Numerical analysis Books
Cambridge University Press Approximation Theory and Methods
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£59.84
Cambridge University Press Modelling of Computer and Communication Systems 24 Cambridge Computer Science Texts Series Number 24
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£36.04
Cambridge University Press Interval Methods for Systems of Equations
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£105.45
Cambridge University Press Noisy Information and Computational Complexity
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£40.84
Cambridge University Press On L1Approximation 93 Cambridge Tracts in Mathematics Series Number 93
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£105.45
Cambridge University Press A Handbook of Fourier Theorems
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£37.99
Cambridge University Press Numerical Recipes in Pascal First Edition The Art of Scientific Computing
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£75.99
Cambridge University Press Numerical Recipes Routines and Examples in BASIC First Edition
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£42.74
Cambridge University Press Numerical Simulation of Unsteady Flows and Transition to Turbulence
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£131.40
Cambridge University Press Acta Numerica 1992 Volume 1
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£41.83
Cambridge University Press Perspectives of Nonlinear Dynamics
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£64.59
Cambridge University Press Numerical Recipes in Fortran Example Book The Art Of Scientific Computing
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£40.84
Cambridge University Press Numerical Mathematics A Laboratory Approach
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£100.70
Cambridge University Press Acta Numerica 1993 Volume 2 Acta Numerica Series Number 2
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£85.50
Cambridge University Press Parallel Scientific Computing in C and Mpi
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£71.24
Cambridge University Press ObjectOriented Programming via Fortran 9095
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£60.79
Cambridge University Press Introductory Computational Physics
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£24.99
Cambridge University Press Noisy Info Computational Compl
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£110.20
Cambridge University Press Numerical Recipes in Fortran 90 Volume 2 Volume 2 of Fortran Numerical Recipes The Art of Parallel Scientific Computing Fortran Numerical Recipes v 2
Book SynopsisNumerical Recipes in Fortran 90 starts with a detailed introduction to the Fortran 90 language and then presents the basic concepts of parallel programming. All 350+ routines from the second edition of Numerical Recipes are presented in Fortran 90. Many are completely reworked algorithmically so as to be 'parallel-ready' and to utilise Fortran 90's advanced language features. Numerical Recipes in Fortran 90 emphasises general principles, but throughout there are also numerous hints and tips. This volume is intended for use with the original Numerical Recipes in Fortran, 2nd Edition (now called Numerical Recipes in Fortran 77) and does not discuss how the individual programs are used, or how the mathematical methods are used. An excellent guide for Fortran programmers interested in moving to Fortran 90, or C/C++ programmers interested in parallel programming.Trade Review'This new edition begins with three completely new chapters that provide a detailed introduction to the Fortran 90 language and then present the basic concepts of parallel programming, all with the same clarity and good cheer for which Numerical Recipes is famous.' L'Enseignement Mathématique' … certainly recommendable'. Eric de Sturler, ITW NieuwsTable of Contents1. Introduction to Fortran 90 language features; 2. Introduction to parallel programming; 3. Numerical recipes utility functions for Fortran 90; Part I. Fortran 90 Code chapters: 4. Preliminaries; 5. Solution of linear algebraic equations; 6. Interpolation and extrapolation; 7. Integration of functions; 8. Evaluation of functions; 9. Special functions; 10. Random numbers; 11. Sorting; 12. Root finding and nonlinear sets of equations; 13. Minimization or maximization of functions; 14. Eigensystems; 15. Fast Fourier transform; 16. Fourier and spectral applications; 17. Statistical description of Data; 18. Modelling of data; 19. Integration of ordinary differential equations; 20. Two point boundary value problems; 21. Integral equations and inverse theory; 22. Partial differential equations; 23 Less-numerical algorithms; Part II. Appendices: 24. Listing of utility modules (nrtype and nrutil); 25. Listing of explicit interfaces; 26. Index of programs and dependencies.
£59.84
Cambridge University Press The Numerical Solution of Integral Equations of the Second Kind 4 Cambridge Monographs on Applied and Computational Mathematics Series Number 4
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£100.70
Cambridge University Press Numerical Solution of Partial Differential Equations
Book SynopsisThe 2005 second edition of a highly successful graduate text giving a complete introduction to partial differential equations and numerical analysis. Revised to include new sections on finite volume methods, modified equation analysis, multigrid, and conjugate gradient methods.Trade Review' … attractive text … very clear and supported by many illuminating figures. Therefore, the book is suitable for a course for applied mathematicians or engineers at the advanced undergraduate level.' Math. Meth. Oper. Res.Table of Contents1. Introduction; 2. Parabolic equations in one space variable; 3. 2-D and 3-D parabolic equations; 4. Hyperbolic equations in one space dimension; 5. Consistency, convergence and stability; 6. Linear second order elliptic equations in two dimensions; 7. Iterative solution of linear algebraic equations; Bibliography; Index.
£47.49
Cambridge University Press Dynamic Multilevel Methods and the Numerical Simulation of Turbulence
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£87.39
Cambridge University Press Special Functions 71 Encyclopedia of Mathematics and its Applications Series Number 71
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£139.65
Cambridge University Press Level Set Methods and Fast Marching Methods
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£52.24
Cambridge University Press Strongly Elliptic Systems and Boundary Integral Equations
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£48.47
Cambridge University Press Writing Scientific Software A Guide To Good Style
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£45.59
Cambridge University Press Weather Prediction by Numerical Process Cambridge Mathematical Library
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£64.59
Cambridge University Press Finite Elements Theory Fast Solvers and Applications in Solid Mechanics
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£54.14
Cambridge University Press Fundamentals of Engineering Numerical Analysis
Book SynopsisThis text introduces numerical methods and shows how to develop, analyse, and use them. Complete MATLAB programs are now available at www.cambridge.org/Moin, with more than 30 exercises. This thorough and practical book is a first course in numerical analysis for new graduate students in engineering and physical science.Trade Review'… thorough and practical …' Mathematical ReviewsTable of Contents1. Interpolation; 2. Numerical differentiation - finite differences; 3. Numerical integration; 4. Numerical solution of ordinary differential equations; 5. Numerical solution of partial differential equations; 6. Discrete transform methods; Appendix. A review of linear algebra.
£63.64
Cambridge University Press Foundations of Computational Mathematics Hong Kong 2008 363 London Mathematical Society Lecture Note Series Series Number 363
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£59.22
Cambridge University Press Acta Numerica 1999 Volume 8 Acta Numerica Series Number 8
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£90.25
Cambridge University Press Direct Numerical Simulations of GasLiquid Multiphase Flows
Book SynopsisAccurately predicting the behaviour of multiphase flows is a problem of immense industrial and scientific interest. Modern computers can now study the dynamics in great detail and these simulations yield unprecedented insight. This book provides a comprehensive introduction to direct numerical simulations of multiphase flows for researchers and graduate students.Trade Review"This book provides a comprehensive introduction to direct numerical simulations of multiphase flows. It is useful for researchers and graduate students in computational engineering science who are interested in the development and application of numerical simulation methods for multiphase incompressible flows." Arnold Reusken, Mathematical ReviewsTable of ContentsPreface; 1. Introduction; 2. Fluid mechanics with interfaces; 3. Numerical solutions of the Navier–Stokes equations; 4. Advecting a fluid interface; 5. The volume-of-fluid method; 6. Advecting marker points - front tracking; 7. Surface tension; 8. Disperse bubbly flows; 9. Atomization and breakup; 10. Droplet collision, impact and splashing; 11. Extensions; Appendix A. Interfaces: description and definitions; Appendix B. Distributions on the interface; Appendix C. Cube-chopping; Appendix D. Dynamics of liquid sheets; Bibliography; Index.
£99.75
Cambridge University Press Geometry and Topology for Mesh Generation
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£105.45
Cambridge University Press SchwarzChristoffel Mapping 08 Cambridge Monographs on Applied and Computational Mathematics Series Number 8
Book SynopsisA comprehensive look at the Schwarz-Christoffel transformation, including its many applications.Trade Review'Altogether an excellent book written by the masters of the SC mapping who command both theory and numerics.' Dieter Gaier, Zbl. MATHTable of ContentsPreface; 1. Introduction; 2. Essentials; 3. Numerical methods; 4. Variations; 5. Applications; Using the SC toolbox.
£54.14
Cambridge University Press Introductory Computational Physics
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£52.24
Cambridge University Press A Practical Guide to the Invariant Calculus 26 Cambridge Monographs on Applied and Computational Mathematics Series Number 26
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£72.19
Cambridge University Press Fundamentals of Engineering Numerical Analysis
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£94.99
Cambridge University Press Exact and Approximate Controllability for Distributed Parameter Systems A Numerical Approach 117 Encyclopedia of Mathematics and its Applications Series Number 117
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£133.95
Cambridge University Press Nonlocal Continuum Limits of pLaplacian Problems on Graphs
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£17.00
Cambridge University Press Inverse Problems and Data Assimilation
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£66.50
Cambridge University Press HighAccuracy Finite Difference Methods
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£71.24
Cambridge University Press The Mathematics of Signal Processing Cambridge Texts in Applied Mathematics Series Number 48
Book SynopsisArising from courses taught by the authors, this largely self-contained treatment is ideal for mathematicians who are interested in applications or for students from applied fields who want to understand the mathematics behind their subject. Early chapters cover Fourier analysis, functional analysis, probability and linear algebra, all of which have been chosen to prepare the reader for the applications to come. The book includes rigorous proofs of core results in compressive sensing and wavelet convergence. Fundamental is the treatment of the linear system y=Îx in both finite and infinite dimensions. There are three possibilities: the system is determined, overdetermined or underdetermined, each with different aspects. The authors assume only basic familiarity with advanced calculus, linear algebra and matrix theory and modest familiarity with signal processing, so the book is accessible to students from the advanced undergraduate level. Many exercises are also included.Trade Review'Damelin and Miller provide a very detailed and thorough treatment of all the important mathematics related to signal processing. This includes the required background information found in elementary mathematics courses, so their book is really self-contained. The style of writing is suitable not only for mathematicians, but also for practitioners from other areas. Indeed, Damelin and Miller managed to write their text in a form that is accessible to nonspecialists, without giving up mathematical rigor.' Kai Diethelm, Computing Reviews'In the last 20 years or so, many books on wavelets have been published; most of them deal with wavelets from either the engineering or the mathematics perspective, but few try to connect the two viewpoints. The book under review falls under the last category … Overall, the book is a good addition to the literature on engineering mathematics.' Ahmed I. Zayed, Mathematical ReviewsTable of Contents1. Introduction; 2. Normed vector spaces; 3. Analytic tools; 4. Fourier series; 5. Fourier transforms; 6. Compressive sensing; 7. Discrete transforms; 8. Linear filters; 9. Windowed Fourier transforms, continuous wavelets, frames; 10. Multiresolution analysis; 11. Discrete wavelet theory; 12. Biorthogonal filters and wavelets; 13. Parsimonious representation of data; Bibliography; Index.
£105.45
Cambridge University Press The Cambridge Companion to Baseball
Book SynopsisProvides an introduction to numerical methods for students in engineering courses. This book covers the solution of equations, interpolation and data fitting, solution of differential equations, eigenvalue problems and optimisation. The algorithms are implemented in Python 3, a high-level programming language that rivals MATLAB® in readability and ease of use.Trade Review'… a practical introduction, pushing the theory as far in the background as possible.' The European Mathematical Society (euro-math-soc.eu)'This book is nicely focused on the most frequently encountered types of numerical problems that scientists and engineers usually face and the most common and robust algorithms for solving them. The text is just the right size for a semester-long course for upper-division undergraduates or first-year graduate students … this is a well-written text that is logically organized, attractively presented, and supported with challenging problems.' Anthony J. Duben, Computing ReviewsTable of Contents1. Introduction to Python; 2. Systems of linear algebraic equations; 3. Interpolation and curve fitting; 4. Roots of equations; 5. Numerical differentiation; 6. Numerical integration; 7. Initial value problems; 8. Two-point boundary value problems; 9. Symmetric matrix eigenvalue problems; 10. Introduction to optimization.
£85.49
Cambridge University Press Foundations of Signal Processing
Book SynopsisThis comprehensive, accessible textbook covers the basics of signal processing, building up from fundamental principles to practical applications. It uses engineering notation to make mathematical concepts easy to follow, includes numerous homework problems and is accompanied by an extensive Mathematica® companion and instructor solutions manual.Trade Review'This is a major book about a serious subject - the combination of engineering and mathematics that goes into modern signal processing: discrete time, continuous time, sampling, filtering, and compression. The theory is beautiful and the applications are so important and widespread.' Gil Strang, Massachusetts Institute of Technology'A refreshing new approach to teaching the fundamentals of signal processing. Starting from basic concepts in algebra and geometry, [the authors] bring the reader to deep understandings of modern signal processing. Truly a gem!' Rico Malvar, Microsoft Research'A wonderful book that connects together all the elements of modern signal processing … it's all here and seamlessly integrated, along with a summary of history and developments in the field. A real tour-de-force, and a must-have on every signal processor's shelf!' Robert D. Nowak, University of Wisconsin, Madison'Finally a wonderful and accessible book for teaching modern signal processing to undergraduate students.' Stéphane Mallat, École Normale Supérieure'Most introductory signal processing textbooks focus on classical transforms, and study how these can be used. Instead, Foundations of Signal Processing encourages readers to think of signals first. It develops a 'signal-centric' view, one that focuses on signals, their representation and approximation, through the introduction of signal spaces. Unlike most entry-level signal processing texts, this general view, which can be applied to many different signal classes, is introduced right at the beginning. From this, starting from basic concepts, and placing an emphasis on intuition, this book develops mathematical tools that give the readers gets a fresh perspective on classical results, while providing them with the tools to understand many state of the art signal representation techniques.' Antonio Ortega, University of Southern California'Foundations of Signal Processing … is a pleasure to read. Drawing on the authors' rich experience of research and teaching of signal processing and signal representations, it provides an intellectually cohesive and modern view of the subject from the geometric point of view of vector spaces. Emphasizing Hilbert spaces, where fine technicalities can be relegated to backstage, this textbook strikes an excellent balance between intuition and mathematical rigor, that will appeal to both undergraduate and graduate engineering students. The last two chapters, on sampling and interpolation, and on localization and uncertainty, take full advantage of the machinery developed in the previous chapters to present these two very important topics of modern signal processing, that previously were only found in specialized monographs. The explanations of advanced topics are exceptionally lucid, exposing the reader to the ideas and thought processes behind the results and their derivation. Students will learn … why things work, at a deep level, which will equip them for independent further reading and research. I look forward to using this text in my own teaching.' Yoram Bresler, University of Illinois, Urbana-ChampaignTable of Contents1. On rainbows and spectra; 2. From Euclid to Hilbert: 2.1 Introduction; 2.2 Vector spaces; 2.3 Hilbert spaces; 2.4 Approximations, projections, and decompositions; 2.5 Bases and frames; 2.6 Computational aspects; 2.A Elements of analysis and topology; 2.B Elements of linear algebra; 2.C Elements of probability; 2.D Basis concepts; Exercises with solutions; Exercises; 3. Sequences and discrete-time systems: 3.1 Introduction; 3.2 Sequences; 3.3 Systems; 3.4 Discrete-time Fourier Transform; 3.5 z-Transform; 3.6 Discrete Fourier Transform; 3.7 Multirate sequences and systems; 3.8 Stochastic processes and systems; 3.9 Computational aspects; 3.A Elements of analysis; 3.B Elements of algebra; Exercises with solutions; Exercises; 4. Functions and continuous-time systems: 4.1 Introduction; 4.2 Functions; 4.3 Systems; 4.4 Fourier Transform; 4.5 Fourier series; 4.6 Stochastic processes and systems; Exercises with solutions; Exercises; 5. Sampling and interpolation: 5.1 Introduction; 5.2 Finite-dimensional vectors; 5.3 Sequences; 5.4 Functions; 5.5 Periodic functions; 5.6 Computational aspects; Exercises with solutions; Exercises; 6. Approximation and compression: 6.1 Introduction; 6.2 Approximation of functions on finite intervals by polynomials; 6.3 Approximation of functions by splines; 6.4 Approximation of functions and sequences by series truncation; 6.5 Compression; 6.6 Computational aspects; Exercises with solutions; Exercises; 7. Localization and uncertainty: 7.1 Introduction; 7.2 Localization for functions; 7.3 Localization for sequences; 7.4 Tiling the time–frequency plane; 7.5 Examples of local Fourier and wavelet bases; 7.6 Recap and a glimpse forward; Exercises with solutions; Exercises.
£59.84
John Wiley & Sons Inc The Scaled Boundary Finite Element Method
Book SynopsisAn informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlightedTable of ContentsPreface xv Acknowledgements xix About the Companion Website xxi 1 Introduction 1 1.1 Numerical Modelling 1 1.2 Overview of the Scaled Boundary Finite Element Method 6 1.3 Features and Example Applications of the Scaled Boundary Finite Element Method 10 1.3.1 Linear Elastic Fracture Mechanics: Crack Terminating at Material Interface 11 1.3.2 Automatic Mesh Generation Based on Quadtree/Octree 13 1.3.3 Treatment of Non-matching Meshes 14 1.3.4 Crack Propagation 17 1.3.5 Adaptive Analysis 17 1.3.6 TransientWave Scattering in an Alluvial Basin 19 1.3.7 Automatic Image-based Analysis 19 1.3.7.1 Two-dimensional Elastoplastic Analysis of Cast Iron 20 1.3.7.2 Three-dimensional Concrete Specimen 22 1.3.8 Automatic Analysis of STL Models 24 1.4 Summary 26 Part I Basic Concepts and MATLAB Implementation of the Scaled Boundary Finite Element Method in Two Dimensions 27 2 Basic Formulations of the Scaled Boundary Finite Element Method 31 2.1 Introduction 31 2.2 Modelling of Geometry in Scaled Boundary Coordinates 31 2.2.1 S-domains: Scaling Requirement on Geometry, Scaling Centre and Scaling of Boundary 31 2.2.2 S-elements: Boundary Discretization of S-domains 37 2.2.3 Scaled Boundary Transformation 40 2.2.3.1 Scaled Boundary Coordinates 40 2.2.3.2 Coordinate Transformation of Partial Derivatives 42 2.2.3.3 Geometrical Properties in Scaled Boundary Coordinates 44 2.3 Governing Equations of Linear Elasticity in Scaled Boundary Coordinates 50 2.4 Semi-analytical Representation of Displacement and Strain Fields 51 2.5 Derivation of the Scaled Boundary Finite Element Equation by the Virtual Work Principle 53 2.5.1 Virtual Displacement and Strain Fields in Scaled Boundary Coordinates 54 2.5.2 Nodal Force Functions 54 2.5.3 The Scaled Boundary Finite Element Equation 55 2.6 Computer Program Platypus: Coefficient Matrices of an S-element 63 2.6.1 Element Coefficient Matrices of a 2-node Line Element 63 2.6.2 Assembly of Coefficient Matrices of an S-element 67 3 Solution of the Scaled Boundary Finite Element Equation by Eigenvalue Decomposition 73 3.1 Solution Procedure for the Scaled Boundary Finite Element Equations in Displacement 73 3.2 Pre-conditioning of Eigenvalue Problems 77 3.3 Computer Program Platypus: Solution of the Scaled Boundary Finite Element Equation of a Bounded S-element by the Eigenvalue Method 78 3.4 Assembly of S-elements and Solution of Global System of Equations 84 3.4.1 Assembly of S-elements 84 3.4.2 Surface Tractions 85 3.4.3 Enforcing Displacement Boundary Conditions 87 3.5 Computer Program Platypus: Assembly and Solution 87 3.5.1 Assembly of Global Stiffness Matrix 87 3.5.2 Assembly of Load Vector 95 3.5.3 Solution of Global System of Equations 96 3.5.4 Utility Functions 97 3.6 Examples of Static Analysis Using Platypus 102 3.7 Evaluation of Internal Displacements and Stresses of an S-element 111 3.7.1 Integration Constants and Internal Displacements 111 3.7.2 Strain/Stress Modes and Strain/Stress Fields 112 3.7.3 Shape Functions of Polygon Elements Modelled as S-elements 114 3.8 Computer Program Platypus: Internal Displacements and Strains 114 3.9 Body Loads 132 3.10 Dynamics and Vibration Analysis 135 3.10.1 Mass Matrix and Equation of Motion 135 3.10.2 Natural Frequencies and Mode Shapes 140 3.10.3 Response History Analysis Using the Newmark Method 143 4 Automatic Polygon Mesh Generation for Scaled Boundary Finite Element Analysis 149 4.1 Introduction 149 4.2 Basics of Geometrical Representation by Signed Distance Functions 150 4.3 Computer Program Platypus: Generation of Polygon S-elementMesh 154 4.3.1 Mesh Data Structure 157 4.3.2 Centroid of a Polygon 165 4.3.3 Converting a TriangularMesh to an S-elementMesh 166 4.3.4 Use of Polygon Meshes Generated by PolyMesher in a Scaled Boundary Finite Element Analysis 171 4.3.5 Dividing Edges of Polygons into Multiple Elements 172 4.4 Examples of Scaled Boundary Finite Element Analysis Using Platypus 175 4.4.1 A Deep Beam 178 4.4.1.1 Static Analysis 186 4.4.1.2 Modal Analysis 189 4.4.1.3 Response History Analysis 190 4.4.1.4 Pure Bending of a Beam: 2 Line Elements on an Edge of Polygons 190 4.4.2 A Circular Hole in an Infinite Plane Under Remote Uniaxial Tension 193 4.4.3 An L-shaped Panel 197 4.4.3.1 Static Analysis 203 4.4.3.2 Modal Analysis 204 4.4.3.3 Response History Analysis 207 5 Modelling Considerations in the Scaled Boundary Finite Element Analysis 209 5.1 Effect of Location of Scaling Centre on Accuracy 209 5.2 Mesh Transition 212 5.2.1 Local Mesh Refinement 212 5.2.2 Rapid Mesh Transition 214 5.2.3 Effect of Nonuniformity of Line Element Length on the Boundary of S-elements 216 5.3 Connecting Non-matching Meshes of Multiple Domains 218 5.3.1 Computer Program Platypus: Combining Two Non-matching Meshes 220 5.3.2 Computer Program Platypus: Modelling of a Problem by Multiple Domains with Non-matching Meshes 223 5.3.3 Examples 225 5.4 Modelling of Stress Singularities 234 Part II Theory and Applications of the Scaled Boundary Finite Element Method 237 6 Derivation of the Scaled Boundary Finite Element Equation in Three Dimensions 239 6.1 Introduction 239 6.2 Scaling of Boundary 239 6.3 Boundary Discretization of an S-domain 242 6.3.1 Isoparametric Quadrilateral Elements 243 6.3.1.1 Four-node Quadrilateral Element 243 6.3.1.2 Quadrilateral Element of Variable Number of Nodes 245 6.3.2 Isoparametric Triangular Elements 246 6.3.2.1 Three-node Triangular Elements 247 6.3.2.2 Six-node Triangular Elements 248 6.4 Scaled Boundary Transformation of Geometry 249 6.5 Geometrical Properties in Scaled Boundary Coordinates 253 6.6 Governing Equations of Elastodynamics with Geometry in Scaled Boundary Coordinates 257 6.7 Derivation of the Scaled Boundary Finite Element Equation by the Galerkin’s Weighted Residual Technique 259 6.7.1 Displacement, Strain Fields and Nodal Force Functions in Scaled Boundary Coordinates 259 6.7.2 The Scaled Boundary Finite Element Equation 262 6.8 Unified Formulations in Two andThree Dimensions 267 6.9 Formulation of the Scaled Boundary Finite Element Equation as a System of First-order Differential Equations 268 6.10 Properties of Coefficient Matrices 269 6.10.1 Coefficient Matrices [E0] and [M0] 270 6.10.2 Coefficient Matrix [E2] 270 6.10.3 Matrix [Zp] 271 6.11 Linear Completeness of the Scaled Boundary Finite Element Solution 272 6.11.1 Constant Displacement Field 272 6.11.2 Linear Displacement Field 273 6.12 Scaled Boundary Finite Element Equation in Stiffness 278 7 Solution of the Scaled Boundary Finite Element Equation in Statics by Schur Decomposition 281 7.1 Introduction 281 7.2 Basics of Matrix Exponential Function 283 7.3 Schur Decomposition 287 7.3.1 Introduction 287 7.3.2 Treatment of the Diagonal Block of Eigenvalues of 0 288 7.4 Solution Procedure for a Bounded S-element by Schur Decomposition 291 7.4.1 Transformation of the Scaled Boundary Finite Element Equation 291 7.4.2 Enforcing the Boundary Condition at the Scaling Centre 292 7.4.3 Determining the Solution for Displacement and Nodal Force Functions 294 7.4.4 Determining the Static Stiffness Matrix 295 7.5 Solution of Displacement and Stress Fields of an S-element 295 7.5.1 Integration Constants 295 7.5.2 Stress Modes and Stresses on the Boundary 296 7.6 Block-diagonal Schur Decomposition 297 7.7 Solution Procedure by Block-diagonal Schur Decomposition 303 7.7.1 General Solution of the Scaled Boundary Finite Element Equation 303 7.7.1.1 [Zp] Having No Eigenvalues of Zero 304 7.7.1.2 [Zp] Having Eigenvalues of Zero 304 7.7.2 Solution for Bounded S-elements 305 7.7.3 Solution for Unbounded S-elements 307 7.7.3.1 [Zp] Having No Eigenvalues of Zero 307 7.7.3.2 [Zp] Having Eigenvalues of Zero 308 7.8 Displacements and Stresses of an S-element by Block-diagonal Schur Decomposition 310 7.8.1 Integration Constants and Displacement Fields 310 7.8.2 Stress Modes and Stress Fields 311 7.8.3 Shape Functions of Polytope Elements 312 7.9 Body Loads 313 7.10 Mass Matrix 315 7.11 Remarks 317 7.12 Examples 319 7.12.1 Circular Cavity in Full-plane 319 7.12.2 Bi-materialWedge 322 7.12.3 Interface Crack in Anisotropic Bi-material Full-plane 325 7.13 Summary 327 8 High-order Elements 329 8.1 Lagrange Interpolation 330 8.2 One-dimensional Spectral Elements 333 8.2.1 Shape Functions 334 8.2.2 Numerical Integration of Element Coefficient Matrices 337 8.2.2.1 Gauss-Legendre Quadrature 337 8.2.2.2 Gauss-Lobatto-Legendre Quadrature 338 8.3 Two-dimensional Quadrilateral Spectral Elements 341 8.3.1 Shape Functions 341 8.3.2 Integration of Element Coefficient Matrices by Gauss-Lobatto-Legendre Quadrature 342 8.4 Examples 344 8.4.1 A Cantilever Beam Subject to End Loading 345 8.4.2 A Circular Hole in an Infinite Plate 347 8.4.3 An L-shaped Panel 349 8.4.4 A 3D Cantilever Beam Subject to End-shear Loading 351 8.4.5 A Pressurized Hollow Sphere 352 9 Quadtree/Octree Algorithm of Mesh Generation for Scaled Boundary Finite Element Analysis 355 9.1 Introduction 355 9.1.1 Mesh Generation 355 9.1.2 The Quadtree/Octree Algorithm 357 9.2 Data Structure of S-element Meshes 360 9.3 Quadtree/Octree Mesh Generation of Digital Images 361 9.3.1 Illustration of Quadtree Decomposition of Two-dimensional Images by an Example 361 9.3.2 Octree Decomposition 366 9.4 Solutions of S-elements with the Same Pattern of Node Configuration 370 9.4.1 Two-dimensional S-elements 370 9.4.2 Three-dimensional S-elements 372 9.5 Examples of Image-based Analysis 374 9.5.1 A 2D Concrete Specimen 374 9.5.2 A 3D Concrete Specimen 376 9.6 Quadtree/Octree Mesh Generation for CAD Models 378 9.6.1 Quadtree/Octree Grid 380 9.6.2 Trimming of Boundary Cells 381 9.7 Examples Using Quadtree/Octree Meshes of CAD Models 383 9.7.1 Square Body with Multiple Holes 384 9.7.2 An Evolving Void in a Square Body 385 9.7.3 Adaptive Analysis of an L-shaped Panel 386 9.7.4 A Mechanical Part 387 9.7.5 STL Models 389 9.8 Remarks 394 10 Linear Elastic Fracture Mechanics 395 10.1 Introduction 395 10.2 Basics of Fracture Analysis: Asymptotic Solutions, Stress Intensity Factors, and the T-stress 397 10.2.1 Crack in Homogeneous Isotropic Material 397 10.2.2 Interfacial Cracks between Two Isotropic Materials 401 10.2.3 Interfacial Cracks between Two AnisotropicMaterials 402 10.2.4 Multi-materialWedges 405 10.3 Modelling of Singular Stress Fields by the Scaled Boundary Finite Element Method 406 10.4 Stress Intensity Factors and the T-stress of a Cracked Homogeneous Body 407 10.5 Definition and Evaluation of Generalized Stress Intensity Factors 416 10.6 Examples of Highly Accurate Stress Intensity Factors and T-stress 432 10.6.1 A Single Edge-cracked Rectangular Body Under Tension 433 10.6.2 A Single Edge-cracked Rectangular Body Under Bending 435 10.6.3 A Centre-cracked Rectangular Body Under Tension 437 10.6.4 A Double Edge-cracked Rectangular Body Under Tension 438 10.6.5 A Single Edge-cracked Rectangular Body Under End Shearing 439 10.7 Modelling of Crack Propagation 440 10.7.1 Modelling of Crack Paths by Polygon Meshes 442 10.7.2 Modelling of Crack Paths by Quadtree Meshes 443 10.7.3 Examples of Crack PropagationModelling 444 10.7.3.1 Fatigue Crack Propagation Using Polygon Mesh 444 10.7.3.2 Crack Propagation in a Beam with Three Holes 447 Appendix A Governing Equations of Linear Elasticity 449 A.1 Three-dimensional Problems 449 A.1.1 Strain 449 A.1.2 Stress and Equilibrium Equation 450 A.1.3 Stress-strain Relationship and Material Elasticity Matrix 451 A.1.4 Boundary Conditions 453 A.2 Two-dimensional Problems 454 A.2.1 Elasticity Matrix in Plane Stress 455 A.2.2 Elasticity Matrix in Plane Strain 456 A.3 Unified Expressions of Governing Equations 457 Appendix B Matrix Power Function 459 B.1 Definition of Matrix Power Function 459 B.2 Application to Solution of System of Ordinary Differential Equations 460 B.3 Computation of Matrix Power Function by Eigenvalue Method 461 Bibliography 463 Index 475
£106.35
John Wiley & Sons Inc Finite Elements
Book SynopsisApproaches computational engineering sciences from the perspective of engineering applications Uniting theory with hands-on computer practice, this book gives readers a firm appreciation of the error mechanisms and control that underlie discrete approximation implementations in the engineering sciences. Key features: Illustrative examples include heat conduction, structural mechanics, mechanical vibrations, heat transfer with convection and radiation, fluid mechanics and heat and mass transport Takes a cross-discipline continuum mechanics viewpoint Includes Matlab toolbox and .m data files on a companion website, immediately enabling hands-on computing in all covered disciplines Website also features eight topical lectures from the author's own academic courses It provides a holistic view of the topic from covering the different engineering problems that can be solved using finite element to how each pTable of ContentsPreface viii Notation xi 1 COMPUTATIONAL ENGINEERING SCIENCE 1 1.1 Engineering simulation 1 1.2 A problem solving environment 2 1.3 Problem statements in engineering 4 1.4 Decisions on forming WSN 6 1.5 Discrete approximate WSh implementation 8 1.6 Chapter summary 9 1.7 Chapter references 10 2 PROBLEM STATEMENTS 11 2.1 Engineering simulation 11 2.2 Continuum mechanics viewpoint 12 2.3 Continuum conservation law forms 12 2.4 Constitutive closure for conservation law PDEs 14 2.5 Engineering science continuum mechanics 18 2.6 Chapter references 20 3 SOME INTRODUCTORY MATERIAL 21 3.1 Introduction 21 3.2 Multi-dimensional PDEs, separation of variables 22 3.3 Theoretical foundations, GWSh 27 3.4 A legacy FD construction 28 3.5 An FD approximate solution 30 3.6 Lagrange interpolation polynomials 31 3.7 Chapter summary 32 3.8 Exercises 34 3.9 Chapter references 34 4 HEAT CONDUCTION35 4.1 A steady heat conduction example 35 4.2 Weak form approximation, error minimization 37 4.3 GWSN discrete implementation, FE basis38 4.4 Finite element matrix statement 41 4.5 Assembly of {WS}e to form algebraic GWSh 43 4.6 Solution accuracy, error distribution 45 4.7 Convergence, boundary heat flux 47 4.8 Chapter summary 47 4.9 Exercises 48 4.10 Chapter reference 48 5 STEADY HEAT TRANSFER, n =149 5.1 Introduction 49 5.2 Steady heat transfer, n = 1 50 5.3 FE k = 1 trial space basis matrix library 52 5.4 Object-oriented GWSh programming 55 5.5 Higher completeness degree trial space bases58 5.6 Global theory, asymptotic error estimate 62 5.7 Non-smooth data, theory generalization 66 5.8 Temperature dependent conductivity, non-linearity 69 5.9 Static condensation, p-elements 72 5.10 Chapter summary 75 5.11 Exercises 76 5.12 Computer labs 77 5.13 Chapter references 78 6 ENGINEERING SCIENCES, n =1 79 6.1 Introduction 79 6.2 The Euler-Bernoulli beam equation 80 6.3 Euler-Bernoulli beam theory GWSh reformulation 85 6.4 The Timoshenko beam theory 92 6.5 Mechanical vibrations of a beam 99 6.6 Fluid mechanics, potential flow 106 6.7 Electromagnetic plane wave propagation110 6.8 Convective-radiative finned cylinder heat transfer 112 6.9 Chapter summary 120 6.10 Exercises122 6.10 Computer labs 123 6.11 Chapter references 124 7 STEADY HEAT TRANSFER, n > 1 125 7.1 Introduction 125 7.2 Multi-dimensional FE bases and DOF 126 7.3 Multi-dimensional FE operations 129 7.4 The NC k = 1,2 basis FE matrix library 132 7.5 NC basis {WS}e template, accuracy, convergence 136 7.6 The tensor product basis element family 139 7.7 Gauss numerical quadrature, k = 1 TP basis library 141 7.8 Convection-radiation BC GWSh implementation 146 7.9 Linear basis GWSh template unification 150 7.10 Accuracy, convergence revisited 152 7.11 Chapter summary 153 7.12 Exercises155 7.13 Computer labs 155 7.14 Chapter references 156 8 FINITE DIFFERENCES OF OPINION 159 8.1 The FD-FE correlation159 8.2 The FV-FE correlation162 8.3 Chapter summary 167 8.4 Exercises168 9 CONVECTION-DIFFUSION, n = 1 169 9.1 Introduction169 9.2 The Galerkin weak statement 170 9.3 GWSh completion for time dependence172 9.4 GWSh + qTS algorithm templates 173 9.5 GWSh + qTS algorithm asymptotic error estimates 175 9.6 Performance verification test cases 177 9.7 Dispersive error characterization 180 9.8 A modified Galerkin weak statement 184 9.9 Verification problem statements revisited 187 9.10 Unsteady heat conduction 190 9.11 Chapter summary 193 9.12 Exercises 193 9.13 Computer labs 194 9.14 Chapter references 195 10 CONVECTION-DIFFUSION, n > 1 197 10.1 The problem statement 197 10.2 GWSh + qTS formulation reprise 198 10.3 Matrix library additions, templates 200 10.4 mPDE Galerkin weak forms, theoretical analyses 202 10.5 Verification, benchmarking and validation 207 10.6 Mass transport, the rotating cone verification 208 10.7 The gaussian plume benchmark 211 10.8 The steady n-D Peclet problem verification 213 10.9 Mass transport, a validated n = 3 experiment 215 10.10 Numerical linear algebra, matrix iteration 222 10.11 Newton and AF TP jacobian templates 227 10.12 Chapter summary 229 10.13 Exercises231 10.14 Computer labs 231 10.15 Chapter references232 11 ENGINEERING SCIENCES, n > 1 235 11.1 Introduction 235 11.2 Structural mechanics236 11.3 Structural mechanics, virtual work FE form 240 11.4 Plane stress/strain, GWSh implementation 242 11.5 Elasticity computer lab 246 11.6 Fluid mechanics, incompressible-thermal flow 251 11.7 Vorticity-streamfunction GWSh + qTS algorithm 254 11.8 An isothermal INS validation experiment 258 11.9 Multi-mode convection heat transfer262 11.10 Mechanical vibrations, normal mode GWSh 267 11.11 Normal modes of a vibrating membrane270 11.12 Multi-physics solid-fluid mass transport 276 11.13 Chapter summary 280 11.14 Exercises 282 11.15 Computer labs283 11.14 Chapter references 284 12 CONCLUSION 287 Index 289
£89.25
Society for Industrial & Applied Mathematics,U.S. Numerical Analysis: Theory and Experiments
Book SynopsisThis textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems—interpolation, integration, linear systems, zero finding, and differential equations—are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises.Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.
£91.20
World Scientific Publishing Co Pte Ltd Explorations In Numerical Analysis And Machine Learning With Julia
£85.50
