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

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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Kinetics of diffusion-controlled enzymatic reactions with charged substrates

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PMC Biophysics 2010年第1期3卷 1-5页

作者： Lu, Benzhuo McCammon, J Andrew 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 100190 China Department of Chemistry and Biochemistry Center for Theoretical Biological Physics Department of Pharmacology Howard Hughes Medical Institute La Jolla CA 92093-0365 United States

The Debye-Hückel limiting law (DHL) has often been used to estimate rate constants of diffusion-controlled reactions under different ionic strengths. Two main approximations are adopted in DHL: one is that the solution of the linearized Poisson-Boltzmann equation for a spherical cavity is used to estimate the excess electrostatic free energy of a solution;the other is that details of electrostatic interactions of the solutes are neglected. This makes DHL applicable only at low ionic strengths and dilute solutions (very low substrate/solute concentrations). We show in this work that through numerical solution of the Poisson-Nernst-Planck equations, diffusion-reaction processes can be studied at a variety of conditions including realistically concentrated solutions, high ionic strength, and certainly with non-equilibrium charge distributions. Reaction rate coefficients for the acetylcholine-acetylcholinesterase system are predicted to strongly depend on both ionic strength and substrate concentration. In particular, they increase considerably with increase of substrate concentrations at a fixed ionic strength, which is open to experimental testing. This phenomenon is also verified on a simple model, and is expected to be general for electrostatically attracting enzyme-substrate systems. © 2010 Lu and McCammon.

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A new reconstruction algorithm in tomography with geometric feature-preserving regularization

A new reconstruction algorithm in tomography with geometric ...

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International Conference on BioMedical engineering and Informatics (BMEI)

作者： Chong Chen Guoliang Xu Institute of Computational Mathematics and Scientific Engineering Computing State Key Laboratory of Scientific and Engineering Computing Chinese Academy of Sciences Beijing China Institute of Computational Mathematics and Scientific Engineering Computing State Key Laboratory of Scientific and Engineering Computing Chinese Academy and Sciences Beijing China

We present a new optimization-based reconstruction model with geometric feature-preserving regularization. The previous construction approach of optimization-based requires generally solving a tremendously large discrete linear system. In addition, the analytic algorithms, such as, back-projection related methods, Fourier transform based reconstruction algorithms, are sensitive to noise. These disadvantages motivate us naturally to present a new optimization-based regularization algorithm, as distinct from traditionally constructing a discrete linear system, that is based upon a continuous energy functional model like analytic one. Some theoretical derivations and numerical computing of our model are discussed. Experimental results illustrate the desirable performance of the algorithm under various noiseless data situations. And the geometric feature-preserving regularizer is used in numerical simulations to demonstrate the robustness and effectiveness of the algorithm under various contaminated data scenarios.

关键词： Image reconstruction Noise Distributed databases mathematical model computational modeling Numerical models Computed tomography

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Hybrid Distributed-/Shared-Memory Parallelization For Re-initializing Level Set Functions

Hybrid Distributed-/Shared-Memory Parallelization For Re-ini...

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IEEE International Conference on High Performance computing and Communications (HPCC)

作者： Oliver Fortmeier H. Martin Bucker Institute for Scientific Computing Center for Computational Engineering Science (CCES) RWTH Aachen University Aachen Germany

The ever-increasing power of high-performance computers and advances in numerical techniques make possible the realistic study of two-phase flow problems in three spatial dimensions. Unfortunately, today, there is often still a gap between the design of numerical algorithms and the characteristics of the hardware on which the algorithms are executed. For the solution of a particular sub problem of a two-phase flow problem, we develop a numerical algorithm that aims to match the architecture of a cluster of nodes with multi-core chips. The algorithm is concerned with the re-initialization of level set function used to keep track of the interface between two phases of a fluid. It consists of a hybrid MPI/OpenMP parallelization strategy, using a domain decomposition approach on the outermost level of parallelization. On the inner level, a parallel region handles an individual sub domain. So, a domain decomposition approach based on MPI is combined with an OpenMP approach leading to a hybrid distributed-/shared-memory parallelization. Numerical experiments show that using such a hybrid strategy scales better than a pure MPI parallelization on two different Xeon-based clusters of quad-core processors using up to 1024 cores.

关键词： Level set Nearest neighbor searches Parallel algorithms mathematical model Program processors Equations

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Flexible alignment of images using B-spline reparameterization and L2-gradient flows

Flexible alignment of images using B-spline reparameterizati...

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Congress on Image and Signal Processing, CISP

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

In this paper, we present a new flexible alignment method to align two or more similar images. By minimizing an energy functional measuring the difference of the initial image and target image, a L 2 -gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and a semi-implicit Euler scheme in the temporal direction. The experimental results show that the proposed method is efficient, effective and capable of capturing large variation of the initial and the target images.

关键词： Spline Image registration Linear systems Correlation Equations

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Wave propagation and boundary absorbing with the high order finite element method

Wave propagation and boundary absorbing with the high order ...

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第七届计算物理国际会议

作者： Wensheng Zhang Chaowei Wang 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 P.O.Box 2719 100190

Wave propagation simulation has important applications in oil ***, the finite difference method is the most popular numerical method for simulation of wave propa gation as it has high computational efficiency and is easy to handle boundary *** this paper, we focus on how to simulate wave propagation efficiently by high order Lagrange element on triangular *** the mass matrix must be inverted at each time step, the mass lumping technique is required to improve *** low order such as linear Lagrange element, the mass lumping can be implemented by using the quadratic rules for numerical integration, but it is not obvious for high order Lagrange finite element.

关键词： wave equation finite element mass lumping boundary absorbing

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Fast Facial Fitting Based on Mixture Appearance Model with 3D Constraint

Fast Facial Fitting Based on Mixture Appearance Model with 3...

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Chinese Conference on Pattern Recognition (CCPR)

作者： Xiangsheng Huang Lujin Gong Xiaoyan Wang Institute of Automation Chinese Academy and Sciences Beijing China State Key Laboratory of Scientific and Engineering Computing AMSS Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy and Sciences Beijing China College of Computer Science and Technology Zhejiang University of Technology Hangzhou China

Fast facial points fitting plays an important role in applications such as Human-Computer Interaction, entertainment, surveillance, and is highly relevant to the techniques of facial expression analysis, face recognition, 3D face model generation, etc. Active Appearance Models (AAMs) are generative models commonly used to fit face. They are sensitive to illumination and expression changes because they use only raw intensity to build observation models. In this paper, a real time facial points fitting approach using mixture observation models is presented. Furthermore, the 3D modes are used to constrain the AAM so that it can only generate model instances that can also be generated with the 3D modes. Finally, we give a derivative process for fast energy minimization using the inverse compositional algorithm. A coarse-to-fine fitting strategy is used for realtime and robust facial points fitting. We apply this algorithm to facial expression cloning of 3D Avatar system. Experimental results demonstrate that fitting the AAM with mixture observation models and 3D constraint outperforms other classical algorithms.

关键词： Three dimensional displays Shape Active appearance model Solid modeling Face Pixel Robustness

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Electric-potential reconstructions of single particles using L2-gradient flows

Electric-potential reconstructions of single particles using...

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International Conference on BioMedical engineering and Informatics (BMEI)

作者： Ming Li Guoliang Xu Carlos O. S. Sorzano Roberto Melero Chandrajit Bajaj State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy and Sciences Beijing China Biocomputing Unit. Centro Nacional de Biotecnologia CSIC Campus University Autonoma Madrid Mexico Austin Department of Computer Sciences and Institute of Computational Engineering & Sciences University of Texas Austin Austin TX USA

In this paper, we present a stable, reliable and robust method for reconstructing a three dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy functional consisting of a fidelity term and a regularization term, a L 2 -gradient flow is derived. The flow is integrated by a finite element method in the spatial direction and an explicit Euler scheme in temporal direction. The experimental results show that the proposed method is efficient and effective.

关键词： Image reconstruction Spline Three dimensional displays Adenoviruses Microscopy Finite element methods

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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface

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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2010年 6130 LNCS卷 VI页

作者： Mourrain, Bernard Schaefer, Scott Xu, Guoliang GALAAD Inria Méditerranée 2004 route des Lucioles 06902 Sophia Antipolis Cedex France Texas A and M University Department of Computer Science College Station TX 77843-3112 United States Chinese Academy of Science Institute of Computational Mathematics and Scientific/Engineering Computing Beijing 100080 China

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A Parallel Algorithm for Adaptive Local Refinement of Tetrahedral Meshes Using Bisection

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Numerical mathematics(Theory,Methods and Applications) 2009年第1期2卷 65-89页

作者： Lin-Bo Zhang 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 100080 China.

Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.

关键词： Adaptive refinement bisection tetrahedral mesh parallel algorithm MPI.

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