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Accuracy of generalized gradient approximation functionals for density-functional perturbation theory calculations

Physical Review B 2014年第6期89卷 064305-064305页

作者： Lianhua He Fang Liu Geoffroy Hautier Micael J. T. Oliveira Miguel A. L. Marques Fernando D. Vila J. J. Rehr G.-M. Rignanese Aihui Zhou LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Applied Mathematics Central University of Finance and Economics Beijing 100081 China European Theoretical Spectroscopy Facility (ETSF) Institute of Condensed Matter and Nanosciences (IMCN) Université Catholique de Louvain Chemin des Étoiles 8 1348 Louvain-la-Neuve Belgium Center for Computational Physics University of Coimbra Rua Larga 3004-516 Coimbra Portugal Institut Lumière Matière UMR5306 Université Lyon 1-CNRS Université de Lyon F-69622 Villeurbanne Cedex France Department of Physics University of Washington Seattle Washington 98195 USA

We assess the validity of various exchange-correlation functionals for computing the structural, vibrational, dielectric, and thermodynamical properties of materials in the framework of density-functional perturbation theory (DFPT). We consider five generalized-gradient approximation (GGA) functionals (PBE, PBEsol, WC, AM05, and HTBS) as well as the local density approximation (LDA) functional. We investigate a wide variety of materials including a semiconductor (silicon), a metal (copper), and various insulators (SiO2 α-quartz and stishovite, ZrSiO4 zircon, and MgO periclase). For the structural properties, we find that PBEsol and WC are the closest to the experiments and AM05 performs only slightly worse. All three functionals actually improve over LDA and PBE in contrast with HTBS, which is shown to fail dramatically for α-quartz. For the vibrational and thermodynamical properties, LDA performs surprisingly very well. In the majority of the test cases, it outperforms PBE significantly and also the WC, PBEsol and AM05 functionals though by a smaller margin (and to the detriment of structural parameters). On the other hand, HTBS performs also poorly for vibrational quantities. For the dielectric properties, none of the functionals can be put forward. They all (i) fail to reproduce the electronic dielectric constant due to the well-known band gap problem and (ii) tend to overestimate the oscillator strengths (and hence the static dielectric constant).

关键词： PERTURBATION (Quantum dynamics) SILICON THERMODYNAMICS DIELECTRIC devices DIELECTRICS

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Finite-Difference Solution of the Helmholtz Equation Based on Two Domain Decomposition Algorithms

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Journal of Applied Mathematics and Physics 2013年第4期1卷 18-24页

作者： Wensheng Zhang Yunyin Dai Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Institute of Computational Mathematics and Scientific/Engineering Computing LSEC Beijing China

In this paper, wave simulation with the finite difference method for the Helmholtz equation based on the domain decomposition method is investigated. The method solves the problem by iteratively solving subproblems defined on smaller subdomains. Two domain decomposition algorithms both for nonoverlapping and overlapping methods are described. More numerical computations including the benchmark Marmousi model show the effectiveness of the proposed algorithms. This method can be expected to be used in the full-waveform inversion in the future.

关键词： Finite Difference Domain Decomposition Nonoverlapping Overlapping Helmholtz Equation Preconditioner

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Frequency-domain Elastic wave Simulation Based on the Nonoverlapping Domain Decomposition Method

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American Journal of computational Mathematics 2013年第3期3卷 21-26页

作者： Wensheng Zhang Yinyun Dai Institute of Computational Mathematics and Scientific/Engineering Computing LSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing P.R.China

A new wave simulation technique for the elastic wave equation in the frequency domain based on a no overlapping domain decomposition algorithm is investigated. The boundary conditions and the finite difference discrimination of the elastic wave equation are derived. The algorithm of no overlapping domain decomposition method is given. The method solves the elastic wave equation by iteratively solving sub problems defined on smaller sub domains. Numerical computations both for homogeneous and inhomogeneous media show the effectiveness of the proposed method. This method can be used in the full-waveform inversion.

关键词： Finite Difference Nonoverlapping DDM Elastic wave Equation Wave Simulation Preconditioner Absorbing Boundary Conditions

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Finite-Difference Solution of the Helmholtz Equation Based on Two Domain Decomposition Algorithms

Finite-Difference Solution of the Helmholtz Equation Based o...

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2013 World Congress on engineering and Technology(CET 2013)

作者： Wensheng Zhang Yunyin Dai Institute of Computational Mathematics and Scientific/Engineering Computing LSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences

关键词： Finite Difference Domain Decomposition Nonoverlapping Overlapping Helmholtz Equation Preconditioner

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Frequency-domain Elastic wave Simulation Based on the Nonoverlapping Domain Decomposition Method

Frequency-domain Elastic wave Simulation Based on the Nonove...

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The Conference on Psychology and Applications(CPA 2013);International Conference on Molecular,Atomic,Nuclear and Particle Physics(MANPP 2013);International Conference on Mathematics and System science(MSS 2013)

作者： Wensheng Zhang Yinyun Dai Institute of Computational Mathematics and Scientific/Engineering Computing LSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences

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Full-waveform Velocity Inversion Based on the Acoustic Wave Equation

Full-waveform Velocity Inversion Based on the Acoustic Wave ...

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作者： Wensheng Zhang Jia Luo Institute of Computational Mathematics and Scientific/Engineering Computing LSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences

Full-waveform velocity inversion based on the acoustic wave equation in the time domain is investigated in this paper. The inversion is the iterative minimization of the misfit between observed data and synthetic data obtained by a numerical solution of the wave equation. Two inversion algorithms in combination with the CG method and the BFGS method are described respectively. Numerical computations for two models including the benchmark Marmousi model with complex structure are implemented. The inversion results show that the BFGS-based algorithm behaves better in inversion than the CG-based algorithm does. Moreover, the good inversion result for Marmousi model with the BFGS-based algorithm suggests the quasi-Newton methods can provide an important tool for large-scale velocity inversion. More computations demonstrate the correctness and effectives of our inversion algorithms and code.

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RETRACTED ARTICLE: Preface to the special issue on “Practical methods and rigorous theories in numerical algebra and scientific computing”

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Journal of engineering Mathematics 2014年第1期91卷 211-211页

作者： Bai, Zhong-Zhi Duff, Iain S. State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing People’s Republic of China R18 Rutherford Appleton Laboratory Harwell Oxford Campus Didcot UK

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Full-waveform Velocity Inversion Based on the Acoustic Wave Equation

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American Journal of computational Mathematics 2013年第3期3卷 13-20页

作者： Wensheng Zhang Jia Luo Institute of Computational Mathematics and Scientific/Engineering Computing LSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing P. R. China

关键词： Finite Difference Acoustic Wave Equation Full-waveform Inversion CG Method BFGS Method Marmousi Model

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A Subspace Version of the Powell–Yuan Trust-Region Algorithm for Equality Constrained Optimization

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Journal of the Operations Research Society of China 2013年第4期1卷 425-451页

作者： Geovani Nunes Grapiglia Jinyun Yuan Ya-xiang Yuan Departamento de Matemática Universidade Federal do ParanáCentro PolitécnicoCx.postal 19.08181531-980CuritibaParanáBrazil The Capes Foundation Ministry of Education of BrazilCx.postal 25070.040-020BrasíliaDistrito FederalBrazil State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesZhongguancundonglu 55Beijing 100190P.R.China

This paper studied subspace properties of the Celis–Dennis–Tapia(CDT)subproblem that arises in some trust-region algorithms for equality constrained opti*** analysis is an extension of that presented by Wang and Yuan(***.104:241–269,2006)for the standard trust-region *** suitable conditions,it is shown that the trial step obtained from the CDT subproblem is in the subspace spanned by all the gradient vectors of the objective function and of the constraints computed until the current *** on this observation,a subspace version of the Powell–Yuan trust-region algorithm is proposed for equality constrained optimization problems where the number of constraints is much lower than the number of variables. The convergence analysis is given and numerical results arealso reported.

关键词： Constrained optimization Trust-region methods Subspace methods

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Recent Development in Symmetries and Integrability of Difference Equations

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Frontiers of Mathematics in China 2013年第5期8卷 999-1000页

作者： Xingbiao HU Qingping LIU Senyue LOU Changzheng QU Youjin ZHANG Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Department of Mathematics China University of Mining and Technology~Beijing i00083 China Shanghai Key Laboratory of Trustworthy Computing East China Normal University Shanghai 200062 China Faculty of Sciences Ningbo University Ningbo 315211 China Center for Nonlinear Studies Ningbo University Ningbo 315211 China Department of Mathematical Sciences Tsinghua University Beijing 100084 China

Difference equations or discrete systems are mathematical models of various fields such as physics, chemistry, biology, and economics and have been subjects of extensive study of both pure mathematicians and applied mathematicians. Through its interaction with modern integrable systems, the theory of difference equations is enriched greatly and has been undergoing a rapid development. SIDE-10, the tenth of a series of biennial conferences devoted to Symmetries and Integrability of Difference Equations and related topics, was held during 10-16 June, 2012 at Ningbo, China. It was sponsored and supported by the National Natural science Foundation of China, Ningbo Association of science and Technology, Ningbo University, Academy of Mathematics and Systems science of Chinese Academy of sciences, China University of Mining and Technology （Beijing）, Tsinghua University, and Shanghai University. The conference attracted over 100 participants from more than a dozen of countries. During the conference, 44 contributed talks were arranged and the topics covered by the meeting include

关键词： DIFFERENCE algebra INTEGRABLE functions DIFFERENTIAL geometry

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