Direct Methods for Sparse Linear Systems

Author: Timothy A. Davis

Publisher: SIAM

ISBN: 9780898718881

Category: Linear systems

Page: 217

View: 3889

Presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.

Direct methods for sparse matrices

Author: Iain S. Duff,A. M. Erisman,John Ker Reid

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Mathematics

Page: 341

View: 4440

This book provides practical approaches to the efficient use of sparsity--a key to solving large problems in many fields, including computational science and engineering, where mathematical models give rise to very large systems of linear equations. The emphasis is on practicality, with conclusions based on concrete experience. Non-numeric computing techniques have been included as well as frequent illustrations in an attempt to bridge the gap between the written word and the working computer code. Exercises have been included to strengthen understanding of the material as well as to extend it for students and researchers in engineering, mathematics, and computer science.

Computational Methods for Large Sparse Power Systems Analysis

An Object Oriented Approach

Author: S. A. Soman,S. A. Khaparde,Shubha Pandit

Publisher: Springer Science & Business Media

ISBN: 9780792375913

Category: Computers

Page: 333

View: 7220

Computational methods in Power Systems require significant inputs from diverse disciplines, such as data base structures, numerical analysis etc. Strategic decisions in sparsity exploitation and algorithm design influence large-scale simulation and high-speed computations. Selection of programming paradigm shapes the design, its modularity and reusability. This has a far reaching effect on software maintenance. Computational Methods for Large Sparse Power Systems Analysis: An Object Oriented Approach provides a unified object oriented (OO) treatment for power system analysis. Sparsity exploitation techniques in OO paradigm are emphasized to facilitate large scale and fast computing. Specific applications like large-scale load flow, short circuit analysis, state estimation and optimal power flow are discussed within this framework. A chapter on modeling and computational issues in power system dynamics is also included. Motivational examples and illustrations are included throughout the book. A library of C++ classes provided along with this book has classes for transmission lines, transformers, substation etc. A CD-ROM with C++ programs is also included. It contains load flow, short circuit analysis and network topology processor applications. Power system data is provided and systems up to 150 buses can be studied. Other Special Features: This book is the first of its kind, covering power system applications designed with an OO perspective. Chapters on object orientation for modeling of power system computations, data structure, large sparse linear system solver, sparse QR decomposition in an OO framework are special features of this book.

Understanding and Implementing the Finite Element Method

Author: Mark S. Gockenbach

Publisher: SIAM

ISBN: 0898716144

Category: Mathematics

Page: 363

View: 7666

The ?nite element method is the most powerful general-purpose technique for comput­ing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the ?nite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics. Understanding and Implementing the Finite Element Method includes a carefully documented collection of MATLAB® programs implementing the ideas presented in the book. Readers will bene?t from a careful explanation of data structures and speci?c coding strategies and will learn how to write a ?nite element code from scratch. Students can use the MATLAB codes to experiment with the method and extend them in various ways to learn more about programming ?nite elements. This practical book should provide an excellent foundation for those who wish to delve into advanced texts on the subject, including advanced undergraduates and beginning graduate students in mathematics, engineering, and the physical sciences.Preface; Part I: The Basic Framework for Stationary Problems. Chapter 1: Some Model PDEs; Chapter 2: The weak form of a BVP; Chapter 3: The Galerkin method; Chapter 4: Piecewise polynomials and the finite element method; Chapter 5: Convergence of the finite element method; Part II Data Structures and Implementation. Chapter 6: The mesh data structure; Chapter 7: Programming the finite element method: Linear Lagrange triangles; Chapter 8: Lagrange triangles of arbitrary degree; Chapter 9: The finite element method for general BVPs; Part III: Solving the Finite Element Equations. Chapter 10: Direct solution of sparse linear systems; Chapter 11: Iterative methods: Conjugate gradients; Chapter 12: The classical stationary iterations; Chapter 13: The multigrid method; Part IV: Adaptive Methods. Chapter 14: Adaptive mesh generation; Chapter 15: Error estimators and indicators; Bibliography; Index.

Parallel Processing for Scientific Computing

Author: Michael A. Heroux,Padma Raghavan,Horst D. Simon

Publisher: SIAM

ISBN: 9780898718133

Category: Parallel processing (Electronic computers)

Page: 397

View: 7183

Parallel processing has been an enabling technology in scientific computing for more than 20 years. This book is the first in-depth discussion of parallel computing in 10 years; it reflects the mix of topics that mathematicians, computer scientists, and computational scientists focus on to make parallel processing effective for scientific problems. Presently, the impact of parallel processing on scientific computing varies greatly across disciplines, but it plays a vital role in most problem domains and is absolutely essential in many of them. Parallel Processing for Scientific Computing is divided into four parts: The first concerns performance modeling, analysis, and optimization; the second focuses on parallel algorithms and software for an array of problems common to many modeling and simulation applications; the third emphasizes tools and environments that can ease and enhance the process of application development; and the fourth provides a sampling of applications that require parallel computing for scaling to solve larger and realistic models that can advance science and engineering.

Finite Difference Methods for Ordinary and Partial Differential Equations

Steady-State and Time-Dependent Problems

Author: Randall J. LeVeque

Publisher: SIAM

ISBN: 9780898717839

Category: Differential equations

Page: 339

View: 8789

This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

Computer Solution of Large Linear Systems

Author: Gerard Meurant

Publisher: Elsevier

ISBN: 9780080529516

Category: Mathematics

Page: 776

View: 3540

This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Applied Parallel Computing

State of the Art in Scientific Computing

Author: Jack Dongarra,Kaj Madsen

Publisher: Springer Science & Business Media

ISBN: 3540290672

Category: Computers

Page: 1174

View: 2443

Introduction The PARA workshops in the past were devoted to parallel computing methods in science and technology. There have been seven PARA meetings to date: PARA’94, PARA’95 and PARA’96 in Lyngby, Denmark, PARA’98 in Umea, ? Sweden, PARA 2000 in Bergen, N- way, PARA 2002 in Espoo, Finland, and PARA 2004 again in Lyngby, Denmark. The ?rst six meetings featured lectures in modern numerical algorithms, computer science, en- neering, and industrial applications, all in the context of scienti?c parallel computing. This meeting in the series, the PARA 2004 Workshop with the title “State of the Art in Scienti?c Computing”, was held in Lyngby, Denmark, June 20–23, 2004. The PARA 2004 Workshop was organized by Jack Dongarra from the University of Tennessee and Oak Ridge National Laboratory, and Kaj Madsen and Jerzy Was ́niewski from the Technical University of Denmark. The emphasis here was shifted to high-performance computing (HPC). The ongoing development of ever more advanced computers provides the potential for solving increasingly dif?cult computational problems. However, given the complexity of modern computer architectures, the task of realizing this potential needs careful attention. For example, the failure to exploit a computer’s memory hi- archy can degrade performance badly. A main concern of HPC is the development of software that optimizes the performance of a given computer. The high cost of state-of-the-art computers can be prohibitive for many workplaces, especially if there is only an occasional need for HPC.

Acta Numerica 1993:

Author: Arieh Iserles

Publisher: Cambridge University Press

ISBN: 9780521443562

Category: Mathematics

Page: 334

View: 3708

Continuing the tradition established with the 1992 volume, this 1993's Acta Numerica presents six invited papers on a broad range of topics from numerical analysis. Papers treat each topic at a level intelligible by any numerical analyst from graduate student to professional.

Meshfree Approximation Methods with MATLAB

Author: Gregory E. Fasshauer

Publisher: World Scientific

ISBN: 981270633X

Category: Technology & Engineering

Page: 500

View: 9167

Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations.

Iterative Methods for Linear Systems

Theory and Applications

Author: Maxim A. Olshanskii,Eugene E. Tyrtshnikov

Publisher: SIAM

ISBN: 1611973457

Category: Mathematics

Page: 247

View: 3915

Iterative Methods for Linear Systems offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.

Scientific Computing with Case Studies

Author: Dianne P. O'Leary

Publisher: SIAM

ISBN: 0898717728

Category: Mathematical models

Page: 383

View: 7630

This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.

Numerical Methods for Large Eigenvalue Problems

Revised Edition

Author: Yousef Saad

Publisher: SIAM

ISBN: 1611970725

Category: Mathematics

Page: 276

View: 4558

This revised edition discusses numerical methods for computing the eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method and automatic multilevel substructuring.

Laser Spectroscopy IV

Proceedings of the Fourth International Conference, Rottarch-Egern, Fed. Rep. of Germany, June 11-15, 1979

Author: David Padua

Publisher: Springer Science & Business Media

ISBN: 038709766X

Category: Computers

Page: 2175

View: 7533

Traditionally, the discipline of parallel computing has encompassed a wide range of topics ranging from machine organization all the way to applications. The Encyclopedia of Parallel Computing is likewise broad in scope, covering machine organization, programming, algorithms, and applications. Within each area, the Encyclopedia covers concepts, designs, and specific implementations. In the area of algorithms, the encyclopedia will cover (1) concepts such as cache-oblivious algorithms and systolic algorithms, (2) specific numerical and non-numerical algorithms such as parallel matrix-matrix multiplication and graph algorithms to, for example, find connected components in parallel, and (3) implementations of algorithms in the form of widely used libraries such as LAPACK. In the area of architecture, the encyclopedia will contain (1) concepts such as sequential consistency and cache coherency, (2) machine classes such as shared-memory multiprocessors and dataflow machines, and (3) specific machines such as IBM's cell processor and Intel's multicore machines. In the area of software, it will cover (1) concepts such as races and autoparallelization, and (2) designs in the form of parallel programming languages, library interfaces, and operating systems. The encyclopedia also will cover application issues emphasizing the type of parallel computation involved and the magnitude in terms of computational requirements of the applications.Each encyclopedia entry will be concise and clear and will contain references to the literature for readers wishing to study the topic of the entry in depth. The broad coverage--together with extensive pointers to the literature for in-depth study'will make the encyclopedia an invaluable reference tool for researchers, practitioners and students alike.

Parallel Numerical Algorithms

Author: David E. Keyes,Ahmed Sameh,V. Venkatakrishnan

Publisher: Springer Science & Business Media

ISBN: 9401154120

Category: Mathematics

Page: 395

View: 3090

In this volume, designed for computational scientists and engineers working on applications requiring the memories and processing rates of large-scale parallelism, leading algorithmicists survey their own field-defining contributions, together with enough historical and bibliographical perspective to permit working one's way to the frontiers. This book is distinguished from earlier surveys in parallel numerical algorithms by its extension of coverage beyond core linear algebraic methods into tools more directly associated with partial differential and integral equations - though still with an appealing generality - and by its focus on practical medium-granularity parallelism, approachable through traditional programming languages. Several of the authors used their invitation to participate as a chance to stand back and create a unified overview, which nonspecialists will appreciate.