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scalable algorithms FOR THE SOLUTION OF NAVIERS EQUATIONS OF ELASTICITY

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 1995年第1-3期63卷 149-178页

作者： AXELSSON, O NEYTCHEVA, M UNIV NIJMEGEN FAC MATH & INFORMAT 6525 ED NIJMEGEN NETHERLANDS

Very large scale mathematical modelling such as accurate modelling using Navier's equations of elasticity needs both massively parallel computing and scalable algorithms. It is shown in this paper that efficient methods must be scalable with respect to the speedup measured as the ratio of the computing time of the best sequential algorithm on one processor and the computing time of the parallel algorithm on p processors. For a class of multilevel methods for elliptic partial differential equations it is shown how to balance the coarsest mesh size to the finest and the number of processors to the size of the problem to get smallest computing time and maximal efficiency. It turns out that the number of processors should grow slowly in proportion with the problem size. Further, it should grow slightly slower (by a logarithmic or a polylogarithmic function) for asymptotically maximal efficiency than the number of processors required for minimal computing time.

关键词： PARALLEL COMPUTING scalable algorithms OPTIMAL EFFICIENCY MATHEMATICAL MODELING EQUATIONS OF ELASTICITY

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scalable algorithms in the Age of Big Data and Network Sciences: Characterization, Primitives, and Techniques 18

Scalable Algorithms in the Age of Big Data and Network Scien...

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11th ACM International Conference on Web Search and Data Mining

作者： Teng, Shang-Hua Univ Southern Calif Los Angeles CA 90007 USA

ISBN: (纸本)9781450355810

In the age of network sciences and machine learning, efficient algorithms are now in higher demand more than ever before. Big Data fundamentally challenges the classical notion of efficient algorithms: algorithms that used to be considered efficient, according to polynomial-time characterization, may no longer be adequate for solving today's problems. It is not just desirable, but essential, that efficient algorithms should be scalable. In other words, their complexity should be nearly linear or sub-linear with respect to the problem size. Thus, scalability, not just polynomial-time computability, should be elevated as the central complexity notion for characterizing efficient computation. Using several basic tasks in network analysis, machine learning, and optimization as examples - in this talk - I will highlight a family of fundamental algorithmic techniques for designing provably-good scalable algorithms.

关键词： scalable algorithms graph sparsification local algorithms advanced sampling big data network sciences machine learning

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scalable algorithms for communication networks

Scalable algorithms for communication networks

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作者： Chen, Li-yen University of Michigan

学位级别：Ph.D.

Network scalability has emerged as the essential problem in designing architectures and protocols for large-scale communication systems. Minor efficiencies, that can be tolerated in small networks, can accumulate and become a dominant factor determining the performance of large networks. In this thesis, we consider three problems that are related to scalability. First, we examine the size of routing tables as the number of nodes in the network increases. It is shown that the widely used shortest-path and straight-line routing algorithm can be implemented only when nodes' memory increases with the network size. On the other hand, it is established that there exist information-efficient algorithms, e.g., column-first routing protocol, that route packets correctly even if each node in the network is capable of storing information on a fixed number of destinations only. In the second part, we present a novel computational model utilizing time encoding, that enables a distributed scheduling mechanism. The scheduling algorithm we propose achieves performance comparable to centralized algorithms under uniform traffic. Exploiting a connection between switch scheduling and interval packing, we argue that the distributed nature of the algorithm limits the maximum relative load to 1−e −2 under the worst-case scenario. The stability of the algorithm can be improved by enabling reversibility in distributed decision making. Finally, we discuss the bandwidth sharing problem for multi-hop networks. A buffer management policy that utilizes only simple packet attributes delivers a constant fraction of the maximum possible throughput. Moreover, the policy is robust to heavy traffic loads in the sense that the throughput does not degrade due to congestion.

关键词： scalable algorithms Routing Switch Scheduling Bandwidth Sharing Thesis

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scalable algorithms for Delaunay Mesh Generation

Scalable Algorithms for Delaunay Mesh Generation

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作者： Slatton, Andrew G. The Ohio State University

学位级别：Ph.D.

Delaunay refinement is a useful tool for sampling and meshing. Pioneered by Ruppert and Chew for piecewise-linear complexes in R 2, Delaunay refinement has been extended to myriad classes of shapes including smooth 1- and 2-manifolds, volumes bounded by smooth 2-manifolds, and piecewise-smooth complexes. Delaunay refinement algorithms often carry certain guarantees regarding the geometric and topological closeness of output to input, as well as guarantees of the quality of mesh elements, making meshes generated via Delaunay refinement a natural choice for simulation and rendering. A major shortcoming of Delaunay refinement is its scalability: as the size of the mesh grows, the data structures necessary to carry out Delaunay refinement efficiently (such as the Delaunay triangulation and its dual, the Voronoi diagram) also grow, and this incurs memory thrashing when generating dense meshes. In this dissertation, we improve Delaunay refinement in two main capacities: (1) we improve the memory scalability of Delaunay refinement to allow for the generation of truly huge meshes, and (2) we improve the time scalability of Delaunay refinement by developing a novel parallel algorithm. To address the issue of memory scalability, we developed a localized refinement method embodying a divide-and-conquer paradigm for meshing smooth surfaces. The algorithm divides the sampling of the input domain via octree and meshes one node of the octree at a time, thus reducing memory requirements. Our theoretical results show that the algorithm terminates, and that the output is not only consistent, but also is geometrically close to the input and is a subcomplex of the Delaunay triangulation of the sampling restricted to the input surface. Our initial work nicely addresses the aforementioned shortcoming of Delaunay refinement, but only for smooth 2-manifolds. In later work, we extended this technique to another important input class: volumes bounded by smooth 2-manifolds. It is not immediat

关键词： Computer Science Mesh generation Delaunay Parallel algorithms scalable algorithms

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p4est: scalable algorithms FOR PARALLEL ADAPTIVE MESH REFINEMENT ON FORESTS OF OCTREES

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2011年第3期33卷 1103-1133页

作者： Burstedde, Carsten Wilcox, Lucas C. Ghattas, Omar Univ Texas Austin Inst Computat Engn & Sci Austin TX 78712 USA Univ Texas Austin Dept Mech Engn Jackson Sch Geosci Austin TX 78712 USA

We present scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected two-dimensional quadtrees or three-dimensional octrees, referred to as a forest of octrees. By distributing the union of octants from all octrees in parallel, we combine the high scalability proven previously for adaptive single-octree algorithms with the geometric flexibility that can be achieved by arbitrarily connected hexahedral macromeshes, in which each macroelement is the root of an adapted octree. A key concept of our approach is an encoding scheme of the interoctree connectivity that permits arbitrary relative orientations between octrees. Based on this encoding we develop interoctree transformations of octants. These form the basis for high-level parallel octree algorithms, which are designed to interact with an application code such as a numerical solver for partial differential equations. We have implemented and tested these algorithms in the p4est software library. We demonstrate the parallel scalability of p4est on its own and in combination with two geophysics codes. Using p4est we generate and adapt multioctree meshes with up to 5.13 x 10(11) octants on as many as 220,320 CPU cores and execute the 2:1 balance algorithm in less than 10 seconds per million octants per process.

关键词： forest of octrees parallel adaptive mesh refinement Morton code scalable algorithms large-scale scientific computing

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Route to exascale: Novel mathematical methods, scalable algorithms and Computational Science skills

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JOURNAL OF COMPUTATIONAL SCIENCE 2016年第May期14卷 1-4页

作者： Alexandrov, Vassil ICREA Barcelona Supercomp Ctr Barcelona Spain

This editorial outlines the research context, the needs and challenges on the route to exascale. In particular the focus is on novel mathematical methods and mathematical modeling approaches together with scalable scientific algorithms that are needed to enable key science applications at extreme-scale. This is especially true as HPC systems continue to scale up in compute node and processor core count. These extreme-scale systems require novel mathematical methods to be developed that lead to scalable scientific algorithms to hide network and memory latency, have very high computation/communication overlap, have minimal communication, have fewer synchronization points. It stresses the need of scalability at all levels, starting from mathematical methods level through algorithmic level, and down to systems level in order to achieve overall scalability. It also points out that with the advances of Data Science in the past few years the need of such scalable mathematical methods and algorithms able to handle data and compute intensive applications at scale becomes even more important. The papers in the special issue are selected to address one or several key challenges on the route to exascale. (C) 2016 Published by Elsevier B.V.

关键词： Novel mathematical methods scalable algorithms Exascale computing Computational Science research methods HPC

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Monte Carlo scalable algorithms for Computational Finance

Monte Carlo scalable algorithms for Computational Finance

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International Conference on Computational Science (ICCS) on the Ascent of Computational Excellence

作者： Alexandrov, V. N. Gonzalez Martel, Christian Strassburg, J. ICREA C Jordi Girona29Edifici Nexus 2 E-08034 Barcelona Spain Univ Las Palma Dept Metodos Cuantitativos Econ Gest Las Palmas Gran Canaria Spain

With the latest developments in the area of advanced computer architectures, we are already seeing large scale machines at petascale level and we are faced with the exascale computing. challenge. All these require scalability at system, algorithmic and mathematical model level. In particular, efficient scalable algorithms are required to bridge the performance gap. In this paper, examples of various approaches of designing scalable algorithms for such advanced architectures will be given. We will briefly present our approach to Monte Carlo scalable algorithms for Linear Algebra and explain how these approaches are extended to the field of Computational Finance. Implementation examples will be presented using Linear Algebra Problems and problems from Computational Finance. Furthermore, the corresponding properties of these algorithms will be outlined and discussed.

关键词： scalable algorithms Computational Finance Monte Carlo

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: scalable algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees

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SIAM Journal on Scientific Computing 2011年第3期33卷 1103-1133页

作者： Carsten Burstedde Lucas C. Wilcox Omar Ghattas

$5.13\times10^{11}$ octants on as many as 220,320

关键词： 65M50 65Y05 68W10 65D18 forest of octrees parallel adaptive mesh refinement Morton code scalable algorithms large-scale scientific computing

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Monte Carlo scalable algorithms for Computational Finance

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Procedia Computer Science 2011年 4卷 1708-1715页

作者： V.N. Alexandrov Christian González Martel J. Straßburg ICREA and Barcelona Supercomputing Centre C/ Jordi Girona 29 Edifici Nexus II E-08034 Barcelona Spain Departamento de Métodos Cuantitativos en Economía y Gestión University of Las Palmas Las Palmas Spain

With the latest developments in the area of advanced computer architectures, we are already seeing large scale machines at petascale level and we are faced with the exascale computing challenge. All these require scalability at system, algorithmic and mathematical model level. In particular, e_cient scalable algorithms are required to bridge the performance gap. In this paper, examples of various approaches of designing scalable algorithms for such advanced architectures will be given. We will briefly present our approach to Monte Carlo scalable algorithms for Linear Algebra and explain how these approaches are extended to the field of Computational Finance. Implementation examples will be presented using Linear Algebra Problems and problems from Computational Finance. Furthermore, the corresponding properties of these algorithms will be outlined and discussed.

关键词： scalable algorithms Computational Finance Monte Carlo

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scalable parallel algorithms for geometric pattern recognition

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 1999年第3期58卷 466-486页

作者： Boxer, L Miller, R Rau-Chaplin, A Niagara Univ Dept Comp & Informat Sci New York NY 14109 USA SUNY Buffalo Dept Comp Sci & Engn Buffalo NY 14260 USA Dalhousie Univ Fac Comp Sci Halifax NS B3J 2X4 Canada

This paper considers a variety of geometric pattern recognition problems on input sets of size n using a coarse grained multicomputer model consisting of p processors with Omega(n/p) local memory each (i.e., Omega(n/p) memory cells of Theta(log n) bits apiece), where the processors are connected to an arbitrary interconnection network. It introduces efficient scalable parallel algorithms for a number of geometric problems including the rectangle finding problem, the maximal equally spaced collinear points problem, and the point set pattern matching problem. All of the algorithms presented are scalable in that they are applicable and efficient over a very wide range of ratios of problem size to number of processors. In addition to the practicality imparted by scalability, these algorithms are easy to implement in that all required communications can be achieved by a small number of calls to standard global routing operations. (C) 1999 Academic Press.

关键词： parallel algorithms computational geometry scalable algorithms coarse grained multicomputer

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