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Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrodinger Equation

Communications in computational Physics 2013年第7期14卷 393-411页

作者： Shanshan Jiang Lijin Wang Jialin Hong College of Science Beijing University of Chemical TechnologyBeijing 100029P.R.China School of Mathematical Sciences Graduate University of Chinese Academy of SciencesBeijing 100049P.R.China State Key Laboratory of Scientific and Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering ComputingAcademy of Mathematics and System ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100190P.R.China

In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger *** is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete *** experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision.

关键词： Stochastic nonlinear Schrodinger equations stochasticmulti-symplectic Hamiltonian systems multi-symplectic integrators

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Existence theory for Rosseland equation and its homogenized equation

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Applied mathematics and Mechanics(English Edition) 2012年第12期33卷 1595-1612页

作者：张乔夫崔俊芝 State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.

关键词： nonlinear elliptic equations fixed points mixed boundary conditions growthconditions maximal regularitys homogenized equation

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Residual-based a posteriori error control for Space-time finite element approximations of parabolic optimal control problems

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PAMM 2014年第1期14卷

作者： Wei Gong Michael Hinze Zhaojie Zhou Institute of Computational Mathematics The State Key Laboratory of Scientific and Engineering Computing (LSEC) Academy of Mathematics and Systems Science Chinese Academy of Sciences. University of Hamburg Department of Mathematics Bundesstraße 55 20146 Hamburg. School of Mathematics Science Shendong Normal University 250014 Ji'nan China.

In this paper we investigate a space-time finite element approximation of parabolic optimal control problems. The first order optimality conditions are transformed into an elliptic equation of fourth order in space and second order in time involving only the state or the adjoint state in the space-time domain. We derive a priori and a posteriori error estimates for the time discretization of the state and the adjoint state. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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True Amplitude Seismic Migration Operator in 3-D Heterogeneous Media

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Chinese Journal of Geophysics 2013年第3期47卷 577-582页

作者： Xing-Fu CUI Guan-Quan ZHANG Ya-Li WU Computer Center of Exploration & Development Research Institute of Liaohe Oilfield Branch Company PetroChina Panjin 124010 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy Sciences Beijing 100080 China

In this paper, one-way wave equations with true amplitude are established by the decomposition of the wave field operator for wave equation in 3-D heterogeneous media. Moreover, the Split Step Fourier (SSF) and Fourier Finite Difference (FFD) migration operators with true amplitude are derived mathematically and specific steps are given.

关键词： One-way wave equation True amplitude migration Split step Fourier migration operator Fourier finite difference migration operator

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Multifractal computation for nuclear classification and hepatocellular carcinoma grading

Multifractal computation for nuclear classification and hepa...

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10th IASTED International Conference on Biomedical engineering, BioMed 2013

作者： Atupelage, Chamidu Nagahashi, Hiroshi Yamaguchi, Masahiro Kimura, Fumikazu Abe, Tokiya Hashiguchi, Akinori Sakamoto, Michiie Department of Computational Intelligence and Systems Science Tokyo Institute of Technology Japan Imaging Science and Engineering Laboratory Tokyo Institute of Technology Japan Global Scientific Information and Computing Center Tokyo Institute of Technology Japan Department of Pathology School of Medicine Keio University Japan

ISBN: (纸本)9780889869530

Hepatocellular carcinoma (HCC) is graded mainly based on the characteristics of liver cell nuclei. This paper proposes a textural feature descriptor and a novel computational method for classifying liver cell nuclei and grading the HCC histological images. The proposed textural feature descriptor observes local and spatial characteristics of the texture patterns by using multifractal computation. The textural features are utilized for nuclear segmentation, fiber region detection, and liver cell nuclei classification. Four categories of nuclear features are computed such as texture, geometry, spatial distribution, and surrounding texture, for HCC classification. Significance of liver cell nuclei classification method is evaluated by classifying non-neoplastic and tumor tissues. Furthermore, characteristics of the liver cell nuclei were utilized for grading a set of HCC images into four classes and obtained 97.77% classification accuracy.

关键词： Grading

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Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

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Communications in computational Physics 2013年第1期13卷 107-128页

作者： Bo Zhang Benzhuo Lu Xiaolin Cheng Jingfang Huang Nikos P.Pitsianis Xiaobai Sun JAndrew McCammon Department of Computer Science Duke UniversityNC 27708USA Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100910China Center for Molecular Biophysics Oak Ridge National LaboratoryTN 37831USA Department of Mathematics University of North CarolinaChapel HillNC 27599USA Department of Electrical and Computer Engineering Aristotle UniversityThessaloniki54124Greece Department of Chemistry&Biochemistry Center for Theoretical Biological PhysicsDepartment of PharmacologyHoward Hughes Medical InstituteUniversity of CaliforniaSan DiegoCA 92093USA

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann(AFMPB)*** introduce and discuss the following components in order:the Poisson-Boltzmann model,boundary integral equation reformulation,surface mesh generation,the nodepatch discretization approach,Krylov iterative methods,the new version of fast multipole methods(FMMs),and a dynamic prioritization technique for scheduling parallel *** each component,we also remark on feasible approaches for further improvements in efficiency,accuracy and applicability of the AFMPB solver to largescale long-time molecular dynamics *** potential of the solver is demonstrated with preliminary numerical results.

关键词： Biomolecular system electrostatics Poisson-Boltzmann equation fast multipole methods mesh generation directed acyclic graph dynamic prioritization parallelization

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A Substructuring Preconditioner for Three-Dimensional Maxwell's Equations

Lecture Notes in Computational Science and Engineering

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Lecture Notes in computational Science and engineering 2013年 91卷 73-84页

作者： Hu, Qiya Shu, Shi Zou, Jun LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science The Chinese Academy of Sciences Beijing 100080 China School of Mathematics and Computational Science Xiangtan University Hunan 411105 China Department of Mathematics The Chinese University of Hong Kong Shatin N.T. Hong Kong

ISBN: (纸本)9783642352744

We propose a new nonoverlapping domain decomposition preconditioner for the discrete system arising from the edge element discretization of the three-dimensional Maxwell's equations. This preconditioner uses the simplest coarse edge element space induced by the coarse triangulation. We will show that the rate of the PCG convergence with this substructuring preconditioner is quasi-optimal, and is independent of large variations of the coefficients across the local interfaces. © Springer-Verlag Berlin Heidelberg 2013.

关键词： Maxwell equations

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An Absorbing-Layer Method of Seismic 3-D Migration for Irregular Survey Objects

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Chinese Journal of Geophysics 2013年第5期45卷 740-746页

作者： Yu-Xue WANG Guan-Quan ZHANG Rui-Fen ZHOU Yu-Ming ZHAO Department of Mathematics Daqing Petroleum Institute Daqing 151400 China Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China Department of Mechanical Engineering Daqing Petroleum Institute Daqing 151400 China No.2 Company of Drilling Daqing Petroleum Administration Brueau Daqing 163413 China

3-D seismic migration for an irregular acquisition geometry usually needs zero trace padding to form a regular area. The benefit of zero padding is easy to do 3-D migration, but it will reduce the computational efficiency and migration quality. In this paper we use an additional absorbing thin layer surrounding the irregular geometry instead of zero padding. It has greatly decreased computational cost and improved the migration quality. In order to form an absorbing layer, a damping factor is added to one-way wave equation. Since the wave field value attenuates quickly when the wave penetrates this thin layer, the reflection with the boundary condition that the wave-field value is zero is very small. Since the migration algorithm with the zero-boundary condition is easy to be implemented, 3-D migration for an irregular acquisition geometry can be done directly. The effectivity of this method is illustrated by processing the practical data.

关键词： Irregular acquisition geometry Migration Absorbing layer

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A discrete weighted Helmholtz decomposition and its application

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Numerische Mathematik 2013年第1期125卷 153-189页

作者： Hu, Q. Shu, S. Zou, J. LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematical and System Sciences The Chinese Academy of Sciences Beijing 100080 China Department of Mathematics Xiangtan University Hunan 411105 China Department of Mathematics The Chinese University of Hong Kong Shatin N.T. Hong Kong

We propose a discrete weighted Helmholtz decomposition for edge element functions. The decomposition is orthogonal in a weighted L~2 inner product and stable uniformly with respect to the jumps in the discontinuous weight function. As an application, the new Helmholtz decomposition is applied to demonstrate the quasi-optimality of a preconditioned edge element system for solving a saddle-point Maxwell system in non-homogeneous media by a non-overlapping domain decomposition preconditioner, i.e., the condition number grows only as the logarithm of the dimension of the local subproblem associated with an individual subdomain, and more importantly, it is independent of the jumps of the physical coefficients across the interfaces between any two subdomains of different media. Numerical experiments are presented to validate the effectiveness of the non-overlapping domain decomposition preconditioner.

关键词： discrete Helmholtz decomposition discrete element degradation WEIGHTING FUNCTIONS condition number decomposition logarithm (log) non-overlapping

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AFMPB: An adaptive fast multipole Poisson-Boltzmann solver for calculating electrostatics in biomolecular systems

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Computer Physics Communications 2013年第11期184卷 2618-2619页

作者： Lu, Benzhuo Cheng, Xiaolin Huang, Jingfang McCammon, J. Andrew Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China Center for Molecular Biophysics Oak Ridge National Laboratory Oak Ridge TN 37831 United States Department of Mathematics University of North Carolina at Chapel Hill Chapel Hill NC 27599-3250 United States Department of Chemistry and Biochemistry University of California San Diego CA 92093 United States Center for Theoretical Biological Physics University of California San Diego CA 92093 United States Department of Pharmacology Howard Hughes Medical Institute University of California San Diego CA 92093 United States

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of the fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://***/∼lubz/*** and a mirror site at http://***/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. © 2013 Elsevier B.V. All rights reserved.

关键词： Numerical methods

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