Domain Decomposition Methods for Nonlocal Total Variation Image Restoration

Nonlocal total variation (TV) regularization (Gilboa and Osher in Multiscale Model Simulat 7(3): 1005–1028, 2008; Zhou and Schölkopf in Pattern recognition, proceedings of the 27th DAGM symposium. Springer, Berlin, pp 361–368, 2005) has been widely used for the natural image processing, since it is able to preserve repetitive textures and details of images. However, its applications have been limited in practice, due to the high computational cost for large scale problems. In this paper, we apply domain decomposition methods (DDMs) (Xu et al. in Inverse Probl Imag 4(3):523–545, 2010) to the nonlocal TV image restoration. By DDMs, the original problem is decomposed into much smaller subproblems defined on subdomains. Each subproblem can be efficiently solved by the split Bregman algorithm and Bregmanized operator splitting algorithm in Zhang et al. (SIAM J Imaging Sci 3(3):253–276, 2010). Furthermore, by using coloring technique on the domain decomposition, all subproblems defined on subdomains with same colors can be computed in parallel. Our numerical examples demonstrate that the proposed methods can efficiently solve the nonlocal TV based image restoration problems, such as denoising, deblurring and inpainting. It can be computed in parallel with a considerable speedup ratio and speedup efficiency.     

A Parallel Grid Modification and Domain Decomposition Algorithm for Local Phenomena Capturing and Load Balancing

Lion's nonoverlapping Schwarz domain decomposition method based on a finite difference discretization is applied to problems with fronts or layers. For the purpose of getting accurate approximation of the solution by solving small linear systems, grid refinement is made on subdomains that contain fronts and layers and uniform coarse grids are applied on subdomains in which the solution changes slowly and smoothly. In order to balance loads among different processors, we employ small subdomains with fine grids for rapidly-changing-solution areas, and big subdomains with coarse grids for slowly-changing-solution areas. Numerical implementations in the SPMD mode on an nCUBE2 machine are conducted to show the efficiency and accuracy of the method.     

Uzawa Conjugate Gradient Domain Decomposition Methods for Coupled Stokes Flows

This paper deals with nonoverlapping domain decomposition methods for two coupled Stokes flows, based on the duality theory. By introducing a fictitious variable in the transmission condition and using saddle-point equations, the problem is restated as a linearly constrained maximization problem. According to whether constraints are uncoupled Stokes problems or uncoupled Poisson problems, two Uzawa-type domain decomposition algorithms are proposed. The results of some numerical experiments on a model problem are given.     

Implementation of spectral basis functions in BEM/FEM/GSM Domain Decomposition Methods devoted to scattering and radiation applications

In this paper, we discuss several improvements of a substructuring Domain Decomposition Method (DDM) devoted to Electromagnetic computations, based on the Boundary Element Method (BEM) and the Finite Element Method (FEM). This computation procedure is applied to the analysis of antenna performance on board vehicles as well as Radar Cross Section (RCS). The benefits of the subdomain Computational Electromagnetic Method are mainly the ability to deal with collaborative studies involving several companies, and the reduction of the computation costs by one or more orders of magnitude, especially in the context of parametric studies. Furthermore, this paper proposes a Spectral Basis Function (SBF) defined on fictitious surfaces surrounding equipment, to deal with both the computation of antenna far field patterns and RCS in a multi-domain mode. By masking the complexity of the equipment (wires, thin surfaces, materials, supply network, weapons) the external domain of the vehicle can be closed so that the Combined Field Integral Equation (CFIE) can be used, which is better conditioned than the Electric Field Integral Equation (EFIE). This calculation procedure leads to a faster convergence when using iterative Multi Level Fast Multiple Algorithms (MLFMA). The accuracy and efficiency of this technique is assessed by performing the computation of the diffraction and radiation of several test-objects in a multi-domain way cross compared with reference integral equation results.     

Internet域名解析过程中信道的负载平衡研究

分析了解过程中负载的分布情况,为负载平衡提出了改进方案,并作了性能分析。     

On the Scalability of Data-Parallel Decomposition Algorithms for Stochastic Programs

This paper develops a data-parallel implementation of the L-shaped decomposition algorithm for stochastic linear programs with recourse. The algorithm decomposes the problem into independent scenario subproblems that are solved concurrently. These subproblems are structurally identical and can be solved on SIMD machines, such as the Connection Machine CM-2. The coordinating master program is a dense linear program and is solved efficiently by spreading its non-zero coefficients among multiple processors and using dense linear algebra subroutines. The parallel solution of the master program removes the serial bottleneck of the algorithm. The resulting implementation achieves good speed-ups and is scalable. Numerical results on the Connection Machine CM-2 and comparisons with a benchmark control-parallel implementation are included.     

Numerical Integrations and Unit Resolution Multipliers for Domain Decomposition Methods with Nonmatching Grids

In this paper, we are concerned with the non-overlapping domain decomposition method (DDM) with nonmatching grids for three-dimensional problems. The weak continuity of the DDM solution on the interface is imposed by some Lagrange multiplier. We shall first analyze the influence of the numerical integrations over the interface on the (non-conforming) approximate solution. Then we will propose a simple approach to construct multiplier spaces, one of which can be simply spanned by some smooth basis functions with local compact supports, and thus makes the numerical integrations on the interface rather simple and inexpensive. Also it is shown this multiplier space can generate an optimal approximate solution. Numerical results are presented to compare the new method with the point to point method widely used in engineering.     

气象资料三维变分同化阶段区域分解并行实现

变分同化由于能明显改善同化质量,正在成为数值天气预报的主流同化方法．研究三维变分同化的并行计算,提出了三维变分同化的阶段区域分解、观测资料的自适应划分算法、计算与通信重叠的矩阵转置和周边区域通信以及文件I／O方法,在此基础上实现了MPI并行三维变分原型系统,在由8个双CPU节点组成的Linux机群上并行加速比达到了11．9．     

基于主题的DDS系统的扩展性设计与实现

基于主题的发布订阅系统存在着表达能力较弱的缺点,订阅者没有办法很好的描述自己对于订阅事件的要求,从而降低了订阅者接收数据的有效性,浪费了系统资源,同时也影响了用户体验.本文提出了一种对基于主题的发布订阅系统(DataDistribution Service,DDS)进行扩展的方法,使其具有一定的基于内容的发布订阅能力.文章在详细分析现有系统问题的基础上,提出采用增加关键字描述的方式来使得订阅者能够更细粒度的描述自己的订阅要求的方法,并分析其可行性.进行整体设计,以尽可能保留原系统优点及体系结构为前提,修改其匹配算法,最终实现了对原系统的扩展,完成了基于内容的发布订阅功能,提升了用户体验.     

EIGRP不等价链路负载均衡网络方案分析与实施

负载均衡建立在现有网络结构之上,提升了网络的数据处理能力、灵活性和可用性,具有低成本且有效透明的优点。负载均衡之一链路的负载可以极大地提高链路的传输效率和利用率,EIGRP协议非常好地支持了不等价的链路负载均衡。本文针对某一网络结构,论述了EIGRP协议负载均衡的特点,分析了EIGRP协议不等价负载均衡配置方法,实现了网络架构的不等价链路的负载均衡。     

时域有限差分中各向异性完全匹配层的实现方法

本文讨论了如何在给定边界层数的条件下,通过调整各介质层吸收层的介质参数来实现入射波的最佳吸收,并利用自适应遗传算法对算法中的边界参数进行优化。     

Domain Decomposition Preconditioners for Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains

In this article we consider the application of Schwarz-type domain decomposition preconditioners for discontinuous Galerkin finite element approximations of elliptic partial differential equations posed on complicated domains, which are characterized by small details in the computational domain or microstructures. In this setting, it is necessary to define a suitable coarse-level solver, in order to guarantee the scalability of the preconditioner under mesh refinement. To this end, we exploit recent ideas developed in the so-called composite finite element framework, which allows for the definition of finite element methods on general meshes consisting of agglomerated elements. Numerical experiments highlighting the practical performance of the proposed preconditioner are presented.     

一种用计算域分解的等几何分析并行化方法

提出一种按照计算域分解的并行化方法来构建等几何分析的刚度矩阵和右侧向量.将计算域分解成为若干个不相交的子区域,然后为每个区域分配一个处理器,所有处理器并行进行子区域上面的计算,所有处理器完成子区域的计算以后,使用一个快速的归并算法完成线性系统的装配.实验表明,本文提出的方法在8核的机器上可以达到6.46的加速比,能够在4秒左右的时间计算680万个矩阵元素个数.使用Intel MKL稀疏求解器来求解线性系统,本文的等几何分析求解器能够在大约10秒的时间内求解52万的自由度,本文的方法比ISOGAT速度要快上万倍.     

WIN32线程同步方法分析与实现

文章分析了WIN32线程同步的一般方法，并提出了一种的经实践证实也是切实可行线的线程同步方法。     

WIN32线程同步方法分析与实现

文章分析了WIN32线程同步的一般方法,并提出了一种新的经实践证实也是切实可行的线程同步方法.     

提高两工位钻削动平衡机转子校正精度的方法

介绍了研制的两工位半自动动平衡机去重系统的组成、工作过程,重点对动平衡转子二次平面分离技术以及系统的误差进行了研究,提出了校正环节闭环系统的设计,通过相应的计算,为提高平衡机去重精度提出了实用的方法。     

Bregmanized Domain Decomposition for Image Restoration

Computational problems of large-scale data are gaining attention recently due to better hardware and hence, higher dimensionality of images and data sets acquired in applications. In the last couple of years non-smooth minimization problems such as total variation minimization became increasingly important for the solution of these tasks. While being favorable due to the improved enhancement of images compared to smooth imaging approaches, non-smooth minimization problems typically scale badly with the dimension of the data. Hence, for large imaging problems solved by total variation minimization domain decomposition algorithms have been proposed, aiming to split one large problem into N>1 smaller problems which can be solved on parallel CPUs. The N subproblems constitute constrained minimization problems, where the constraint enforces the support of the minimizer to be the respective subdomain. In this paper we discuss a fast computational algorithm to solve domain decomposition for total variation minimization. In particular, we accelerate the computation of the subproblems by nested Bregman iterations. We propose a Bregmanized Operator Splitting–Split Bregman (BOS-SB) algorithm, which enforces the restriction onto the respective subdomain by a Bregman iteration that is subsequently solved by a Split Bregman strategy. The computational performance of this new approach is discussed for its application to image inpainting and image deblurring. It turns out that the proposed new solution technique is up to three times faster than the iterative algorithm currently used in domain decomposition methods for total variation minimization.