Direct Methods

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Direct Methods for Sparse Linear Systems

Timothy A. Davis
Direct Methods for Sparse Linear Systems Book PDF

Author : Timothy A. Davis
Publisher : SIAM
Page : 228 pages
File Size : 41,8 Mb
Release : 2006-09-01
Category : Computers
ISBN : 9780898716139

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Direct Methods for Sparse Linear Systems by Timothy A. Davis Pdf

The sparse backslash book. Everything you wanted to know but never dared to ask about modern direct linear solvers. Chen Greif, Assistant Professor, Department of Computer Science, University of British Columbia.Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods. Its choice of scope is excellent John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara.Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis 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.With a strong emphasis on MATLAB and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.Audience This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index.

Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows

V.V. Aristov
Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows Book PDF

Author : V.V. Aristov
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401008662

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Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows by V.V. Aristov Pdf

This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.

Direct Methods in the Calculus of Variations

Bernard Dacorogna
Direct Methods in the Calculus of Variations Book PDF

Author : Bernard Dacorogna
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 54,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642514401

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Direct Methods in the Calculus of Variations by Bernard Dacorogna Pdf

In recent years there has been a considerable renewal of interest in the clas sical problems of the calculus of variations, both from the point of view of mathematics and of applications. Some of the most powerful tools for proving existence of minima for such problems are known as direct methods. They are often the only available ones, particularly for vectorial problems. It is the aim of this book to present them. These methods were introduced by Tonelli, following earlier work of Hilbert and Lebesgue. Although there are excellent books on calculus of variations and on direct methods, there are recent important developments which cannot be found in these books; in particular, those dealing with vector valued functions and relaxation of non convex problems. These two last ones are important in appli cations to nonlinear elasticity, optimal design . . . . In these fields the variational methods are particularly effective. Part of the mathematical developments and of the renewal of interest in these methods finds its motivations in nonlinear elasticity. Moreover, one of the recent important contributions to nonlinear analysis has been the study of the behaviour of nonlinear functionals un der various types of convergence, particularly the weak convergence. Two well studied theories have now been developed, namely f-convergence and compen sated compactness. They both include as a particular case the direct methods of the calculus of variations, but they are also, both, inspired and have as main examples these direct methods.

Direct Methods in the Theory of Elliptic Equations

Jindrich Necas
Direct Methods in the Theory of Elliptic Equations Book PDF

Author : Jindrich Necas
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 49,6 Mb
Release : 2011-10-06
Category : Mathematics
ISBN : 9783642104558

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Direct Methods in the Theory of Elliptic Equations by Jindrich Necas Pdf

Nečas’ book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner, presents Nečas’ work essentially in the form it was published in 1967. It gives a timeless and in some sense definitive treatment of a number issues in variational methods for elliptic systems and higher order equations. The text is recommended to graduate students of partial differential equations, postdoctoral associates in Analysis, and scientists working with linear elliptic systems. In fact, any researcher using the theory of elliptic systems will benefit from having the book in his library. The volume gives a self-contained presentation of the elliptic theory based on the "direct method", also known as the variational method. Due to its universality and close connections to numerical approximations, the variational method has become one of the most important approaches to the elliptic theory. The method does not rely on the maximum principle or other special properties of the scalar second order elliptic equations, and it is ideally suited for handling systems of equations of arbitrary order. The prototypical examples of equations covered by the theory are, in addition to the standard Laplace equation, Lame’s system of linear elasticity and the biharmonic equation (both with variable coefficients, of course). General ellipticity conditions are discussed and most of the natural boundary condition is covered. The necessary foundations of the function space theory are explained along the way, in an arguably optimal manner. The standard boundary regularity requirement on the domains is the Lipschitz continuity of the boundary, which "when going beyond the scalar equations of second order" turns out to be a very natural class. These choices reflect the author's opinion that the Lame system and the biharmonic equations are just as important as the Laplace equation, and that the class of the domains with the Lipschitz continuous boundary (as opposed to smooth domains) is the most natural class of domains to consider in connection with these equations and their applications.

Direct Methods

Aurora Angela Pisano,Konstantinos Vassilios Spiliopoulos,Dieter Weichert
Direct Methods Book PDF

Author : Aurora Angela Pisano,Konstantinos Vassilios Spiliopoulos,Dieter Weichert
Publisher : Springer Nature
Page : 253 pages
File Size : 47,6 Mb
Release : 2020-07-16
Category : Science
ISBN : 9783030488345

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Direct Methods by Aurora Angela Pisano,Konstantinos Vassilios Spiliopoulos,Dieter Weichert Pdf

This book provides an overview of direct methods such as limit and shakedown analysis, which are intended to do away with the need for cumbersome step-by-step calculations and determine the loading limits of mechanical structures under monotone, cyclic or variable loading with unknown loading history. The respective contributions demonstrate how tremendous advances in numerical methods, especially in optimization, have contributed to the success of direct methods and their practical applicability to engineering problems in structural mechanics, pavement and general soil mechanics, as well as the design of composite materials. The content reflects the outcomes of the workshop “Direct Methods: Methodological Progress and Engineering Applications,” which was offered as a mini-symposium of PCM-CMM 2019, held in Cracow, Poland in September 2019.

Direct Methods for Limit States in Structures and Materials

Konstantinos Spiliopoulos,Dieter Weichert
Direct Methods for Limit States in Structures and Materials Book PDF

Author : Konstantinos Spiliopoulos,Dieter Weichert
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 46,5 Mb
Release : 2013-08-13
Category : Technology & Engineering
ISBN : 9789400768277

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Direct Methods for Limit States in Structures and Materials by Konstantinos Spiliopoulos,Dieter Weichert Pdf

Knowing the safety factor for limit states such as plastic collapse, low cycle fatigue or ratcheting is always a major design consideration for civil and mechanical engineering structures that are subjected to loads. Direct methods of limit or shakedown analysis that proceed to directly find the limit states offer a better alternative than exact time-stepping calculations as, on one hand, an exact loading history is scarcely known, and on the other they are much less time-consuming. This book presents the state of the art on various topics concerning these methods, such as theoretical advances in limit and shakedown analysis, the development of relevant algorithms and computational procedures, sophisticated modeling of inelastic material behavior like hardening, non-associated flow rules, material damage and fatigue, contact and friction, homogenization and composites.

Direct Methods for Solving Macromolecular Structures

S. Fortier
Direct Methods for Solving Macromolecular Structures Book PDF

Author : S. Fortier
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 45,5 Mb
Release : 2013-06-29
Category : Science
ISBN : 9789401590938

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Direct Methods for Solving Macromolecular Structures by S. Fortier Pdf

This book of the proceedings of the 1997 NATO Advanced Study Institute (ASI) on Direct Methods for Solving Macromolecular Structures was assembled from the lecturers' contributions and represents a comprehensive and in-depth overview of crystallographic structure determination methods for macromolecules. While having a focus based on the direct methods, the Institute adopted an inclusive and broad perspective. Thus, both direct and experimental phasing techniques are presented in this book, highlighting their complementarities and synergies. As weil, methodologies spanning the full crystallographic image reconstruction process - from low resolution envelope definition to high resolution atomic refinement- are discussed. The first part of the book introduces the array of tools currently used in structure determination, whether originating from a mathematical, computational or experimental framework. This section of the book displays the variety and ingenuity of old and new phasing approaches developed to solve increasingly complex structures. Some of the contributions focus on recent developments and/or implementations that have given older approaches a new life. A case in point is the re-implementation of Buerger's superposition approach, which is now solving protein structures. Another beautiful example is found in the introduction to the traditional multiple isomorphous replacement approach where new techniques, such as site-directed mutagenesis and the use of inert gases in the preparation of heavy atom derivatives, are described. Equally impressive are the presentations of newer approaches, which take advantage of advances on the experimental front (e. g.

Theory and Practice of Direct Methods in Crystallography

M. F. C. Ladd,R. A. Palmer
Theory and Practice of Direct Methods in Crystallography Book PDF

Author : M. F. C. Ladd,R. A. Palmer
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461329794

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Theory and Practice of Direct Methods in Crystallography by M. F. C. Ladd,R. A. Palmer Pdf

Direct methods of crystal structure determination are usually associated with techniques in which phases for a set of structure factors are determined from the corresponding experimental amplitudes by probabilistic calcula tions. It is thus implied that such ab initio phase calculations do not require a knowledge of atomic positions, and this basis distinguishes direct methods from other techniques for structure determination. An acceptably wider interpretation of the term direct methods leads to other important applica tions involving, inter alia, the use of heavy atoms, resolution-limited phase data for large molecules, rotation functions, and Fourier series. These topics are discussed in the later chapters of this book. Although some earlier theoretical investigations were made by Harker and Kaspar, direct methods may be considered to have begun around the year 1950. Important landmarks in the development of the subject include the book by Hauptmann and Karle, The Centrosymmetric Crystal (1953), the definitive paper by Karle and Karle in Acta Crystallographica (1966), and the recent (1978) sophisticated program package MULTAN 78 produced mainly by Germain, Main, and Woolfson. Woolfson's book, Direct Methods in Crystallography, was published in 1961, but because of the rapid progress in direct methods, much of it soon became outmoded. It is interesting to note that direct methods nearly came into being many years earlier. Certainly the E2 relationship was used implicitly by Lonsdale in 1928 in determining the crystal structure of hexamethylbenzene.

Direct Methods for Sparse Matrices

Iain S. Duff,A. M. Erisman,John Ker Reid
Direct Methods for Sparse Matrices Book PDF

Author : Iain S. Duff,A. M. Erisman,John Ker Reid
Publisher : Oxford University Press
Page : 451 pages
File Size : 42,6 Mb
Release : 2017
Category : Electronic book
ISBN : 9780198508380

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Direct Methods for Sparse Matrices by Iain S. Duff,A. M. Erisman,John Ker Reid Pdf

The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields.This second edition is a complete rewrite of the first edition published 30 years ago. Much has changed since that time. Problems have grown greatly in size and complexity; nearly all examples in the first edition were of order less than 5,000 in the first edition, and are often more than a millionin the second edition. Computer architectures are now much more complex, requiring new ways of adapting algorithms to parallel environments with memory hierarchies. Because the area is such an important one to all of computational science and engineering, a huge amount of research has been done inthe last 30 years, some of it by the authors themselves. This new research is integrated into the text with a clear explanation of the underlying mathematics and algorithms.New research that is described includes new techniques for scaling and error control, new orderings, new combinatorial techniques for partitioning both symmetric and unsymmetric problems, and a detailed description of the multifrontal approach to solving systems that was pioneered by the research ofthe authors and colleagues. This includes a discussion of techniques for exploiting parallel architectures and new work for indefinite and unsymmetric systems.

Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows

V.V. Aristov
Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows Book PDF

Author : V.V. Aristov
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 49,6 Mb
Release : 2001-11-30
Category : Science
ISBN : 1402003889

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Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows by V.V. Aristov Pdf

This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.

Direct Methods in the Calculus of Variations

Enrico Giusti
Direct Methods in the Calculus of Variations Book PDF

Author : Enrico Giusti
Publisher : World Scientific
Page : 412 pages
File Size : 40,9 Mb
Release : 2003-01-15
Category : Mathematics
ISBN : 9789814488297

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Direct Methods in the Calculus of Variations by Enrico Giusti Pdf

This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory. Contents:Semi-Classical TheoryMeasurable FunctionsSobolev SpacesConvexity and SemicontinuityQuasi-Convex FunctionalsQuasi-MinimaHölder ContinuityFirst DerivativesPartial RegularityHigher Derivatives Readership: Graduate students, academics and researchers in the field of analysis and differential equations. Keywords:Reviews:“This book must be recommended both to beginners in variational calculus and to more confirmed specialists in regularity theory of elliptic problems. It will become a reference in the calculus of variations and it contains in one volume of a reasonable size a very clear presentation of deep results.”Zentralblatt MATH “It can be recommended for graduate courses or post-graduate courses in the calculus of variations, or as reference text.”Studia Universitatis Babes-Bolyai, Series Mathematica “The exposition is always clear and self-contained … therefore this book may serve well as a textbook for a graduate course on the subject. Each chapter is complemented with detailed historical notes and interesting results which may be difficult to find elsewhere.”Mathematical Reviews

Direct Methods for Limit and Shakedown Analysis of Structures

Paolo Fuschi,Aurora Angela Pisano,Dieter Weichert
Direct Methods for Limit and Shakedown Analysis of Structures Book PDF

Author : Paolo Fuschi,Aurora Angela Pisano,Dieter Weichert
Publisher : Springer
Page : 315 pages
File Size : 44,8 Mb
Release : 2015-01-06
Category : Technology & Engineering
ISBN : 9783319129280

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Direct Methods for Limit and Shakedown Analysis of Structures by Paolo Fuschi,Aurora Angela Pisano,Dieter Weichert Pdf

Articles in this book examine various materials and how to determine directly the limit state of a structure, in the sense of limit analysis and shakedown analysis. Apart from classical applications in mechanical and civil engineering contexts, the book reports on the emerging field of material design beyond the elastic limit, which has further industrial design and technological applications. Readers will discover that “Direct Methods” and the techniques presented here can in fact be used to numerically estimate the strength of structured materials such as composites or nano-materials, which represent fruitful fields of future applications. Leading researchers outline the latest computational tools and optimization techniques and explore the possibility of obtaining information on the limit state of a structure whose post-elastic loading path and constitutive behavior are not well defined or well known. Readers will discover how Direct Methods allow rapid and direct access to requested information in mathematically constructive manners without cumbersome step-by-step computation. Both researchers already interested or involved in the field and practical engineers who want to have a panorama of modern methods for structural safety assessment will find this book valuable. It provides the reader with the latest developments and a significant amount of references on the topic.

Direct Methods in Control Problems

Peter Falb
Direct Methods in Control Problems Book PDF

Author : Peter Falb
Publisher : Springer Nature
Page : 311 pages
File Size : 46,8 Mb
Release : 2020-01-02
Category : Science
ISBN : 9780817647230

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Direct Methods in Control Problems by Peter Falb Pdf

Various general techniques have been developed for control and systems problems, many of which involve indirect methods. Because these indirect methods are not always effective, alternative approaches using direct methods are of particular interest and relevance given the advances of computing in recent years. The focus of this book, unique in the literature, is on direct methods, which are concerned with finding actual solutions to problems in control and systems, often algorithmic in nature. Throughout the work, deterministic and stochastic problems are examined from a unified perspective and with considerable rigor. Emphasis is placed on the theoretical basis of the methods and their potential utility in a broad range of control and systems problems. The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers and may be used as a textbook for a graduate course or seminar on direct methods in control.

Advances in Direct Methods for Materials and Structures

Olga Barrera,Alan Cocks,Alan Ponter
Advances in Direct Methods for Materials and Structures Book PDF

Author : Olga Barrera,Alan Cocks,Alan Ponter
Publisher : Springer
Page : 0 pages
File Size : 49,5 Mb
Release : 2018-08-03
Category : Technology & Engineering
ISBN : 3319867067

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Advances in Direct Methods for Materials and Structures by Olga Barrera,Alan Cocks,Alan Ponter Pdf

This book offers a state-of-the-art overview and includes recent developments of various direct computational analysis methods. It is based on recently developed and widely employed numerical procedures for limit and shakedown analysis of structures and their extensions to a wide range of physical problems relevant to the design of materials and structural components. The book can be used as a complementary text for advanced academic courses on computational mechanics, structural mechanics, soil mechanics and computational plasticity and it can be used a research text.

The Direct Method in Soliton Theory

Ryogo Hirota
The Direct Method in Soliton Theory Book PDF

Author : Ryogo Hirota
Publisher : Cambridge University Press
Page : 220 pages
File Size : 47,7 Mb
Release : 2004-07-22
Category : Mathematics
ISBN : 0521836603

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The Direct Method in Soliton Theory by Ryogo Hirota Pdf

Account of method of solving soliton equations by the inventor of the method.