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Rotated block triangular preconditioning based on PMHSS

Science China Mathematics 2013年第12期56卷 2523-2538页

作者： BAI Zhong-Zhi State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of Sciences

Based on the PMHSS preconditioning matrix, we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks, and analyze the eigen-properties of the corresponding preconditioned matrices. Numerical experiments show that these rotated block triangular pre- conditioners can be competitive to and even more efficient than the PMHSS preconditioner when they are used to accelerate Krylov subspeme iteration methods for solving block two-by-two linear systems with coefficient matrices possibly of nonsymmetric sub-blocks.

关键词： block two-by-two matrix PMHSS preconditioner block triangular preconditioning product-typepreconditioning eigen-properties

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A software platform for continuum modeling of ion channels based on unstructured mesh

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Computational Science and Discovery 2014年第1期7卷

作者： Tu, B. Bai, S.Y. Chen, M.X. Xie, Y. Zhang, L.B. Lu, B.Z. State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Center for System Biology Department of Mathematics Soochow University Suzhou215006 China

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson-Nernst-Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels. © 2014 IOP Publishing Ltd.

关键词： Finite element method

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Journal of the Operations Research Society of China

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Journal of the Operations Research Society of China 2013年第1期1卷 1-2页

作者： Ya-xiang Yuan State Key Laboratory of Scientific/Engineering Computing Institute of Comptational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesZhong Guan Cun Donglu 55Beijing 100190P.R.China

I am very pleased to present the first issue of Journal of the Operations Research Society of China.I believe that the launch of this new journal is not only a festival for the Operations Research Society of China,but... 详细信息

关键词： journal Society community.

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A Counter-Example to a Conjecture of Ben-Tal,Nemirovski and Roos

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Journal of the Operations Research Society of China 2013年第1期1卷 155-157页

In this short note,we present a counter-example to a conjecture made by Ben-Tal et *** SIAM ***.13:535–560,2002.

关键词： Counter-example Conjecture Quadratic constrained optimization Robust solution

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Search for heavy resonances decaying to a Z boson and a photon in pp collisions at s=13 TeV with the ATLAS detector

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Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics 2017年 764卷 11-30页

作者： Aaboud, M. Aad, G. Abbott, B. Abdallah, J. Abdinov, O. Abeloos, B. Aben, R. AbouZeid, O.S. Abraham, N.L. Abramowicz, H. Abreu, H. Abreu, R. Abulaiti, Y. Acharya, B.S. Adachi, S. Adamczyk, L. Adams, D.L. Adelman, J. Adomeit, S. Adye, T. Affolder, A.A. Agatonovic-Jovin, T. Agricola, J. Aguilar-Saavedra, J.A. Ahlen, S.P. Ahmadov, F. Aielli, G. Akerstedt, H. Åkesson, T.P.A. Akimov, A.V. Alberghi, G.L. Albert, J. Albrand, S. Alconada Verzini, M.J. Aleksa, M. Aleksandrov, I.N. Alexa, C. Alexander, G. Alexopoulos, T. Alhroob, M. Ali, B. Aliev, M. Alimonti, G. Alison, J. Alkire, S.P. Allbrooke, B.M.M. Allen, B.W. Allport, P.P. Aloisio, A. Alonso, A. Alonso, F. Alpigiani, C. Alshehri, A.A. Alstaty, M. Alvarez Gonzalez, B. Álvarez Piqueras, D. Alviggi, M.G. Amadio, B.T. Amako, K. Amaral Coutinho, Y. Amelung, C. Amidei, D. Amor Dos Santos, S.P. Amorim, A. Amoroso, S. Amundsen, G. Anastopoulos, C. Ancu, L.S. Andari, N. Andeen, T. Anders, C.F. Anders, G. Anders, J.K. Anderson, K.J. Andreazza, A. Andrei, V. Angelidakis, S. Angelozzi, I. Anger, P. Angerami, A. Anghinolfi, F. Anisenkov, A.V. Anjos, N. Annovi, A. Antel, C. Antonelli, M. Antonov, A. Anulli, F. Aoki, M. Aperio Bella, L. Arabidze, G. Arai, Y. Araque, J.P. Arce, A.T.H. Arduh, F.A. Arguin, J-F. Argyropoulos, S. Arik, M. Armbruster, A.J. Armitage, L.J. Arnaez, O. Arnold, H. Arratia, M. Arslan, O. Artamonov, A. Artoni, G. Artz, S. Asai, S. Asbah, N. Ashkenazi, A. Åsman, B. Asquith, L. Assamagan, K. Astalos, R. Atkinson, M. Atlay, N.B. Augsten, K. Avolio, G. Axen, B. Ayoub, M.K. Azuelos, G. Baak, M.A. Baas, A.E. Baca, M.J. Bachacou, H. Bachas, K. Backes, M. Backhaus, M. Bagiacchi, P. Bagnaia, P. Bai, Y. Baines, J.T. Baker, O.K. Baldin, E.M. Balek, P. Balestri, T. Balli, F. Balunas, W.K. Banas, E. Banerjee, Sw. Bannoura, A.A.E. Barak, L. Barberio, E.L. Barberis, D. Barbero, M. Barillari, T. Barisits, M-S Barklow, T. Barlow, N. Barnes, S.L. Barnett, B.M. Barnett, R.M. Barnovska-Blenessy, Z. Baroncelli, A. Barone, G. Barr, A.J. Barranco Navarro, L. Barreiro, F. Barreiro Gui Department of Physics University of Adelaide Adelaide Australia Physics Department SUNY Albany Albany NY United States Department of Physics University of Alberta Edmonton AB Canada Department of Physics Ankara University Ankara Turkey Istanbul Aydin University Istanbul Turkey Division of Physics TOBB University of Economics and Technology Ankara Turkey LAPP CNRS/IN2P3 Université Savoie Mont Blanc Annecy-le-Vieux France High Energy Physics Division Argonne National Laboratory Argonne IL United States Department of Physics University of Arizona Tucson AZ United States Department of Physics The University of Texas at Arlington Arlington TX United States Physics Department University of Athens Athens Greece Physics Department National Technical University of Athens Zografou Greece Department of Physics The University of Texas at Austin Austin TX United States Institute of Physics Azerbaijan Academy of Sciences Baku Azerbaijan Institut de Física d'Altes Energies (IFAE) The Barcelona Institute of Science and Technology Barcelona Spain Institute of Physics University of Belgrade Belgrade Serbia Department for Physics and Technology University of Bergen Bergen Norway Physics Division Lawrence Berkeley National Laboratory University of California Berkeley CA United States Department of Physics Humboldt University Berlin Germany Albert Einstein Center for Fundamental Physics Laboratory for High Energy Physics University of Bern Bern Switzerland School of Physics and Astronomy University of Birmingham Birmingham United Kingdom Department of Physics Bogazici University Istanbul Turkey Department of Physics Engineering Gaziantep University Gaziantep Turkey Istanbul Bilgi University Faculty of Engineering and Natural Sciences Istanbul Turkey Bahcesehir University Faculty of Engineering and Natural Sciences Istanbul Turkey Centro de Investigaciones Universidad Antonio Narino Bogota Colombia INFN Sezione di Bologna Italy Dipartimento di Fis

This Letter presents a search for new resonances with mass larger than 250 GeV, decaying to a Z boson and a photon. The dataset consists of an integrated luminosity of 3.2 fb−1 of pp collisions collected at s=13 TeV w... 详细信息

This Letter presents a search for new resonances with mass larger than 250 GeV, decaying to a Z boson and a photon. The dataset consists of an integrated luminosity of 3.2 fb⁻¹ of pp collisions collected at s=13 TeV with the ATLAS detector at the Large Hadron Collider. The Z bosons are identified through their decays either to charged, light, lepton pairs (e⁺e⁻, μ⁺μ⁻) or to hadrons. The data are found to be consistent with the expected background in the whole mass range investigated and upper limits are set on the production cross section times decay branching ratio to Zγ of a narrow scalar boson with mass between 250 GeV and 2.75 TeV. © 2016 The Author(s)

关键词： Z bosons CROSS sections (Nuclear physics) PHOTON-photon interactions LARGE Hadron Collider (France & Switzerland) DILEPTON production NUCLEAR counters

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A New Analysis on the Barzilai-Borwein Gradient Method

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Journal of the Operations Research Society of China 2013年第2期1卷 187-198页

作者： Yu-Hong Dai State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100190P.R.China

Due to its simplicity and efficiency,the Barzilai and Borwein(BB)gradi-ent method has received various attentions in different *** paper presents a new analysis of the BB method for two-dimensional strictly convex quadratic *** analysis begins with the assumption that the gradient norms at the first two iterations are *** show that there is a superlinear convergence step in at most three consecutive ***,we provide a better convergence relation for the BB *** influence of the starting point and the condition number to the convergence rate is comprehensively addressed.

关键词： Unconstrained optimization Barzilai and Borwein gradient method Quadratic function R-superlinear convergence Condition number

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Feasible Barzilai-Borwein-like methods for extreme symmetric eigenvalue problems

Feasible Barzilai-Borwein-like methods for extreme symmetric...

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作者： Jiang, Bo Dai, Yu-Hong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing 100190 China

This paper aims to study feasible Barzilai-Borwein (BB)-like methods for extreme symmetric eigenvalue problems. For the two-dimensional case, we establish the local superlinear convergence result of FLBB, FSBB, FABB, and FADBB algorithms. A counter-example is also given, showing that the algorithms may cycle or stop at a non-stationary point. In order to circumvent the difficulty, we propose a safeguard in choosing the stepsize. We also adopt an adaptive non-monotone line search with an improved line search to ensure the global convergence of AFBB-like methods. Numerical experiments on a set of test problems from UF Sparse Matrix Collection demonstrate that, comparing several available codes including eigs, irbleigs and jdcg, AFBB-like methods are very useful for large-scale sparse extreme symmetric eigenvalue problems. © 2013 Copyright Taylor and Francis Group, LLC.

关键词： Eigenvalues and eigenfunctions

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A trust region method based on a new affine scaling technique for simple bounded optimization

A trust region method based on a new affine scaling techniqu...

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作者： Wang, Xiao Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences PO Box 2719 Beijing 100190 China

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 depends on the distances of the current iterate to the boundaries, the gradient of the objective function and the trust region radius. This scaling technique is different from the existing ones. It is motivated by our analysis of the linear programming case. The trial step is obtained by minimizing the quadratic approximation to the objective function in the scaled trust region. It is proved that our algorithm guarantees that at least one accumulation point of the iterates is a stationary point. Preliminary numerical experience on problems with simple bounds from the CUTEr collection is also reported. The numerical performance reveals that our method is effective and competitive with the famous algorithm LANCELOT. It also indicates that the new scaling technique is very effective and might be a good alternative to that used in the subroutine fmincon from Matlab optimization toolbox. © 2013 Copyright Taylor and Francis Group, LLC.

关键词： Nonlinear programming

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Advances in biomolecular surface meshing and its applications to mathematical modeling

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Chinese Science Bulletin 2013年第16期58卷 1843-1849页

作者： CHEN MinXin LU BenZhuo Center for System Biology Department of Mathematics Soochow University State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics Academy of Mathematics and Systems Science National Center for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences

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).

关键词：数学建模分子表面应用啮合生物表面网格分子结构分子建模

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A Cone Constrained Convex Program:Structure and Algorithms

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Journal of the Operations Research Society of China 2013年第1期1卷 37-53页

作者： Liqun Qi Yi Xu Ya-Xiang Yuan Xinzhen Zhang Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomKowloonHong KongChina State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAMSSChinese Academy of SciencesZhong Guan Cun Donglu 55Beijing100190P.R.China Department of Mathematics School of ScienceTianjin UniversityTianjin300072China

In this paper,we consider the positive semi-definite space tensor cone constrained convex program,its structure and *** study defining functions,defining sequences and polyhedral outer approximations for this positive semidefinite space tensor cone,give an error bound for the polyhedral outer approximation approach,and thus establish convergence of three polyhedral outer approximation algorithms for solving this *** then study some other approaches for solving this structured convex *** include the conic linear programming approach,the nonsmooth convex program approach and the bi-level program *** numerical examples are presented.

关键词： Convex program Space tensor Positive semi-definiteness Cone Algorithms

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