求解Maxwell线性元鞍点系统的基于HX预条件子的Uzawa算法

首先对含跳系数的H~1型和H(curl)型椭圆问题的线性有限元方程,分别设计了基于AMG预条件子和基于节点辅助空间预条件子(HX预条件子)的PCG法.数值实验表明,算法的迭代次数基本不依赖于系数跳幅和离散网格"尺寸".然后以此为基础,对Maxwell方程组鞍点问题的第一类N(e)d(e)lec线性棱元离散系统设计并分析了一种基于HX预条件子的Uzawa算法.当系数光滑时,理论上证明了算法的收敛率与网格规模无关.数值实验表明,新算法对跳系数情形也是高效和稳定的.     

一种变系数扩散问题有限体积格式的高效预条件子

本文针对一类含变跳系数的扩散问题,在矩形网格下构造了一种节点型MACH类有限体积格式.将相应常跳系数辅助扩散问题离散格式的系数矩阵的逆作为其预条件子.利用该系数矩阵的特殊代数结构,通过降维处理技术和快速傅里叶变换等,为预条件子(该矩阵逆)的数学行为设计了一种低运算复杂度(O(Nln(N)))的直接法.数值实验验证了基于该预条件子的PCG算法的高效性和稳健性.     

一种改进数据流图的子字并行程序表示方法

论文致力于对图像处理算法的串行C程序进行子字并行分析,并重定向到带有多媒体扩展的通用处理器和多媒体专用嵌入式微处理器。图像处理算法的特点决定其是内在可并行的,这种并行粒度介于数据并行(DLP)和指令级并行(ILP)之间,称之为子字并行。但是,当前的编译技术很难充分挖掘和定位程序基本块内的子字并行,对此设计了一种基于流图程序表示的编译方法,能够从串行程序中显式地定位子字并行。扩展了编译器的功能,增加了特定的模式库,基于模式识别的控制流和数据流分析后,产生特定的子字并行流图(SWFG,Sub-WordFlowGraph),并将该图作为中间表示,提供给子字并行指令选择,进而实现有效的子字并行代码产生。     

并行子空间优化在无人机总体设计中的应用

飞机设计是一个多学科的复杂的系统工程,各个学科通常相互影响、相互耦合.这使得飞机设计过程日趋复杂,设计周期越来越长,开发成本越来越高,而并行子空间优化(CSSO)是解决这些问题的一种有效方法.文中对基于神经网络响应面的并行子空间优化算法及其在无人机总体方案设计优化中的应用进行了研究.并行子空间优化算法将多学科耦合的无人机设计优化问题分解为不同的子空间问题,在不同的子空间中建立各自的神经网络响应面,通过响应面完成各子空间之间的数据交换与协调,以此来逼近设计空间最优解.应用结果表明,CSSO算法能有效地应用于无人机总体方案优化设计.     

子字并行加法器的研究与实现

子字并行加法器能够有效提高多媒体应用程序的处理性能。基于门延迟模型对加法器原理及性能进行了分析,设计了进位截断和进位消除两种子字并行控制机制。在这两种机制的指导下,实现了多种子字并行加法器,并对它们的性能进行了比较和分析。结果表明进位消除机制相对于进位截断机制需要较短的延时,较少的逻辑门数以及较低的功耗。在各种子字并行加法器中,Kogge-Stone加法器具有最少的延迟时间,RCA加法器具有最少的逻辑门数和最低的功耗。研究结果可以用于指导子字并行加法器的设计与选择。     

位平面编码存储优化算法及FPGA设计

提出一种基于子块的存储优化算法,可用于解决现有JPEG2000位平面编码器中存在的访问编码块存储器模式失配问题.采用将编码块划分成4×4的子块独立进行编码的策略,将访问同一小波系数的时间间隔从3N2Δt减少至48Δt,同时将访问编码块存储器的次数从(3K-2)N2降低至N2W.该算法不仅兼容现有各种加速技术,而且增加了子块并行的机会.基于FPGA平台实现了一种子块并行合并样本并行的位平面编码器结构,能够将编码时间复杂度从O(N2)降低至O(N),同时节省状态信息存储39%以上.实验结果表明,与目前最快的三层并行结构相比,文中设计的加速比达到了1.3.     

JPEG 2000系数位平面编码的FPGA设计

研究JPEG 2000 标准中系数位平面编码的硬件实现问题,提出一种适合ASIC实现的结构,在保证编码速度的前提下,最大限度减小了片内小波系数缓存量,解决了扫描过程中如何对系数状态字进行读写的问题,大大减少了系统访问系数状态字的频率。设计中幅度细通道和清理通道并行工作,使编码时间比传统非并行工作减少30%以上。在FPGA上对设计进行了仿真验证。     

一种求解H(curl)型椭圆问题的高效并行预条件子及并行实现

本文为一类H(curl)型椭圆问题的线性棱有限元方程,构造了一种基于节点辅助空间预条件子(HX预条件子)和基于简单粗空间的非重叠区域分解相结合的预条件子,并为该预条件子设计了并行算法,编制了基于MPI+OpenMP二级并行架构的并行程序.数值实验结果表明基于该预条件子的并行PCG法具有良好的算法可扩展能力和并行可扩展能力.     

一种分布式并行参数优化算法设计及其应用

并行参数优化算法在科学计算中有广泛应用。随着Spark等分布式平台的快速发展,越来越多并行参数优化算法开始采用分布式平台进行实现。如何在Spark等平台上设计优化算法,避免其运行效率受到框架固定时间开销和网络I/O影响,已经成为亟需解决的问题。本文设计一种分布式与单机多核并行结合的参数优化算法,将其划分为调度部分和独立子问题部分,单机多核并行算法处理子问题,分布式平台负责子问题的跨节点并行。碳通量模型参数优化的实验结果表明,改进的算法能有效节省时间开销,更快地搜索参数空间。     

求解频率分配问题的自适应的多种群蚁群算法

提出一种自适应的多种群蚁群算法用于求解频率分配问题．算法将蚂蚁群体划分为若干个子群体，每个子群体的蚂蚁并行地进行优化．在寻优过程中，算法为每个蚂蚁子群体定义一个收敛系数，根据收敛系数来决定子群体内部的路径的选择和信息量的更新．算法同时根据各个子群体的解的质量和分布情况来自适应地决定信息交流策略，包括选择信息交流的对象和调节信息交流的周期以及信息更新策略，以取得各蚂蚁子群体中解的多样性和收敛性之间的动态平衡．对固定频率分配和最小跨度频率分配问题在并行计算机上的实验结果表明，本文算法不仅具有较快的全局收敛速度，而且有高质量的解和高的效率．     

Analysis of the nonlinear Uzawa algorithm for symmetric saddle point problems

In this paper we discuss the convergence behaviour of the nonlinear Uzawa algorithm for solving saddle point problems presented in a recent paper of Cao [Z.H. Cao, Fast Uzawa algorithm for generalized saddle point problems, Appl. Numer. Math. 46 (2003), pp. 157–171]. For a general case, the results on the convergence of the algorithm are given.     

Multilevel Gradient Uzawa Algorithms for Symmetric Saddle Point Problems

In this paper, we introduce a general multilevel gradient Uzawa algorithm for symmetric saddle point systems. We compare its performance with the performance of the standard Uzawa multilevel algorithm. The main idea of the approach is to combine a double inexact Uzawa algorithm at the continuous level with a gradient type algorithm at the discrete level. The algorithm is based on the existence of a priori multilevel sequences of nested approximation pairs of spaces, but the family does not have to be stable. To ensure convergence, the process has to maintain an accurate representation of the residuals at each step of the inexact Uzawa algorithm at the continuous level. The residual representations at each step are approximated by projections or representation operators. Sufficient conditions for ending the iteration on a current pair of discrete spaces are determined by computing simple indicators that involve consecutive iterations. When compared with the standard Uzawa multilevel algorithm, our proposed algorithm has the advantages of automatically selecting the relaxation parameter, lowering the number of iterations on each level, and improving on running time. By carefully choosing the discrete spaces and the projection operators, the error for the second component of the solution can be significantly improved even when comparison is made with the discretization on standard families of stable pairs.     

An adaptive method for the Stefan problem and its application to endoglacial conduits

This paper concerns an adaptive finite element method for the Stefan one-phase problem. We derive a parabolic variational inequality using the Duvaut transformation. In each time-step we consider an adaptive algorithm based on a combination of the Uzawa method associated with the corresponding multivalued operator and a convergent adaptive method for the linear problem. We justify the convergence of the method. As an application we model an endoglacial conduit in which a phase change phenomenon takes place.     

Non-smooth SOR for L 1-Fitting: Convergence Study and Discussion of Related Issues

In this article, the denoising of smooth (H ¹-regular) images is considered. To reach this objective, we introduce a simple and highly efficient over-relaxation technique for solving the convex, non-smooth optimization problems resulting from the denoising formulation. We describe the algorithm, discuss its convergence and present the results of numerical experiments, which validate the methods under consideration with respect to both efficiency and denoising capability. Several issues concerning the convergence of an Uzawa algorithm for the solution of the same problem are also discussed.     

An Augmented Lagrangian Method for <Emphasis Type="Italic">TV</Emphasis><Subscript><Emphasis Type="Italic">g</Emphasis></Subscript>+<Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-norm Minimization

In this paper, the minimization of a weighted total variation regularization term (denoted TV _g ) with L ¹ norm as the data fidelity term is addressed using the Uzawa block relaxation method. The unconstrained minimization problem is transformed into a saddle-point problem by introducing a suitable auxiliary unknown. Applying a Uzawa block relaxation method to the corresponding augmented Lagrangian functional, we obtain a new numerical algorithm in which the main unknown is computed using Chambolle projection algorithm. The auxiliary unknown is computed explicitly. Numerical experiments show the availability of our algorithm for salt and pepper noise removal or shape retrieval and also its robustness against the choice of the penalty parameter. This last property is useful to attain the convergence in a reduced number of iterations leading to efficient numerical schemes. The specific role of the function g in TV _g is also investigated and we highlight the fact that an appropriate choice leads to a significant improvement of the denoising results. Using this property, we propose a whole algorithm for salt and pepper noise removal (denoted UBR-EDGE) that is able to handle high noise levels at a low computational cost. Shape retrieval and geometric filtering are also investigated by taking into account the geometric properties of the model.     

A note on block-diagonally preconditioned PIU methods for singular saddle point problems

Recently, Bai and Wang [On parameterized inexact Uzawa methods for generalized saddle point problems, Linear Algebra Appl. 428 (2008), pp. 2900–2932] and Gao and Kong [Block diagonally preconditioned PIU methods of saddle point problems, Appl. Math. Comput. 216 (2010), pp. 1880–1887] discussed the parameterized inexact Uzawa (PIU) method and the preconditioned parameterized inexact Uzawa (PPIU) method. In this paper, we further study the block-diagonally preconditioned PIU methods for solving singular saddle point problems, and give the corresponding convergence analysis.     

A FEM–BEM coupling method for a nonlinear transmission problem modelling Coulomb friction contact

A nonlinear transmission problem modelling elastoplastic interface problems with contact and Coulomb friction is reduced to a boundary/domain variational inequality. We present a corresponding FEM/BEM coupling procedure and derive for its Galerkin solution an a priori error estimate. Furthermore we reformulate the problem as an equivalent saddle point problem whose discretization can be solved by the Uzawa algorithm. Convergence of the FEM/BEM coupling method is proved and numerical results are given.     

Fast corrected Uzawa methods for solving symmetric saddle point problems

Abstract We consider the solution of linear systems of saddle point problems by two nonlinear iterative methods, which are similar to Uzawa-type methods and called corrected Uzawa methods. Their convergence rates are analyzed. The results of numerical experiments are presented when we apply them to solve the Stokes equations discretized by mixed finite elements. Keywords: Saddle point problem, Uzawa-type algorithm, Schur complement, Stokes equation     

Distributive relaxations for the spectral stokes operator

The technique of distributive relaxations is presented for the spectral Stokes operator. The sample iterative method is described and its equivalence to the Uzawa algorithm is shown. Furthermore the occurrence of the spectral Pseudo-Laplace operator is demonstrated. Numerical results are presented which show the good performance of the distributive relaxations.