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On Conditioning of Constraints Arising from Variationally Consistent Discretization of Contact Problems and Duality Based Solvers

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COMPUTATIONAL METHODS IN APPLIED MATHEMATICS 2015年第2期15卷 221-231页

作者： Vlach, Oldrich Dostal, Zdenek Kozubek, Tomas VSB Tech Univ Ostrava Ostrava 70833 Czech Republic

Variationally consistent approximation of the non-penetration conditions and friction laws was introduced by Wohlmuth [23] as a powerful tool for the effiective discretization of contact problems. This approach is especially useful when the potential contact interface is large and curved or when non-matching grids are applied. The point of this note is to give bounds on the singular values of the constraint matrices arising from the variationally consistent approximation and to indicate their application in the analysis of the scalable duality based domain decomposition algorithms for the solution of multi-body contact problems [7]. The theoretical results are illustrated by numerical experiments.

关键词： Contact Problems Variationally Consistent Discretization scalable algorithms

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AMIDST: A Java toolbox for scalable probabilistic machine learning

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KNOWLEDGE-BASED SYSTEMS 2019年 163卷 595-597页

作者： Masegosa, Andres R. Martinez, Ana M. Ramos-Lopez, Dario Cabanas, Rafael Salmeron, Antonio Langseth, Helge Nielsen, Thomas D. Madsen, Anders L. Univ Almeria ES-04120 Almeria Spain Aalborg Univ DK-9220 Aalborg Denmark Norwegian Univ Sci & Technol NO-7491 Trondheim Norway HUGIN EXPERT AS DK-9000 Aalborg Denmark Rey Juan Carlos Univ ES-28933 Madrid Spain

The AMIDST Toolbox is an open source Java software for scalable probabilistic machine learning with a special focus on (massive) streaming data. The toolbox supports a flexible modelling language based on probabilistic graphical models with latent variables. AMIDST provides parallel and distributed implementations of scalable algorithms for doing probabilistic inference and Bayesian parameter learning in the specified models. These algorithms are based on a flexible variational message passing scheme, which supports discrete and continuous variables from a wide range of probability distributions. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Probabilistic graphical models scalable algorithms Variational methods Latent variables

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A Distributed and scalable Processing Method Based Upon ADMM

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IEEE SIGNAL PROCESSING LETTERS 2012年第9期19卷 563-566页

作者： Erseghe, Tomaso Univ Padua Dipartimento Ingn Informaz I-35131 Padua Italy

The alternating directionmultipliermethod (ADMM) was originally devised as an iterative method for solving convex minimization problems by means of parallelization, and was recently used for distributed processing. This letter proposes a modification of state-of-the-art ADMM formulations in order to obtain a scalable version, well suited for a wide range of applications such as cooperative localization and smart grid optimizations. The resulting algorithm is distributed and scalable, it assures fast convergence speed and robustness to errors. Its performance is tested with an application example based upon cooperative localization.

关键词： Alternating direction method of multipliers cooperative localization distributed processing optimal power flow scalable algorithms

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scalable approximations to k-cycle transversal problems on dynamic networks

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KNOWLEDGE AND INFORMATION SYSTEMS 2019年第1期61卷 65-84页

作者： Kuhnle, Alan Crawford, Victoria G. Thai, My T. Univ Florida Comp & Informat Sci & Engn Gainesville FL 32603 USA

We study scalable approximation algorithms for the k-cycle transversal problem, which is to find a minimum-size set of edges that intersects all simple cycles of length k in a network. This problem is relevant to network reliability through the important metric of network clustering coefficient of order k. We formulate two algorithms to be both scalable and have good solution quality in practice: CARL and DARC. DARC is able to efficiently update its solution under dynamic node and edge insertion and removal to the network. In our experimental evaluation, we demonstrate that DARC is able to run on networks with billions of 3-cycles within 2 h and is able to dynamically update its solution in microseconds.

关键词： Dynamic networks Cycle transversal Triangle interdiction scalable algorithms

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scalable TFETI based algorithm with adaptive augmentation for contact problems with variationally consistent discretization of contact conditions

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FINITE ELEMENTS IN ANALYSIS AND DESIGN 2019年 156卷 34-43页

作者： Dostal, Zdenek Vlach, Oldrich Brzobohaty, Tomas VSB Tech Univ Ostrava Fac Elect Engn & Comp Sci Dept Appl Math Ostrava Czech Republic VSB Tech Univ Ostrava Natl Supercomp Ctr IT4Innovat Ostrava Czech Republic

A variationally consistent approximation of contact conditions by means of biorthogonal mortars was introduced by Wohlmuth as a powerful theoretically supported tool for the discretization of contact problems. This approach is especially useful when a potential contact interface is large and curved or when nonmatching grids are applied, but its effective implementation into FETI based algorithms is not straightforward due to the ill conditioning of related inequality constraints. In this paper we review the mortar discretization and theoretical results on scalability of the FETI based algorithm and show that the recently proposed adaptive augmentation can overcome the difficulties caused by the ill-conditioning of constraints. We demonstrate the (weak) numerical scalability by numerical experiments and present the results for a difficult real world problem discretized by mortars that show the power of the new algorithm - the number of iterations required to the solution of this problem discretized by mortars is just one third of that required by the original algorithm for the same problem discretized by node-to-node constraints.

关键词： Contact problems Variationally consistent discretization Mortars scalable algorithms

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Graph analysis with high-performance computing

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COMPUTING IN SCIENCE & ENGINEERING 2008年第2期10卷 14-19页

作者： Hendrickson, Bruce Berry, JonatHan W. Sandia Natl Labs Livermore CA 94550 USA

Large, complex graphs arise in many settings including the Internet, social networks, and communication networks. To study such data sets, the authors explored the use of high-performance computing (HPC) for graph algorithms. They found that the challenges in these applications are quite different from those arising in traditional HPC applications and that massively multithreaded machines are well suited for graph problems.

关键词： Computing Combinatorics Combinatorial scalable algorithms Graph Analysis HPC High Performance Computing Combinatorics In Computing

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Highly efficient numerical algorithm based on random trees for accelerating parallel Vlasov-Poisson simulations

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JOURNAL OF COMPUTATIONAL PHYSICS 2013年 250卷 224-245页

作者： Acebron, Juan A. Rodriguez-Rozas, Angel ISCTE Inst Univ Lisboa Dept Informat Sci & Technol P-1649026 Lisbon Portugal Univ Tecn Lisboa INESC ID IST P-1000029 Lisbon Portugal Univ Pau & Pays Adour Equipe Projet Mag IPRA LMA 3D Inria Bordeaux Sud Ouest F-64013 Pau France

An efficient numerical method based on a probabilistic representation for the Vlasov-Poisson system of equations in the Fourier space has been derived. This has been done theoretically for arbitrary dimensional problems, and particularized to unidimensional problems for numerical purposes. Such a representation has been validated theoretically in the linear regime comparing the solution obtained with the classical results of the linear Landau damping. The numerical strategy followed requires generating suitable random trees combined with a Pade approximant for approximating accurately a given divergent series. Such series are obtained by summing the partial contributions to the solution coming from trees with arbitrary number of branches. These contributions, coming in general from multi-dimensional definite integrals, are efficiently computed by a quasi-Monte Carlo method. It is shown how the accuracy of the method can be effectively increased by considering more terms of the series. The new representation was used successfully to develop a Probabilistic Domain Decomposition method suited for massively parallel computers, which improves the scalability found in classical methods. Finally, a few numerical examples based on classical phenomena such as the non-linear Landau damping, and the two streaming instability are given, illustrating the remarkable performance of the algorithm, when compared the results with those obtained using a classical method. (C) 2013 Elsevier Inc. All rights reserved.

关键词： Monte Carlo and quasi Monte-Carlo methods Domain decomposition Vlasov-Poisson system Parallel computing scalable algorithms Random trees

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Graphing trillions of triangles

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INFORMATION VISUALIZATION 2017年第3期16卷 157-166页

作者： Burkhardt, Paul US Natl Secur Agcy 9800 Savage Rd Ft George G Meade MD 20755 USA

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.

关键词： Graph scalable algorithms triangle counting visual analytics parallel programming MapReduce

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SVD computations on the connection machine CM-5/CM-5E: Implementation and accuracy

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 1997年第5期18卷 1462-1478页

作者： Balle, SM Pedersen, PM TECH UNIV DENMARK UNI C DANISH COMP CTR RES & EDUC DK-2800 LYNGBY DENMARK THINKING MACHINES CORP CAMBRIDGE MA 02142 USA

The singular value decomposition (SVD) plays an essential role in many applications. One technique for obtaining the SVD of a real dense matrix is to first reduce the dense matrix: to bidiagonal form and then compute the SVD of the bidiagonal matrix, Guidelines followed to implement this approach efficiently on the Connection Machine CM-5/CM-5E are described. Timing results show that use of the described techniques yields up to 44% of peak performance in the reduction from dense to bidiagonal form. The singular values are achieved by applying the parallel bisection algorithm to the symmetric tridiagonal matrix obtained by doing a perfect-shuffle permutation of the rows and columns of [[0 B-T];[B 0]], where B is the bidiagonal matrix. The singular vectors are computed using inverse iteration on the symmetric tridiagonal matrix. SVD experiments done on bidiagonal matrices are presented and illustrate that this approach yields very good performance as well as orthogonal singular vectors even for ill-conditioned matrices as long as the singular values are computed to very high accuracy. The main conclusion is that extra accuracy in the eigenvalue computation very often enhance orthogonality of the eigenvectors computed with inverse iteration to the point where reorthogonalization is not needed. The conclusions presented regarding the SVD's numerical properties are general to the algorithm and not specific to the Connection Machine implementation.

关键词： distributed-memory massively parallel computers bidiagonalization bidiagonal SVD scalable algorithms accuracy of bidiagonal SVD

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New complexity scalable MPEG encoding techniques for mobile applications

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EURASIP JOURNAL ON APPLIED SIGNAL PROCESSING 2004年第2期2004卷 236-252页

作者： Mietens, S de With, PHN Hentschel, C Philips Res Labs NL-5656 AA Eindhoven Netherlands Eindhoven Univ Technol LogicaCMG Eindhoven NL-5600 MB Eindhoven Netherlands Cottbus Univ Technol D-03044 Cottbus Germany

Complexity scalability offers the advantage of one-time design of video applications for a large product family, including mobile devices, without the need of redesigning the applications on the algorithmic level to meet the requirements of the different products. In this paper, we present complexity scalable MPEG encoding having core modules with modifications for scalability. The interdependencies of the scalable modules and the system performance are evaluated. Experimental results show scalability giving a smooth change in complexity and corresponding video quality. Scalability is basically achieved by varying the number of computed DCT coefficients and the number of evaluated motion vectors, but other modules are designed such they scale with the previous parameters. In the experiments using the "Stefan" sequence, the elapsed execution time of the scalable encoder, reflecting the computational complexity, can be gradually reduced to roughly 50% of its original execution time. The video quality scales between 20 dB and 48 dB PSNR with unity quantizer setting, and between 21.5 dB and 38.5 dB PSNR for different sequences targeting 1500 kbps. The implemented encoder and the scalability techniques can be successfully applied in mobile systems based on MPEG video compression.

关键词： MPEG encoding scalable algorithms resource scalability

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