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Interactively exploring elimination orderings in symbolic sparse Cholesky factorization

Procedia Computer science 2010年第1期1卷 867-874页

作者： Michael Lülfesmann Simon R. Leßenich H. Martin Bücker Institute for Scientic Computing Center for Computational Engineering Science RWTH Aachen University D-52056 Aachen Germany

When large sparse symmetric systems of linear equations are solved by the Cholesky factorization, nonzero elements can be generated at positions where the original matrix contains zero elements. This phenomenon is called fill-in and it is often crucial in large-scale problems. The symbolic Cholesky factorization solely takes into account the nonzero structure of a sparse matrix to determine the nonzero structure of its Cholesky factor. Sequences of elimination graphs are typically used to model this combinatorial problem. We propose an interactive educational module to visualize and explore the symbolic Cholesky factorization in terms of both elimination graphs and matrix representation. We describe the design and implementation of this interactive module that is intended to be used in a face-to-face learning environment.

关键词： Combinatorial scientific computing Symbolic sparse Cholesky factorization Exploration and visualization of elimination graphs and matrix representation Interactive educational module Face-to-face learning environment

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Finite element method for a nonsmooth elliptic equation

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中国高等学校学术文摘·数学 2010年第2期5卷 191-209页

作者： Lili CHANG Wei GONG Ningning YAN State Key Laboratory of Scientific and Engineering Computing Institute of Systems Science Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China

In this paper, we study the finite element method for a nonsmooth elliptic equation. Error analysis is presented, including a priori and a posteriori error estimates as well as superconvergence analysis. We also propose two algorithms for solving the underlying equation. Numerical experiments are employed to confirm our error estimations and the efficiency of our algorithms.

关键词： Finite element method nonsmooth elliptic equation a priori error estimate a posteriori error estimate superconvergence analysis active set method

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

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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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Skel: Generative Software for Producing Skeletal I/O Applications

Skel: Generative Software for Producing Skeletal I/O Applica...

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IEEE International Conference on E-science Workshops

作者： Jeremy Logan Scott Klasky Jay Lofstead Hasan Abbasi Stephane Ethier Ray Grout Seung-Hoe Ku Qing Liu Xiaosong Ma Manish Parashar Norbert Podhorszki Karsten Schwan Matthew Wolf Oak Ridge National Laboratory Oak Ridge TN USA Sandia National Laboratories Albuquerque NM USA Plasma Physics Laboratory Princeton University Princeton NJ USA National Renewable Energy Laboratory Golden CO USA Courant Institute of Mathematical Sciences New York University New York NY USA National Institute for Computational Sciences University of Tennessee Oak Ridge TN USA Department of Computer Science North Carolina State University Raleigh NC USA Department of Electrical & Computer Engineering Rutgers The State University of New Jersey Piscataway NJ USA College of Computing Georgia Tech Atlanta GA USA

Massively parallel computations consist of a mixture of computation, communication, and I/O. Of these three components, implementing an effective parallel I/O solution has often been overlooked by application scientists and has typically been added to large scale simulations only when existing serial techniques have failed. As scientists' teams scaled their codes to run on hundreds of processors, it was common to call on an I/O expert to implement a set of more scalable I/O routines. These routines were easily separated from the calculations and communication, and in many cases, an I/O kernel was derived from the application which could be used for testing I/O performance independent of the application. These I/O kernels developed a life of their own used as a broad measure for comparing different I/O techniques. Unfortunately, as years passed and computation and communication changes required changes to the I/O, the separate I/O kernel used for benchmarking remained static, no longer providing an accurate indicator of the I/O performance of the simulation, and making I/O research less relevant for the application scientists. In this paper we describe a new approach to this problem where I/O kernels are replaced with skeletal I/O applications that are automatically generated from an abstract set of simulation I/O parameters. We realize this abstraction by leveraging the ADIOS [1] middleware's XML I/O specification with additional runtime parameters. Skeletal applications offer all of the benefits of I/O kernels including allowing I/O optimizations to focus on useful I/O patterns. Moreover, since they are automatically generated, it is easy to produce an updated I/O skeleton whenever the simulation's I/O changes. In this paper we analyze the performance of automatically generated I/O skeletal applications for the S3D and GTS codes. We show that these skeletal applications achieve performance comparable to that of the production applications. We wrap up the paper with

关键词： XML Kernel Arrays Benchmark testing Educational institutions Reactive power Hardware

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PerfExpert: An easy-to-use performance diagnosis tool for HPC applications 10

PerfExpert: An easy-to-use performance diagnosis tool for HP...

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Proceedings of the 2010 ACM/IEEE International Conference for High Performance computing, Networking, Storage and Analysis

作者： Burtscher, Martin Kim, Byoung-Do Diamond, Jeff McCalpin, John Koesterke, Lars Browne, James Institute for Computational Engineering and Sciences University of Texas Austin United States Texas Advanced Computing Center University of Texas Austin United States Department of Computer Science University of Texas Austin United States

ISBN: (纸本)9781424475575

HPC systems are notorious for operating at a small fraction of their peak performance, and the ongoing migration to multi-core and multi-socket compute nodes further complicates performance optimization. The readily available performance evaluation tools require considerable effort to learn and utilize. Hence, most HPC application writers do not use them. As remedy, we have developed PerfExpert, a tool that combines a simple user interface with a sophisticated analysis engine to detect probable core, socket, and node-level performance bottlenecks in each important procedure and loop of an application. For each bottleneck, PerfExpert provides a concise performance assessment and suggests steps that can be taken by the programmer to improve performance. These steps include compiler switches and optimization strategies with code examples. We have applied PerfExpert to several HPC production codes on the Ranger supercomputer. In all cases, it correctly identified the critical code sections and provided accurate assessments of their performance. © 2010 IEEE.

关键词： Supercomputers

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RETRACTED ARTICLE: Application of improved genetic algorithm in microstructure optimization of closed-cell material

RETRACTED ARTICLE: Application of improved genetic algorithm...

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作者： Zhao, Junfeng Cui, Junzhi Li, Wei Department of Applied Mathematics Northwestern Polytechnical University Xi'an Shaanxi 710072 China Institute of Computational Mathematics and Science-Engineering Computing Chinese Academy of Sciences Beijing 10080 China Department of Mathematics School of Science Xidian University Xi'an Shaanxi 710071 China

ISBN: (纸本)9781424472369

In this paper, we proposed an improved niche genetic algorithm on the basis of the density clustering-based DBSCAN algorithm which can distinct between niches dynamically and maintain the ability of population diversity. Its application in the field of closed-cell material optimization shows that the algorithm can effectively overcome some shortcomings, such as prematurity, poor local search capabilities in simple genetic algorithms. Moreover, this algorithm can get the results with a higher precision in a short time. © 2010 IEEE.

关键词： Clustering algorithms

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Optimum design for microstructures of closed-cell materials based on thermal conductivity

Optimum design for microstructures of closed-cell materials ...

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2010 International Conference on computational and Information sciences, ICCIS2010

ISBN: (纸本)9780769542706

Taking our proposition about the grid-based simulation for the microstructure of the closed-cell foam into account, and choosing position of voids as optimal variables, this paper builds an optimal model for the two-phase material with maximizing the effective thermal conductivity of the microstructure. Then the paper seeks its solution by using the genetic algorithm. The numerical results show that the optimal model we built is reasonable and the optimal algorithm we used to solve this model is also effective. Furthermore, the results illustrate how the related factors make an effect on the optimal solution. © 2010 IEEE.

关键词： Genetic algorithms

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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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iVisClassifier: An interactive visual analytics system for classification based on supervised dimension reduction

iVisClassifier: An interactive visual analytics system for c...

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IEEE Symposium on Visual Analytics science and Technology (VAST)

作者： Jaegul Choo Hanseung Lee Jaeyeon Kihm Haesun Park School of Computational Science and Engineering Georgia Institute of Technology USA Science and Engineering and Computer Engineering Georgia Institute of Technology USA School of Interactive Computing Georgia Institute of Technology USA

We present an interactive visual analytics system for classification, iVisClassifier, based on a supervised dimension reduction method, linear discriminant analysis (LDA). Given high-dimensional data and associated cluster labels, LDA gives their reduced dimensional representation, which provides a good overview about the cluster structure. Instead of a single two- or three-dimensional scatter plot, iVisClassifier fully interacts with all the reduced dimensions obtained by LDA through parallel coordinates and a scatter plot. Furthermore, it significantly improves the interactivity and interpretability of LDA. LDA enables users to understand each of the reduced dimensions and how they influence the data by reconstructing the basis vector into the original data domain. By using heat maps, iVisClassifier gives an overview about the cluster relationship in terms of pairwise distances between cluster centroids both in the original space and in the reduced dimensional space. Equipped with these functionalities, iVisClassifier supports users' classification tasks in an efficient way. Using several facial image data, we show how the above analysis is performed.

关键词： Data visualization Image color analysis Principal component analysis Space heating Pixel Clustering algorithms

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