Numerical realization of the three-dimensional model of hydrodynamics for shallow water basins on a high-performance system

The paper is dedicated to the development and application of the 3D shallow water hydrodynamics model. Parallel realization of the deepest descent the symmetric successive over relaxation (SSOR) algorithm is presented for solving finite-difference equations obtained after discretization of the initial problem. Estimates for speeding up and increasing the efficiency of the parallel algorithm are given, and the flow velocity distribution for the Azov Sea (South of Russia) and the Lagoon Etang de Berre (South of France) are presented.     

A modified symmetric successive overrelaxation method for augmented systems

In this paper, we establish a modified symmetric successive overrelaxation (MSSOR) method, to solve augmented systems of linear equations, which uses two relaxation parameters. This method is an extension of the symmetric SOR (SSOR) iterative method. The convergence of the MSSOR method for augmented systems is studied. Numerical examples show that the new method is an efficient method.     

Additive polynomial preconditioners for parallel computers

We present a polynomial preconditioner that can be used with the conjugate gradient method to solve symmetric and positive definite systems of linear equations. Each step of the preconditioning is achieved by simultaneously taking an iteration of the SOR method and an iteration of the reverse SOR method (equations taken in reverse order) and averaging the results. This yields a symmetric preconditioner that can be implemented on parallel computers by performing the forward and reverse SOR iterations simultaneously. We give necessary and sufficient conditions for additive preconditioners to be positive definite.

We find an optimal parameter, ω, for the SOR-Additive linear stationary iterative method applied to 2-cyclic matrices. We show this method is asymptotically twice as fast as SSOR when the optimal ω is used.

We compare our preconditioner to the SSOR polynomial preconditioner for a model problem. With the optimal ω, our preconditioner was found to be as effective as the SSOR polynomial preconditioner in reducing the number of conjugate gradient iterations. Parallel implementations of both methods are discussed for vector and multiple processors. Results show that if the same number of processors are used for both preconditioners, the SSOR preconditioner is more effective. If twice as many processors are used for the SOR-Additive preconditioner, it becomes more efficient than the SSOR preconditioner when the number of equations assigned to a processor is small. These results are confirmed by the Blue Chip emulator at the University of Washington.     

A class of iterative methods for finite element equations

A general method in the form of an accelerated preconditioned iterative refinement method (including some wellknown iterative methods and direct factorization methods) is presented for the solution of symmetric, sparse matrix problems. An analysis of one such approximate factorization, the SSOR method, is given, and some inherently advantageous properties of the conjugate gradient acceleration method are pointed out. A comparison is made of the computational complexity and storage in the SSOR preconditioned method with some direct methods applied to second order discretized boundary value problems. For plane problems of average size the direct methods are somewhat faster if enough right hand sides are present. For large enough problems (large number of nodes) the iterative method is faster. For three-dimensional problems no Cholesky factorization method can compete with the SSOR preconditioned method, not even for average sized problems.     

On some ways of approximating inverses of banded matrices in connection with deriving preconditioners based on incomplete block factorizations

A unified approach of deriving band approximate inverses of band symmetric positive definite matrices is considered. Such band approximations to the inverses of successive Schur complements are required throughout incomplete block factorizations of block-tridiagonal matrices. Such block-tridiagonal matrices arise, for example, in finite element solution of second order elliptic differential equations. A sharp decay rate estimate for inverses of blocktridiagonal symmetric positive definite matrices is given in addition. Numerical tests on a number of model elliptic boundary value problems are presented comparing thus derived preconditioning matrices.     

Java multithreading‐based parallel approximate arrow‐type inverses

A new parallel shared memory Java multithreaded design and implementation of the explicit approximate inverse preconditioning, for efficiently solving arrow‐type linear systems on symmetric multiprocessor systems (SMPs), is presented. A new parallel algorithm for computing a class of optimized approximate arrow‐type inverse matrix is introduced. The performance on an SMP, using Java multithreading, is investigated by solving arrow‐type linear systems and numerical results are given. The parallel performance of the construction of the optimized approximate inverse and the explicit preconditioned generalized conjugate gradient square scheme, using a dynamic workload scheduling, is also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Application of the incomplete Cholesky factorization preconditioned Krylov subspace method to the vector finite element method for 3-D electromagnetic scattering problems

The incomplete Cholesky (IC) factorization preconditioning technique is applied to the Krylov subspace methods for solving large systems of linear equations resulted from the use of edge-based finite element method (FEM). The construction of the preconditioner is based on the fact that the coefficient matrix is represented in an upper triangular compressed sparse row (CSR) form. An efficient implementation of the IC factorization is described in detail for complex symmetric matrices. With some ordering schemes our IC algorithm can greatly reduce the memory requirement as well as the iteration numbers. Numerical tests on harmonic analysis for plane wave scattering from a metallic plate and a metallic sphere coated by a lossy dielectric layer show the efficiency of this method.     

新预处理ILUCG法求解稀疏病态线性方程组

大型稀疏病态线性方程组的高效求解在科学计算和工程应用中起着十分重要的作用.对于一般非对称正定的非奇异线性代数方程组,首先介绍常用的不完全LU分解预处理矩阵构造技术;然后给出SSOR预处理分解及其改进分解,并基于ILUCG思想提出新预处理ILUCG法同时给出收敛性分析;最后进行数值模拟仿真试验,数值结果表明该算法是有效可行的,且较之一般的预处理ILUCG方法该法在求解稀疏病态方程组方面具有优越性.     

Algebraic multigrid methods based on element preconditioning

This paper presents a new algebraic multigrid (AMG) solution strategy for large linear systems with a sparse matrix arising from a finite element discretization of some self-adjoint, second order, scalar, elliptic partial differential equation. The AMG solver is based on Ruge/Stübens method. Ruge/Stübens algorithm is robust for M-matrices, but unfortunately the “region of robustness“ between symmetric positive definite M-matrices and general symmetric positive definite matrices is very fuzzy.

For this reason the so-called element preconditioning technique is introduced in this paper. This technique aims at the construction of an M-matrix that is spectrally equivalent to the original stiffness matrix. This is done by solving small restricted optimization problems. AMG applied to the spectrally equivalent M-matrix instead of the original stiffness matrix is then used as a preconditioner in the conjugate gradient method for solving the original problem.

The numerical experiments show the efficiency and the robustness of the new preconditioning method for a wide class of problems including problems with anisotropic elements.     

牙周膜胶原纤维组织切片的显微图像配准

针对牙周膜胶原纤维组织切片在制作过程中对力度和方向非常敏感,极易造成组织变形和空间位移的问题,采用了一种有效的图像配准方法,以便后期对胶原纤维组织空间结构的重建。在Masson染色制成的兔牙周膜石蜡切片的基础上,利用高倍光学显微镜获得了牙周膜的序列切片图像;再采用基于正规步长梯度下降的二维刚性配准和基于对数域对称Demons微分同胚非刚性配准相结合的方法,对牙周膜序列切片图像进行级联配准。实验结果表明,相对于有限元非刚性配准而言,对数域对称Demons微分同胚非刚性配准方法具有较好的优势,其配准每张图片的平均时间为有限元法的3.1%,而配准均方误差平均为有限元法的89%。     

Recursive methods for estimating the radial basis function‐based state‐dependent autoregressive model

Identifying a nonlinear radial basis function‐based state‐dependent autoregressive (RBF‐AR) time series model is the basis for solving the corresponding prediction and control problems. This paper studies some recursive parameter estimation algorithms for the RBF‐AR model. Considering the difficulty of the nonlinear optimal problem arising in estimating the RBF‐AR model, an overall forgetting gradient algorithm is deduced based on the negative gradient search. A numerical method with a forgetting factor is provided to solve the problem of determining the optimal convergence factor. In order to improve the parameter estimation accuracy, the multi‐innovation identification theory is applied to develop an overall multi‐innovation forgetting gradient (O‐MIFG) algorithm. The simulation results indicate that the estimation model based on the O‐MIFG algorithm can capture the dynamics of the RBF‐AR model very well.     

Three‐stage multi‐innovation parameter estimation for an exponential autoregressive time‐series model with moving average noise by using the data filtering technique

This paper studies the data filtering‐based identification algorithms for an exponential autoregressive time‐series model with moving average noise. By means of the data filtering technique and the hierarchical identification principle, the identification model is transformed into three sub‐identification (Sub‐ID) models, and a filtering‐based three‐stage extended stochastic gradient algorithm is derived for identifying these Sub‐ID models. In order to improve the parameter estimation accuracy, a filtering‐based three‐stage multi‐innovation extended stochastic gradient (F‐3S‐MIESG) algorithm is developed by using the multi‐innovation identification theory. The simulation results indicate that the proposed F‐3S‐MIESG algorithm can work well.     

New method to improve the dynamic parameters of liquid crystals: Surface wave treatment of the interface between solid phase and mesophase

Abstract— As a new method to enhance the speed of liquid‐crystal‐display elements, the surface electromagnetic‐wave treatment of the conducting layers has been used. The procedure indicated above improves the control of nematic liquid crystals, decreases the number of layers in a sandwiched structure, decreases the magnitude of the supply voltage, and drastically decrease the relaxation time of the mesophase. The re‐orientation of the liquid‐crystal dipoles under field action can be observed with high speed. Thus, a new method of speed enhancement of pure or nano‐objects‐doped nematic liquid crystal has been demonstrated.     

Robust semiglobal swarm tracking of coupled harmonic oscillators with input saturation and external disturbance

The robust semiglobal swarm tracking problem of N coupled harmonic oscillators and 1 actual leader with input saturation and external disturbance on a directed communication topology is considered, in which the N coupled harmonic oscillators are referred to followers. First, the low‐and‐high gain feedback technique is introduced to construct a relative state‐dependent control algorithm. Then, an observer‐based control algorithm is designed based on the low‐and‐high gain feedback technique and the high‐gain observer design methodology. Sufficient conditions are derived to guarantee robust semiglobal swarm tracking for state‐feedback control and output‐feedback control, respectively. Numerical simulations are finally provided to verify the theoretic results.     

基于对称非负矩阵分解的重叠社区发现方法

针对重叠社区中的重要节点(重叠节点、中心节点、离群节点)及其固有的重叠社区结构的发现问题,提出了一种新的对称非负矩阵分解算法。首先将误差逼近项和非对称惩罚项的和作为目标函数,然后基于梯度更新的原则及非负约束条件推导出该算法。对5个实际网络进行了仿真实验,结果显示所提算法能将实际网络的重要节点及其固有的社区结构发现出来。从社区发现结果的平均导电率和算法的执行时间看,所提方法优于非负矩阵分解社区发现(CDNMF)方法;从准确率和召回率的调和平均值的加权平均值看,所提方法比较适合较大数据集的重叠社区发现。     

Accelerated convergence of the numerical simulation of incompressible flow in general curvilinear co-ordinates by discretizations on overset grids

The convergence rate of a methodology for solving incompressible flow in general curvilinear co-ordinates is analyzed. Overset grids (double-staggered grids type), each defined by the same boundaries as the physical domain are used for discretization. Both grids are Marker and Cell (MAC) quadrilateral meshes with scalar variables (pressure, temperature, etc.) arranged at the center and the Cartesian velocity components at the middle of the sides of the mesh. The problem was checked against benchmark solutions of natural convection in a squeezed cavity, heat transfer in concentric and eccentric horizontal cylindrical annuli and hot cylinder in a duct. Convergence properties of Poisson’s pressure equations which arise from application of the SIMPLE-like procedure are analyzed by several methods: successive overrelaxation, symmetric successive overrelaxation, modified incomplete factorization, and conjugate gradient. A genetic algorithm was developed to solve problems of numerical optimization of calculation time, in a space of iteration numbers and relaxation factors. The application provides a means of making an unbiased comparison between the double-staggered grids method and the standard interpolation method. Furthermore, the convergence rate was demonstrated with the well-known calculation of natural convection heat transfer in concentric horizontal cylindrical annuli. Calculation times when double staggered grids were used were 6–10 times shorter than those achieved by interpolation.     

A new probabilistic relaxation scheme and its application to edgedetection

This paper presents a new scheme for probabilistic relaxation labeling that consists of an update function and a dictionary construction method. The nonlinear update function is derived from Markov random field theory and Bayes' formula. The method combines evidence from neighboring label assignments and eliminates label ambiguity efficiently. This result is important for a variety of image processing tasks, such as image restoration, edge enhancement, edge detection, pixel classification, and image segmentation. The authors successfully applied this method to edge detection. The relaxation step of the proposed edge-detection algorithm greatly reduces noise effects, gets better edge localization such as line ends and corners, and plays a crucial role in refining edge outputs. The experiments show that our algorithm converges quickly and is robust in noisy environments     

Symmetric BEM formulations for 2-D steady-state and transit potential problems

This paper presents a new concept for symmetric boundary element method (SBEM) applicable to 2-D steady-state and transit potential problems. Two kinds of SBEM formulations are derived. Symmetry is obtained simply through matrix manipulation, and no hypersingularity appears. Therefore, SBEM is much easier than the traditional symmetric Galerkin BEM. Compared with the traditional asymmetric BEM, the present SBEM can reduce the computational cost for time domain problems only. However, when applied to BEM/FEM coupling procedure, SBEM can reduce the computational cost for both steady-state and time domain problems. Three numerical examples are included to illustrate the effectiveness and accuracy of the present formulations.     

A recursive hierarchical parametric estimation algorithm for nonlinear systems described by Wiener‐Hammerstein models

In this paper, a recursive hierarchical parametric estimation (RHPE) algorithm is proposed for stochastic nonlinear systems which can be described by Wiener‐Hammerstein (W‐H) mathematical models. The formulation of parameters estimation problem is based on the prediction error approach and the gradient techniques. The convergence analysis of the developed RHPE algorithm is derived using stochastic gradient‐based theory. Wiener‐Hammerstein hydraulic process is treated to prove the efficiency of the proposed approach.