construct geometrically unstructured collocation meshes have shown great potential due to attractive theoretical properties and direct,simple generation and *** investigate properties of these meshes,presenting stability and accuracy results that can be used as guides for generating stochastic collocation grids in multiple dimensions.
Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:...
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Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f(x)+F(x)?0,where X and Y are Banach spaces,and U is an open subset of X,f:U→Y is a nonsmooth function and F:X■Y is a set-valued mapping with closed *** introduce a confined Newton-type method for solving the above nonsmooth generalized equation and analyze the semilocal and local convergence of this ***,under the point-based approximation of f on U and metrically regular property of f+F,we present quadratic rate of convergence of this ***,superlinear rate of convergence of this method is provided under the conditions that f admits p-point-based approximation on U and f+F is metrically *** example of nonsmooth functions that have p-point-based approximation is ***,a numerical experiment is given which illustrates the theoretical result.
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