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An Efficient Real Space method for Orbital-Free Density-Functional Theory

Communications in Computational Physics 2007年第2期2卷 334-357页

作者： Carlos J.Garcıa-Cervera Department of Mathematics University of CaliforniaSanta BarbaraCA 93106USA.

We consider the Thomas-Fermi-von Weizsacker energy functional,with the Wang-Teter correction,and present an efficient real space method for Orbital-Free Density Functional Theory.It is proved that the energy minimizer satisfies a second order quasilinear elliptic equation,even at the points where the electron density vanishes.This information is used to construct an efficient energy minimization method for the resulting constrained problem,based on the truncated newton method for unconstrained optimization.The Wang-Teter kernel is analyzed,and its behavior in real space at short and far distances is determined.A second order accurate discretization of the energy is obtained using finite differences.The efficiency and accuracy of the method is illustrated with numerical simulations in an Aluminium FCC lattice.

关键词： Density functional theory truncated newton method constrained optimization.

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truncated newton-Based Multigrid Algorithm for Centroidal Voronoi Diagram Calculation

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Numerical Mathematics(Theory,methods and Applications) 2012年第2期5卷 242-259页

作者： Zichao Di Maria Emelianenko Stephen Nash Department of Mathematical Sciences George Mason UniversityFairfaxVA 22030USA. Systems Engineering and Operations Research Department George Mason UniversityFairfaxVA 22030USA

In a variety of modern applications there arises a need to tessellate the domain into representative regions,called Voronoi cells.A particular type of such tessellations,called centroidal Voronoi tessellations or CVTs,are in big demand due to their optimality properties important for many applications.The availability of fast and reliable algorithms for their construction is crucial for their successful use in practical settings.This paper introduces a new multigrid algorithm for constructing CVTs that is based on the MG/Opt algorithm that was originally designed to solve large nonlinear optimization problems.Uniform convergence of the new method and its speedup comparing to existing techniques are demonstrated for linear and nonlinear densities for several 1d and 2d problems,and O(k)complexity estimation is provided for a problem with k generators.

关键词： Centroidal Voronoi tessellation optimal quantization truncated newton method Lloyd’s algorithm multilevel method uniform convergence

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Preconditioners and Electron Density Optimization in Orbital-Free Density Functional Theory

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Communications in Computational Physics 2012年第6期12卷 135-161页

作者： Linda Hung Chen Huang Emily A.Carter Program in Applied and ComputationalMathematics Princeton UniversityPrincetonNJ 08544USA Department of Physics Princeton UniversityPrincetonNJ 08544USA Department of Mechanical and Aerospace Engineering and Andlinger Center for Energy and the Environment Princeton UniversityPrincetonNJ 08544USA

Orbital-free density functional theory(OFDFT)is a quantum mechanical method in which the energy of a material depends only on the electron density and ionic positions.We examine some popular algorithms for optimizing the electron density distribution in OFDFT,explaining their suitability,benchmarking their performance,and suggesting some improvements.We start by describing the constrained optimization problem that encompasses electron density optimization.Next,we discuss the line search(including Wolfe conditions)and the nonlinear conjugate gradient and truncated newton algorithms,as implemented in our open source OFDFT code.We finally focus on preconditioners derived from OFDFT energy functionals.Newlyderived preconditioners are successful for simulation cells of all sizes without regions of low electron-density and for small simulation cells with such regions.

关键词： Density functional theory truncated newton method conjugate gradient method constrained optimization benchmarks

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