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On the resilience of parallel sparse hybrid solvers 22

On the resilience of parallel sparse hybrid solvers

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22nd International conference on High Performance Computing

作者： Agullo, Emmanuel Giraud, Luc Zounon, Mawussi Inria Bordeaux France

ISBN: (纸本)9781467384889

As the computational power of high performance computing (HPC) systems continues to increase by using a huge number of CPU cores or specialized processing units, extreme-scale applications are increasingly prone to faults. Consequently, the HPC community has proposed many contributions to design resilient HPC applications. These contributions may be system-oriented, theoretical or numerical. In this study we consider an actual fully-featured parallel sparse hybrid (direct/iterative) linear solver, MAPHYS, and we propose numerical remedies to design a resilient version of the solver. The solver being hybrid, we focus in this study on the iterative solution step, which is often the dominant step in practice. We furthermore assume that a separate mechanism ensures fault detection and that a system layer provides support for setting back the environment (processes, ...) in a running state. The present manuscript therefore focuses on (and only on) strategies for recovering lost data after the fault has been detected (a separate concern beyond the scope of this study), once the system is restored (another separate concern not studied here). The numerical remedies we propose are twofold. Whenever possible, we exploit the natural data redundancy between processes from the solver to perform exact recovery through clever copies over processes. Otherwise, data that has been lost and no longer available on any process is recovered through a so-called interpolation-restart mechanism. This mechanism is derived from [1] by carefully taking into account the properties of the target hybrid solver. These numerical remedies have been implemented in the MAPHYS parallel solver so that we can assess their efficiency on a large number of processing units (up to 12, 288 CPU cores) for solving large-scale real-life problems.

关键词： linear algebra algorithms HPC fault tolerance resilience numerical methods solver Krylov Gmres

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A successful "applications oriented" undergraduate EE course elective: Electronic navigation systems 122

A successful "applications oriented" undergraduate EE course...

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2015 122nd ASEE Annual conference and Exposition

作者： Hartnett, Richard J. Seals, Kelly Charles Crilly, Paul Benjamin U.S. Coast Guard Academy New LondonCT United States

In typical undergraduate Electrical Engineering programs, students take courses in circuit analysis, electronics, programming, signals and systems, digital design, physics, calculus, differential equations, plus some advanced courses such as linear algebra, discrete mathematics, communications systems, digital signal processing, antennas, and control systems. These courses are important, however students sometimes find themselves wondering about specific "real-world" applications for all the theory and information learned in these courses. Certainly as faculty members we make every attempt to discuss applications in class, but the unsettling fact is that some students really want to learn more about "real-world" systems! The purpose of this paper is to present how we connect theory to practice using navigation systems as the particular application. Several "real-world" systems discussed in our junior/senior elective course called Electronic Navigation Systems are highlighted in this paper. One system we learn is the NAVSTAR Global Positioning System (GPS). Students find that shift registers are used to generate a unique 1023 bit pseudo-random binary sequence for each satellite, and they write Matlab code to generate sequences for all satellites (digital design application). After telling our students about Gold codes, they then use their functions to study the auto and cross correlation properties of the sequences, and we highlight how a receiver might use those methods to estimate signal time of arrival for this Code Division Multiplexed Access (CDMA) system employing Binary Phase-Shift Keying (BPSK) signals (communication system application). Using the ranging information from N satellites, students learn that GPS receivers typically solve an over-determined system of N equations (where N>4) for 3-d position (x, y, z), plus receiver time offset (t) relative to GPS system time (linear algebra application). Given actual satellite locations and ranging information, s

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Quantized H[infinity] static output control for linear systems with interval-bounded additive controller coefficient variations 3

Quantized H[infinity] static output control for linear syste...

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3rd International conference on Artificial Intelligence, Modelling and Simulation, AIMS 2015

作者： Guo, Xianggui Wang, Jianliang Liao, Fang Tianjin Key Laboratory for Control Theory and Applications in Complicated System Tianjin University of Technology Tianjin300384 China School of Electrical and Electronic Engineering Nanyang Technological University Singapore639798 Singapore Temasek Laboratories National University of Singapore Singapore117508 Singapore

ISBN: (纸本)9781467386753

This paper investigates insensitive Hinfinity control problems for linear continuous-time systems with input and measurement quantization via static output feedback (SOF). The designed controllers are insensitive to additive interval-bounded controller coefficient variations and are made up of two parts as linear and nonlinear parts. The former is used to achieve the Hinfinity performance against external disturbances, unknown initial states and controller coefficient variations. The latter is used to attenuate the effect of input and measurement quantization simultaneously. It should be mentioned that three novel linear matrix inequality (LMI) conditions by using three different methods without introducing a matrix equality constraint as many existing results are obtained. Finally, a numerical example is presented to show the effectiveness and advantages of the proposed methods. © 2015 IEEE.

关键词： linear matrix inequalities

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The Finite Element Method: theory, Implementation, and applications

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2015年

作者： Mats G Larson Fredrik Bengzon

ISBN: (纸本)9783642447112

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential *** principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its *** have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.

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Passive Macromodeling 1

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丛书名： Wiley Series in Microwave and Optical Engineering

2015年

作者： Grivet-Talocia Stefano Gustavsen Bjorn

ISBN: (数字)9781119140979

ISBN: (纸本)9781118094914

Offers an overview of state of the art passive macromodeling techniques with an emphasis on black-box approachesThis book offers coverage of developments in linear macromodeling, with a focus on effective, proven methods. After starting with a definition of the fundamental properties that must characterize models of physical systems, the authors discuss several prominent passive macromodeling algorithms for lumped and distributed systems and compare them under accuracy, efficiency, and robustness standpoints. The book includes chapters with standard background material (such as linear time-invariant circuits and systems, basic discretization of field equations, state-space systems), as well as appendices collecting basic facts from linear algebra, optimization templates, and signals and transforms. The text also covers more technical and advanced topics, intended for the specialist, which may be skipped at first reading. Provides coverage of black-box passive macromodeling, an approach developed by the authors Elaborates on main concepts and results in a mathematically precise way using easy-to-understand language Illustrates macromodeling concepts through dedicated examples Includes a comprehensive set of end-of-chapter problems and exercises Passive Macromodeling: theory and applications serves as a reference for senior or graduate level courses in electrical engineering programs, and to engineers in the fields of numerical modeling, simulation, design, and optimization of electrical/electronic *** Grivet-Talocia, PhD, is an Associate Professor of Circuit theory at the Politecnico di Torino in Turin, Italy, and President of IdemWorks. Dr. Grivet-Talocia is author of over 150 technical papers published in international journals and conference proceedings. He invented several algorithms in the area of passive macromodeling, making them available through ***ørn Gustavsen, PhD, is a Chief Research Scientist in Energy Systems at SINTEF Energy Res

关键词： Macromodeling linear Time-Invariant Circuits linear Time-Invariant Systems Leplace Transforms Fourier Transforms Lumped LTI Systems The zero-input response The Lyapunov equation The zero-state response Gramians Distributed LTI Systems One-dimensional distributed circuits Two-dimensional distributed circuits Model Order Reduction Curve Fitting Black-Box Macromodeling ARMA modeling The Vector Fitting Algorithm Advance Vector Fitting Time-domain Simulation Multiconductor Transmission Lines Distributed Systems Computational Electromagnetics

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numerical SIMULATION OF FREE SURFACE SEEPAGE IN SATURATED SOIL USING SMOOTHED PARTICLE HYDRODYNAMICS 4

NUMERICAL SIMULATION OF FREE SURFACE SEEPAGE IN SATURATED SO...

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IV International conference on Particle-based methods (PARTICLES 2015)

作者： Peng, Chong Wu, Wei Yu, Haisui Wang, Chun Univ Nat Resources & Life Sci Inst Geotech Engn Feistmantelstr 4 A-1180 Vienna Austria Univ Nottingham Nottingham Ctr Geomech Nottingham NG7 2RD England Shanghai Jiao Tong Univ Sch Architecture Ocean & Civil Engn Shanghai 200240 Peoples R China

ISBN: (纸本)9788494424472

In this paper we present numerical simulations of free surface seepage in saturated soil using Smoothed Particle Hydro dynamics. The modeling of the water seepage is based on mixture theory. Soil skeleton and water are depicted by different kinds of particles. The water particles move according to momentum equations while the soil particles are fixed in position. The interactions between these two phases, consisting of drag force and buoyancy force, are added to the governing equations of the water phase. A non-linear drag force model is adopted. numerical results are compared with that from literature. It is demonstrated that seepage surface and pressure field can be obtained with satisfactory accuracy with the present model.

关键词： Seepage Soil-water coupling Delta-SPH Drag force

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Preconditioning of iterative methods - theory and applications

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numerical linear algebra WITH applications 2015年第6期22卷 901-902页

作者： Axelsson, O. Blaheta, R. Neytcheva, M. Pultarova, I. Acad Sci Czech Republic Inst Geon CS-70300 Ostrava Czech Republic Uppsala Univ Dept Informat Technol Uppsala Sweden Czech Tech Univ Fac Civil Engn Dept Math CR-16635 Prague Czech Republic

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Solving Multiscale linear Programs Using the Simplex Method in Quadruple Precision 3rd

Solving Multiscale Linear Programs Using the Simplex Method ...

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3rd International conference on numerical Analysis and Optimization - theory, methods, applications and Technology Transfer ((NAO)

作者： Ma, Ding Saunders, Michael A. Stanford Univ Dept Management Sci & Engn Stanford CA 94305 USA

ISBN: (纸本)9783319176895;9783319176888

Systems biologists are developing increasingly large models of metabolism and integrated models of metabolism and macromolecular expression. These Metabolic Expression (ME) models lead to sequences of multiscale linear programs for which small solution values of order 10(-6) to 10(-10) are meaningful. Standard LP solvers do not give sufficiently accurate solutions, and exact simplex solvers are extremely slow. We investigate whether double-precision and quadrupleprecision simplex solvers can together achieve reliability at acceptable cost. A double-precision LP solver often provides a reasonably good starting point for a Quad simplex solver. On a range of multiscale examples we find that 34-digit Quad floating-point achieves exceptionally small primal and dual infeasibilities (of order 10(-30)) when no more than 10(-15) is requested. On a significant ME model we also observe robustness in almost all (even small) solution values following relative perturbations of order 10(-6) to non-integer data values. Double and Quad Fortran 77 implementations of the linear and nonlinear optimization solver MINOS are available upon request.

关键词： Flux balance analysis Metabolic expression model Multiscale linear program Simplex method Quadruple precision Gfortran libquadmath MINOS

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A Positive Barzilai-Borwein-Like Stepsize and an Extension for Symmetric linear Systems 3rd

A Positive Barzilai-Borwein-Like Stepsize and an Extension f...

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3rd International conference on numerical Analysis and Optimization - theory, methods, applications and Technology Transfer ((NAO)

作者： Dai, Yu-Hong Al-Baali, Mehiddin Yang, Xiaoqi Chinese Acad Sci State Key Lab Sci & Engn Comp 55ZhongGuanCun DongluPOB 2719 Beijing 100190 Peoples R China Sultan Qaboos Univ Dept Math & Stat Muscat Oman Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

ISBN: (纸本)9783319176895;9783319176888

The Barzilai and Borwein (BB) gradient method has achieved a lot of attention since it performs much more better than the classical steepest descent method. In this paper, we analyze a positive BB-like gradient stepsize and discuss its possible uses. Specifically, we present an analysis of the positive stepsize for two-dimensional strictly convex quadratic functions and prove the R-superlinear convergence under some assumption. Meanwhile, we extend BB-like methods for solving symmetric linear systems and find that a variant of the positive stepsize is very useful in the context. Some useful discussions on the positive stepsize are also given.

关键词： Unconstrained optimization Barzilai and Borwein gradient method Quadratic function R-superlinear convergence Condition number

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An Efficient Task-Based Execution Model for Stochastic linear Solver on Multi-Core and Many-Core Systems 18

An Efficient Task-Based Execution Model for Stochastic Linea...

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18th IEEE International conference on Computational Science and Engineering (CSE)

作者： Ye, Fan Calvin, Christophe Petiton, Serge CEA Saclay Maison Simulat CEA DEN DANS DM2S Gif Sur Yvette France CEA Saclay CEA DEN DANS DM2S Gif Sur Yvette France Univ Lille 1 Lab Informat Fondamentale Lille F-59655 Villeneuve Dascq France

ISBN: (纸本)9781467382977

Monte Carlo methods are a wide range of computational algorithms which depend on repeated random sampling to obtain numerical results. They are of great interest in parallel computing because the samplings are very often independent of one another, which expose abundant parallelism. Such parallelism is well suited for modern processors with large number of cores. In this study, we revisit the Monte Carlo technique for solving linear systems. The conventional implementation of this method, in spite of its abundant parallelism, still exhibits some fundamental bottlenecks which limit performance: (a) relatively large amount of time spent in random number generation, (b) serialized selection of new states, (c) lack of vectorization which leads to low SIMD efficiency for processors with wide vector units, and (d) variable results due to the stochastic nature of algorithm. We propose an efficient task-based execution model for tackling these problems. It provides a new perspective to interpret the theory so we can bypass the inevitable routines in conventional implementation of Monte Carlo method, such as random number generation. The new model also exploits the salient architectural features of modern multi-core system, such as wide vector units and hardware support for irregular memory access. Our work is built on the latest research on task-based scheduling. It shows very promising performance on both multi-core and many-core system. Compared with optimized conventional parallel implementation, we achieved significant speedups (up to 3.68x) on test matrices.

关键词： Monte Carlo method linear algebra Multi-core Many-core Intel Many Integrated Core Architecture (Intel MIC)

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