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2012全国高性能计算学术年会

作者： Yan Xie 谢妍 Bin Tu 涂斌 Benzhuo Lu 卢本卓 Linbo Zhang 张林波 (The State Key Laboratory of Scientific and Engineering Computing(LSEC) Academy of Mathematics and 中国科学院数学与系统科学研究院科学与工程计算国家重点实验室北京100190

本文说明了如何利用三维并行自适应有限元软件包PHG求解生物分子溶液体系的非线性Poisson-Boltzmann方程及电扩散方程，并介绍了一种解决这类问题的新方法，它将网格生成与自适应计算过程结合在一起，可自动产生合适的网格，避免复杂的... 详细信息

本文说明了如何利用三维并行自适应有限元软件包PHG求解生物分子溶液体系的非线性Poisson-Boltzmann方程及电扩散方程，并介绍了一种解决这类问题的新方法，它将网格生成与自适应计算过程结合在一起，可自动产生合适的网格，避免复杂的曲面网格生成步骤。之前的网格生成工作按照：(1) TMSmesh生成高斯曲面的三角网格;(2) TransforMesh删除自相交的三角网格;(3) ISO2Mesh提高表面网格质量，这三个步骤。而基于PHG的自适应加密模块可以在逐次调整网格的同时保持动态负载平衡，高效得到计算网格用于近似求解非线性Poisson-Boltzmann方程。计算了小球模型和DNA模型，分别从误差指示子下降阶和溶剂化能收敛的角度验证了新方法的有效性。

关键词：非线性方程并行计算有限元方法自适应网格生成

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Fast algorithm for beamforming problems in distributed communication of relay networks

Fast algorithm for beamforming problems in distributed commu...

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International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Cong Sun Yaxiang Yuan State Key Laboratory of Scientific and Engineering Computing ICMSEC AMSS Chinese Academy and Sciences Beijing China

A sequential quadratic programming (SQP) method is pro posed to solve the distributed beamforming problem in multiple relay networks. The problem is formulated as the minimization of the total relay transmit power, subject to individual signal-to-interference-and-noise ratio constraints at each receiver, which is a nonconvex quadratic constraint quadratic programming. Rather than solving its semi-definite programming (SDP) relaxation, we apply the SQP method to solve its tightened form to replace its inequality constraints with equalities. Its global convergence is guaranteed. Simulations show that it not only runs much faster, but also performs as good as SDP for calculation results.

关键词： Relays Array signal processing Quadratic programming Interference Signal to noise ratio Peer to peer computing

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Flexible Alignment of Images Using B-Spline Reparameterization Based on Multi-resolution Representations— Computational Methods

Flexible Alignment of Images Using B-Spline Reparameterizati...

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2011 Fourth International Conference on Intelligent Computation Technology and Automation(2011年第四届智能计算技术与自动化国际会议 ICICTA 2011)

作者： Yanmei Zheng Guoliang Xu State Key Laboratory of Scientific and Engineering Computing Institute of Computational MathematicsAcademy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China

we present a new flexible alignment method to align two or more similar images, especially biological images. By minimizing an energy functional measuring the difference of the initial image and target image, an L2 -gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in the temporal direction. Multi-resolution representations are used for achieving efficient multi-scale alignment The experimental results on 2D images show that the proposed method is efficient, effective, robust and capable of capturing the variation of the initial and target images, from large to small scale.

关键词： Flexible alignment Z2 -gradient flow Bi-cubic B-sptine Finite element method Multi-resolution representation

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Hierarchical-control-based output synchronization of coexisting attractor networks

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Chinese Physics B 2010年第2期19卷 127-134页

作者：宋运忠唐贻发 Complex Networks Laboratory College of Electrical Engineering&AutomationHenan Polytechnic University State Key Laboratory of Scientific&Engineering Computing Academy of Mathematics&Systems ScienceChinese Academy of Sciences

This paper introduces the concept of hierarchical-control-based output synchronization of coexisting attractor networks. Within the new framework, each dynamic node is made passive at first utilizing intra-control around its own arena. Then each dynamic node is viewed as one agent, and on account of that, the solution of output synchronization of coexisting attractor networks is transformed into a multi-agent consensus problem, which is made possible by virtue of local interaction between individual neighbours; this distributed working way of coordination is coined as inter-control, which is only specified by the topological structure of the network. Provided that the network is connected and balanced, the output synchronization would come true naturally via synergy between intra and inter-control actions, where the rightness is proved theoretically via convex composite Lyapunov functions. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.

关键词： hierarchical control passive control composite Lyapunov function the Newton--Leipnik equation attractor

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On the complexity of leakage interference minimization for interference alignment

On the complexity of leakage interference minimization for i...

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IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

作者： Ya-Feng Liu Yu-Hong Dai Zhi-Quan Luo State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy and Sciences Beijing China Department of Electronic and Computer Engineering University of Minnesota Minneapolis MN USA

For a general MIMO interference channel, we can determine the feasibility of linear interference alignment via minimizing the leakage interference. This paper gives a complete complexity characterization of the leakage interference minimization problem. It is shown that, when each transmitter (receiver) is equipped with at least three antennas and each receiver (transmitter) is equipped with at least two antennas, the problem of checking whether the interference in the network can be perfectly aligned is strongly NP-hard. Moreover, when each transmit/receive node is equipped with two or more antennas, leakage interference minimization can not be solved (even approximately) in polynomial time, unless P = NP.

关键词： Interference Polynomials Minimization MIMO Complexity theory Receiving antennas

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On the error bounds of nonconforming finite elements

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Science China Mathematics 2010年第11期53卷 2917-2926页

作者： MAO ShiPeng SHI ZhongCi The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L2 norms under the regularity assumption u ∈ H1+s(Ω) with any s > 0. The extensions to other related problems are possible.

关键词： nonconforming finite elements Cea’s lemma error estimates

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Sparse two-sided rank-one updates for nonlinear equations

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Science China Mathematics 2010年第11期53卷 2907-2915页

作者： CHENG MingHou & DAI YuHong state key laboratory of scientific and engineering computing, Institute of Computational Mathematics and scientific/engineering computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 1. State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale sparse problems. To overcome this difficulty, we propose sparse extensions of the TR1 update and give some convergence analysis. The numerical experiments show that some of our extensions are superior to the TR1 update method. Some convergence analysis is also presented.

关键词： TR1 update Broyden rank-one update sparsity

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TWO-SCALE FINITE ELEMENT GREEN'S FUNCTION APPROXIMATIONS WITH APPLICATIONS TO ELECTROSTATIC POTENTIAL COMPUTATION

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Journal of Systems Science & Complexity 2010年第1期23卷 177-193页

作者： Ying YANG Aihui ZHOU Department of Computational Science and Mathematics Guilin University of Electronic Technology Guilin 541004 China. The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China.

In this paper,a two-scale finite element approach is proposed and analyzed for approximationsof Green's function in *** approach is based on a two-scale finite elementspace defined,respectively,on the whole domain with size H and on some subdomain containing singularpoints with size h (h << H).It is shown that this two-scale discretization approach is very *** particular,the two-scale discretization approach is applied to solve Poisson-Boltzmann equationssuccessfully.

关键词： Error analysis finite element Green＇s function Poisson-Boltzmann equation two-scale.

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Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrodinger Equation with Trapped Term

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Communications in Computational Physics 2010年第3期7卷 613-630页

作者： Jialin Hong Linghua Kong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and System ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100190China School of Mathematics and Information Science Jiangxi Normal UniversityNanchangJiangxi 330022China

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.

关键词： Schrodinger equation with trapped term multi-symplectic scheme Fourier spectral method conservation law split-step method

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Convergence analysis of the adaptive finite element method with the red-green refinement

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Science China Mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2,? & SHI ZhongCi 1 1 state key laboratory of scientific and engineering computing, Institute of Computational Mathematics and scientific/engineering computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 2 key laboratory of Mathematics and Applied Mathematics (Peking University), Ministry of Education and School of Mathematical Sciences, Peking University, Beijing 100871, China 3 Graduate University of Chinese Academy of Sciences, Beijing 100190, China 1. State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Mathematics and Applied Mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

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