Numerical analysis Books
Princeton University Press Numerical Methods Design Analysis and Computer
Book SynopsisProvides an exploration of standard numerical analysis topics, as well as non-traditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. This textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering.Trade Review"Distinguishing features are the inclusion of many recent applications of numerical methods and the extensive discussion of methods based on Chebyshev interpolation. This book would be suitable for use in courses aimed at advanced undergraduate students in mathematics, the sciences, and engineering."--Choice "An instructor could assemble several different one-semester courses using this book--numerical linear algebra and interpolation, or numerical solutions of differential equations--or perhaps a two-semester sequence. This is a charming book, well worth consideration for the next numerical analysis course."--William J. Satzer, MAA FocusTable of ContentsPreface xiii Chapter 1: MATHEMATICAL MODELING 1 1.1 Modeling in Computer Animation 2 1.1.1 A Model Robe 2 1.2 Modeling in Physics: Radiation Transport 4 1.3 Modeling in Sports 6 1.4 Ecological Models 8 1.5 Modeling a Web Surfer and Google 11 1.5.1 The Vector Space Model 11 1.5.2 Google's PageRank 13 1.6 Chapter 1 Exercises 14 Chapter 2: BASIC OPERATIONS WITH MATLAB 19 2.1 Launching MATLAB 19 2.2 Vectors 20 2.3 Getting Help 22 2.4 Matrices 23 2.5 Creating and Running .m Files 24 2.6 Comments 25 2.7 Plotting 25 2.8 Creating Your Own Functions 27 2.9 Printing 28 2.10 More Loops and Conditionals 29 2.11 Clearing Variables 31 2.12 Logging Your Session 31 2.13 More Advanced Commands 31 2.14 Chapter 2 Exercises 32 Chapter 3: MONTE CARLO METHODS 41 3.1 A Mathematical Game of Cards 41 3.1.1 The Odds in Texas Holdem 42 3.2 Basic Statistics 46 3.2.1 Discrete Random Variables 48 3.2.2 Continuous Random Variables 51 3.2.3 The Central Limit Theorem 53 3.3 Monte Carlo Integration 56 3.3.1 Buffon's Needle 56 3.3.2 Estimating pi 58 3.3.3 Another Example of Monte Carlo Integration 60 3.4 Monte Carlo Simulation of Web Surfing 64 3.5 Chapter 3 Exercises 67 Chapter 4: SOLUTION OF A SINGLE NONLINEAR EQUATION IN ONE UNKNOWN 71 4.1 Bisection 75 4.2 Taylor's Theorem 80 4.3 Newton's Method 83 4.4 Quasi-Newton Methods 89 4.4.1 Avoiding Derivatives 89 4.4.2 Constant Slope Method 89 4.4.3 Secant Method 90 4.5 Analysis of Fixed Point Methods 93 4.6 Fractals, Julia Sets, and Mandelbrot Sets 98 4.7 Chapter 4 Exercises 102 Chapter 5: FLOATING-POINT ARITHMETIC 107 5.1 Costly Disasters Caused by Rounding Errors 108 5.2 Binary Representation and Base 2 Arithmetic 110 5.3 Floating-Point Representation 112 5.4 IEEE Floating-Point Arithmetic 114 5.5 Rounding 116 5.6 Correctly Rounded Floating-Point Operations 118 5.7 Exceptions 119 5.8 Chapter 5 Exercises 120 Chapter 6: CONDITIONING OF PROBLEMS; STABILITY OF ALGORITHMS 124 6.1 Conditioning of Problems 125 6.2 Stability of Algorithms 126 6.3 Chapter 6 Exercises 129 Chapter 7: DIRECT METHODS FOR SOLVING LINEAR SYSTEMS AND LEAST SQUARES PROBLEMS 131 7.1 Review of Matrix Multiplication 132 7.2 Gaussian Elimination 133 7.2.1 Operation Counts 137 7.2.2 LU Factorization 139 7.2.3 Pivoting 141 7.2.4 Banded Matrices and Matrices for Which Pivoting Is Not Required 144 7.2.5 Implementation Considerations for High Performance 148 7.3 Other Methods for Solving Ax = b 151 7.4 Conditioning of Linear Systems 154 7.4.1 Norms 154 7.4.2 Sensitivity of Solutions of Linear Systems 158 7.5 Stability of Gaussian Elimination with Partial Pivoting 164 7.6 Least Squares Problems 166 7.6.1 The Normal Equations 167 7.6.2 QR Decomposition 168 7.6.3 Fitting Polynomials to Data 171 7.7 Chapter 7 Exercises 175 Chapter 8: POLYNOMIAL AND PIECEWISE POLYNOMIAL INTERPOLATION 181 8.1 The Vandermonde System 181 8.2 The Lagrange Form of the Interpolation Polynomial 181 8.3 The Newton Form of the Interpolation Polynomial 185 8.3.1 Divided Differences 187 8.4 The Error in Polynomial Interpolation 190 8.5 Interpolation at Chebyshev Points and chebfun 192 8.6 Piecewise Polynomial Interpolation 197 8.6.1 Piecewise Cubic Hermite Interpolation 200 8.6.2 Cubic Spline Interpolation 201 8.7 Some Applications 204 8.8 Chapter 8 Exercises 206 Chapter 9: NUMERICAL DIFFERENTIATION AND RICHARDSON EXTRAPOLATION 212 9.1 Numerical Differentiation 213 9.2 Richardson Extrapolation 221 9.3 Chapter 9 Exercises 225 Chapter 10: NUMERICAL INTEGRATION 227 10.1 Newton-Cotes Formulas 227 10.2 Formulas Based on Piecewise Polynomial Interpolation 232 10.3 Gauss Quadrature 234 10.3.1 Orthogonal Polynomials 236 10.4 Clenshaw-Curtis Quadrature 240 10.5 Romberg Integration 242 10.6 Periodic Functions and the Euler-Maclaurin Formula 243 10.7 Singularities 247 10.8 Chapter 10 Exercises 248 Chapter 11: NUMERICAL SOLUTION OF THE INITIAL VALUE PROBLEM FOR ORDINARY DIFFERENTIAL EQUATIONS 251 11.1 Existence and Uniqueness of Solutions 253 11.2 One-Step Methods 257 11.2.1 Euler's Method 257 11.2.2 Higher-Order Methods Based on Taylor Series 262 11.2.3 Midpoint Method 262 11.2.4 Methods Based on Quadrature Formulas 264 11.2.5 Classical Fourth-Order Runge-Kutta and Runge-Kutta-Fehlberg Methods 265 11.2.6 An Example Using MATLAB's ODE Solver 267 11.2.7 Analysis of One-Step Methods 270 11.2.8 Practical Implementation Considerations 272 11.2.9 Systems of Equations 274 11.3 Multistep Methods 275 11.3.1 Adams-Bashforth and Adams-Moulton Methods 275 11.3.2 General Linear m-Step Methods 277 11.3.3 Linear Difference Equations 280 11.3.4 The Dahlquist Equivalence Theorem 283 11.4 Stiff Equations 284 11.4.1 Absolute Stability 285 11.4.2 Backward Differentiation Formulas (BDF Methods) 289 11.4.3 Implicit Runge-Kutta (IRK) Methods 290 11.5 Solving Systems of Nonlinear Equations in Implicit Methods 291 11.5.1 Fixed Point Iteration 292 11.5.2 Newton's Method 293 11.6 Chapter 11 Exercises 295 Chapter 12: MORE NUMERICAL LINEAR ALGEBRA: EIGENVALUES AND ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS 300 12.1 Eigenvalue Problems 300 12.1.1 The Power Method for Computing the Largest Eigenpair 310 12.1.2 Inverse Iteration 313 12.1.3 Rayleigh Quotient Iteration 315 12.1.4 The QR Algorithm 316 12.1.5 Google's PageRank 320 12.2 Iterative Methods for Solving Linear Systems 327 12.2.1 Basic Iterative Methods for Solving Linear Systems 327 12.2.2 Simple Iteration 328 12.2.3 Analysis of Convergence 332 12.2.4 The Conjugate Gradient Algorithm 336 12.2.5 Methods for Nonsymmetric Linear Systems 334 12.3 Chapter 12 Exercises 345 Chapter 13: NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEMS 350 13.1 An Application: Steady-State Temperature Distribution 350 13.2 Finite Difference Methods 352 13.2.1 Accuracy 354 13.2.2 More General Equations and Boundary Conditions 360 13.3 Finite Element Methods 365 13.3.1 Accuracy 372 13.4 Spectral Methods 374 13.5 Chapter 13 Exercises 376 Chapter 14: NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS 379 14.1 Elliptic Equations 381 14.1.1 Finite Difference Methods 381 14.1.2 Finite Element Methods 386 14.2 Parabolic Equations 388 14.2.1 Semidiscretization and the Method of Lines 389 14.2.2 Discretization in Time 389 14.3 Separation of Variables 396 14.3.1 Separation of Variables for Difference Equations 400 14.4 Hyperbolic Equations 402 14.4.1 Characteristics 402 14.4.2 Systems of Hyperbolic Equations 403 14.4.3 Boundary Conditions 404 14.4.4 Finite Difference Methods 404 14.5 Fast Methods for Poisson's Equation 409 14.5.1 The Fast Fourier Transform 411 14.6 Multigrid Methods 414 14.7 Chapter 14 Exercises 418 APPENDIX A REVIEW OF LINEAR ALGEBRA 421 A.1 Vectors and Vector Spaces 421 A.2 Linear Independence and Dependence 422 A.3 Span of a Set of Vectors; Bases and Coordinates; Dimension of a Vector Space 423 A.4 The Dot Product; Orthogonal and Orthonormal Sets; the Gram-Schmidt Algorithm 423 A.5 Matrices and Linear Equations 425 A.6 Existence and Uniqueness of Solutions; the Inverse; Conditions for Invertibility 427 A.7 Linear Transformations; the Matrix of a Linear Transformation 431 A.8 Similarity Transformations; Eigenvalues and Eigenvectors 432 APPENDIX B TAYLOR'S THEOREM IN MULTIDIMENSIONS 436 References 439 Index 445
£76.00
MP-AMM American Mathematical Meromorphic Functions and Linear Algebra
Book SynopsisDescribes in monograph form important applications in numerical methods of linear algebra. This book studies the behavior of the resolvent of a matrix under the perturbation by low rank matrices. It also introduces the basics of value distribution theory of meromorphic scalar functions.Table of ContentsPrologue Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Epilogue Bibliography.
£51.30
John Wiley & Sons Inc The Finite Element Method in Electromagnetics
Book SynopsisUseful in analyzing electromagnetic problems in a variety of engineering circumstances, the finite element method is a powerful simulation technique. This book explains the method's processes and techniques in careful, meticulous prose. It covers not only essential finite element method theory, but also its latest developments and applications.Table of ContentsPreface xix Preface to the First Edition xxiii Preface to the Second Edition xxvii 1 Basic Electromagnetic Theory 1 1.1 Brief Review of Vector Analysis 2 1.2 Maxwell's Equations 4 1.3 Scalar and Vector Potentials 6 1.4 Wave Equations 7 1.5 Boundary Conditions 8 1.6 Radiation Conditions 11 1.7 Fields in an Infinite Homogeneous Medium 11 1.8 Huygen's Principle 13 1.9 Radar Cross Sections 14 1.10 Summary 15 2 Introduction to the Finite Element Method 17 2.1 Classical Methods for Boundary-Value Problems 17 2.2 Simple Example 21 2.3 Basic Steps of the Finite Element Method 27 2.4 Alternative Presentation of the Finite Element Formulation 34 2.5 Summary 36 3 One-Dimensional Finite Element Analysis 39 3.1 Boundary-Value Problem 39 3.2 Variational Formulation 40 3.3 Finite Element Analysis 42 3.4 Plane-Wave Reflection by a Metal-Backed Dielectric Slab 53 3.5 Scattering by a Smooth, Convex Impedance Cylinder 59 3.6 Higher-Order Elements 62 3.7 Summary 74 4 Two-Dimensional Finite Element Analysis 77 4.1 Boundary-Value Problem 77 4.2 Variational Formulation 79 4.3 Finite Element Analysis 81 4.4 Application to Electrostatic Problems 98 4.5 Application to Magnetostatic Problems 103 4.6 Application to Quasistatic Problems: Analysis of Multiconductor Transmission Lines 105 4.7 Application to Time-Harmonic Problems 109 4.8 Higher-Order Elements 128 4.9 Isoparametric Elements 144 4.10 Summary 149 5 Three-Dimensional Finite Element Analysis 151 5.1 Boundary-Value Problem 151 5.2 Variational Formulation 152 5.3 Finite Element Analysis 153 5.4 Higher-Order Elements 160 5.5 Isoparametric Elements 162 5.6 Application to Electrostatic Problems 168 5.7 Application to Magnetostatic Problems 169 5.8 Application to Time-Harmonic Field Problems 176 5.9 Summary 188 6 Variational Principles for Electromagnetics 191 6.1 Standard Variational Principle 192 6.2 Modified Variational Principle 197 6.3 Generalized Variational Principle 201 6.4 Variational Principle for Anisotrpic Medium 203 6.5 Variational Principle for Resistive Sheets 207 6.6 Concluding Remarks 209 7 Eigenvalue Problems: Waveguides and Cavities 211 7.1 Scalar Formulations for Closed Waveguides 212 7.2 Vector Formulations for Closed Waveguides 225 7.3 Open Waveguides 235 7.4 Three-Dimensional Cavities 238 7.5 Summary 239 8 Vector Finite Elements 243 8.1 Two-Dimensional Edge Elements 244 8.2 Waveguide Problem Revisited 256 8.3 Three-Dimensional Edge Elements 259 8.4 Cavity Problem Revisited 270 8.5 Waveguide Discontinuities 274 8.6 Higher-Order Interpolatory Vector Elements 278 8.7 Higher-Order Hierarchical Vector Elements 293 8.8 Computational Issues 305 8.9 Summary 309 9 Absorbing Boundary Conditions 315 9.1 Two-Dimensional Absorbing Boundary Conditions 316 9.2 Three-Dimensional Absorbing Boundary Conditions 323 9.3 Scattering Analysis Using Absorbing Boundary Conditons 328 9.4 Adaptive Absorbing Boundary Conditons 339 9.5 Fictitious Absorbers 348 9.6 Perfectly Matched Layers 350 9.7 Application of PML to Body-of-Revolutions Problems 368 9.8 Summary 371 10 Finite Element-Boundary Integral Methods 379 10.1 Scattering by Two-Dimensional Cavity-Backed Apertures 381 10.2 Scattering by Two-Dimensional Cylindrical Structures 399 10.3 Scattering by Three-Dimensional Cavity-Backed Apertures 411 10.4 Radiation by Microstrip Patch Antennas in a Cavity 425 10.5 Scattering by General Three-Dimensional Bodies 430 10.6 Solution of the Finite Element-Boundary Integral System 436 10.7 Symmetric Finite Element-Boundary Integral Formulations 447 10.8 Summary 462 11 Finite Element-Eigenfunction Expansion Methods 469 11.1 Waveguide Port Boundary Conditions 470 11.2 Open-Region Scattering 487 11.3 Coupled Basis Functions: The Unimoment Method 494 11.4 Finite Element-Extended Boundary Condition Method 502 11.5 Summary 509 12 Finite Element Analysis in the Time Domain 513 12.1 Finite Element Formulation and Temporal Excitation 514 12.2 Time-Domain Discretization 518 12.3 Stability Analysis 523 12.4 Modeling of Dispersive Media 529 12.5 Truncation via Absorbing Boundary Conditions 538 12.6 Truncation via Perfectly Matched Layers 541 12.7 Truncation via Boundary Integral Equations 551 12.8 Time-Domain Wqaveguide Port Boundary Conditions 562 12.9 Hybrid Field-Circuit Analysis 569 12.10 Dual-Field Domain Decomposition and Element-Level Methods 587 12.11 Discontinuous Galerkin Time-Domain Methods 605 12.12 Summary 625 13 Finite Element Analysis of Periodic Structures 637 13.1 Finite Element Formulation for a Unit Cell 638 13.2 Scattering by One-Dimensional Periodic Structures: Frequency-Domain Analysis 651 13.3 Scattering by One-Dimensional Periodic Structures: Time-Domain Analysis 656 13.4 Scattering by Two-Dimensional Periodic Structures: Frequency-Domain Analysis 663 13.5 Scattering by Two-Dimensonal Periodic Structures: Time-Domain Analysis 670 13.6 Analysis of Angular Periodic Strctures 678 13.7 Summary 682 14 Domain Decompsition for Large-Scale Analysis 687 14.1 Schwarz Methods 688 14.2 Schur Complement Methods 693 14.3 FETI-DP Method for Low-Frequency Problems 705 14.4 FETI-DP Method for High-Frequency Problems 728 14.5 Noncomformal FETI-DP Method Based on Cement Elements 743 14.6 Application of Second-Order Transmission Conditions 753 14.7 Summary 760 15 Solution of Finite Element Equations 767 15.1 Decomposition Methods 769 15.2 Conjugate Gradient Methods 778 15.3 Solution of Eigenvalue Problems 791 15.4 Fast Frequency-Sweep Computation 797 15.5 Summary 803 Appendix A: Basic Vector Identities and Integral Theorems 809 Appendix B: The Ritz Procedure for Complex-Valued Problems 813 Appendix C: Green's Functions 817 Appendix D: Singular Integral Evaluation 825 Appendix E: Some Special Functions 829 Index 837
£137.66
Springer-Verlag New York Inc. Handbook of Experimental Structural Dynamics
Book SynopsisHistory of Experimental Structural Mechanics.- Sensors .- Instrumentation.- Applied Digital Signal Processing.- Basic Measurements.- Structural Measurements.- Environmental Measurements.- Design of Tests.- Modal Parameter Estimation.- Modal Analysis of Rotating Systems.- Operating Modal Analysis.- Computational Methods in Structural Dynamics.- Finite/Boundary Element Modeling and Model Reduction.- FE Model Correlation.- Model Updating.- Damping of Materials and Stuctures.- Model Validation/Verification/Calibration.- Uncertainty Quantification and Statistical Issues.- Nonlinear System Analysis.- Rotating System Analysis.- Structural Health Monitoring and Damage Detection.- System Modeling.- Modal Modeling.- Impedance Modeling.- Acoustics of Structural Systems-VibroAcoustics.- Automotive Structural Testing.- Civil Structural Testing.- Aerospace Structural Testing.- Sports Equipment Testing.Table of ContentsHistory of Experimental Structural Mechanics.- Sensors .- Instrumentation.- Applied Digital Signal Processing.- Basic Measurements.- Structural Measurements.- Environmental Measurements.- Design of Tests.- Modal Parameter Estimation.- Modal Analysis of Rotating Systems.- Operating Modal Analysis.- Computational Methods in Structural Dynamics.- Finite/Boundary Element Modeling and Model Reduction.- FE Model Correlation.- Model Updating.- Damping of Materials and Stuctures.- Model Validation/Verification/Calibration.- Uncertainty Quantification and Statistical Issues.- Nonlinear System Analysis.- Rotating System Analysis.- Structural Health Monitoring and Damage Detection.- System Modeling.- Modal Modeling.- Impedance Modeling.- Acoustics of Structural Systems-VibroAcoustics.- Automotive Structural Testing.- Civil Structural Testing.- Aerospace Structural Testing.- Sports Equipment Testing.
£582.71
Springer Introduction to Nonlinear Finite Element Analysis
Book SynopsisPreliminary concepts.- Nonlinear Finite Element Analysis Procedure.- Finite Element Analysis for Nonlinear Elastic Systems.- Finite Element Analysis for Elastoplastic Problems.- Finite Element Analysis for Contact Problems. Table of ContentsPreliminary concepts.- Nonlinear Finite Element Analysis Procedure.- Finite Element Analysis for Nonlinear Elastic Systems.- Finite Element Analysis for Elastoplastic Problems.- Finite Element Analysis for Contact Problems.
£67.49
Society for Industrial & Applied Mathematics,U.S. Iterative Methods for Linear Systems: Theory and
Book SynopsisSystems of linear equations are ubiquitous in numerical analysis and scientific computing. and iterative methods are indispensable for the numerical treatment of such systems. This book offers a 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 perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning. The book supplements standard texts on numerical mathematics for first-year graduate and advanced undergraduate courses and is suitable for advanced graduate classes covering numerical linear algebra and Krylov subspace and multigrid iterative methods. It will be useful to researchers interested in numerical linear algebra and engineers who use iterative methods for solving large algebraic systems.Table of ContentsList of figures; List of algorithms; Preface; 1. Krylov subspace methods; 2. Toeplitz matrices and preconditioners; 3. Multigrid preconditioners; 4. Preconditioners by space decomposition; 5. Some applications; Bibliography; Index.
£81.60
Society for Industrial & Applied Mathematics,U.S. Fundamentals of Numerical Computation
Book Synopsis“If mathematical modeling is the process of turning real phenomena into mathematical abstractions, then numerical computation is largely about the transformation from abstract mathematics to concrete reality. Many science and engineering disciplines have long benefited from the tremendous value of the correspondence between quantitative information and mathematical manipulation.” -from the PrefaceFundamentals of Numerical Computation is an advanced undergraduate-level introduction to the mathematics and use of algorithms for the fundamental problems of numerical computation: linear algebra, finding roots, approximating data and functions, and solving differential equations. The book is organized with simpler methods in the first half and more advanced methods in the second half, allowing use for either a single course or a sequence of two courses. The authors take readers from basic to advanced methods, illustrating them with over 200 self-contained MATLAB functions and examples designed for those with no prior MATLAB experience. Although the text provides many examples, exercises, and illustrations, the aim of the authors is not to provide a cookbook per se, but rather an exploration of the principles of cooking.Professors Driscoll and Braun have developed an online resource that includes well-tested materials related to every chapter. Among these materials are lecture-related slides and videos, ideas for student projects, laboratory exercises, computational examples and scripts, and all the functions presented in the book.
£93.50
Society for Industrial & Applied Mathematics,U.S. PETSc for Partial Differential Equations:
Book SynopsisThe Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers.Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.
£81.60
Society for Industrial & Applied Mathematics,U.S. A Software Repository for Gaussian Quadratures
Book SynopsisThis companion piece to the author’s 2018 book, A Software Repository for Orthogonal Polynomials, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions.The repository contains 60 datasets, each dealing with a particular weight function. Included are classical, quasi-classical, and, most of all, nonclassical weight functions and associated orthogonal polynomials.
£51.85
Society for Industrial & Applied Mathematics,U.S. Numerical Homogenization by Localized Orthogonal
Book SynopsisThis book presents the first survey of the Localized Orthogonal Decomposition (LOD) method, a pioneering approach for the numerical homogenization of partial differential equations with multiscale data beyond periodicity and scale separation. The authors provide a careful error analysis, including previously unpublished results, and a complete implementation of the method in MATLAB. They also reveal how the LOD method relates to classical homogenization and domain decomposition. Illustrated with numerical experiments that demonstrate the significance of the method, the book is enhanced by a survey of applications including eigenvalue problems and evolution problems.Numerical Homogenization by Localized Orthogonal Decomposition is appropriate for graduate students in applied mathematics, numerical analysis, and scientific computing. Researchers in the field of computational partial differential equations will find this self-contained book of interest, as will applied scientists and engineers interested in multiscale simulation.
£41.61
Society for Industrial & Applied Mathematics,U.S. Introduction to Numerical Linear Algebra
Book SynopsisFit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems.Introduction to Numerical Linear Algebra is ideal for a flipped classroom, as it provides detailed explanations that allow students to read on their own and instructors to go beyond lecturing, assumes that the reader has taken a course on linear algebra, but reviews background as needed, and covers several topics not commonly addressed in related introductory books, including diffusion, a toy model of computed tomography, global positioning systems, the use of eigenvalues in analyzing stability of equilibria, a detailed derivation and careful motivation of the QR method for eigenvalues starting from power iteration, a discussion of the use of the SVD for assigning grades, and multigrid methods. This textbook is appropriate for undergraduate and beginning graduate students in mathematics and related fields. It can be used in the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory
£67.15
Society for Industrial & Applied Mathematics,U.S. A Journey through the History of Numerical Linear
Book SynopsisThis expansive volume describes the history of numerical methods proposed to solve linear algebra problems,, from antiquity to the present day. The authors focus on methods for solving linear systems of equations and eigenvalue problems and describe the interplay between numerical methods and the computing tools available at the time. The second part of the book consists of 78 biographies of the main important contributors to the field.A Journey through the History of Numerical Linear Algebra will be of special interest to applied mathematicians, especially researchers in numerical linear algebra, and to applied mathematiciansas well as to and historians of mathematics as well.
£113.90
Society for Industrial & Applied Mathematics,U.S. Advanced Reduced Order Methods and Applications
Book SynopsisReduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications.This book will be of interest to researchers and graduate students in the field of reduced order modeling.
£83.30
Society for Industrial & Applied Mathematics,U.S. Rounding Errors in Algebraic Processes
Book SynopsisRounding Errors in Algebraic Processes was the first book to give systematic analyses of the effects of rounding errors on a variety of key computations involving polynomials and matrices.A detailed analysis is given of the rounding errors made in the elementary arithmetic operations and inner products, for both floating-point arithmetic and fixed-point arithmetic. The results are then applied in the error analyses of a variety of computations involving polynomials as well as the solution of linear systems, matrix inversion, and eigenvalue computations.The conditioning of these problems is investigated. The aim was to provide a unified method of treatment, and emphasis is placed on the underlying concepts.This book is intended for mathematicians, computer scientists, those interested in the historical development of numerical analysis, and students in numerical analysis and numerical linear algebra.Trade Review[This book] combines a rigorous mathematical analysis with a practicality that stems from an obvious first-hand contact with the actual numerical computation. The well-chosen examples alone show vividly both the importance of the study of rounding errors and the perils of its neglect. A. A. Grau, SIAM Review (1966)
£56.95
Society for Industrial & Applied Mathematics,U.S. Classical Analysis of Real-Valued Functions
Book SynopsisDivided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to differential geometry, Fourier series, differential equations, and other subjects. The first section of Classical Analysis of Real-Valued Functions covers the theorems of existence of supremum and infimum of bounded sets on the real line and the Lagrange formula for differentiable functions. Applications of these results are crucial for classical mathematical analysis, andmany are threaded through the text. In the second part of the book, the implicit function theorem plays a central role, while the Gauss–Ostrogradskii formula, surface integration, Heine–Borel lemma, the Ascoli–Arzelà theorem, and the one-dimensional indefinite Lebesgue integral are also covered. This book is intended for students in the first and second years of classical universities majoring in pure and applied mathematics, but students of engineering disciplines will also gain important and helpful insights. It is appropriate for courses in mathematical analysis, functional analysis, real analysis, and calculus and can be used for self-study as well.
£79.05
ISTE Ltd and John Wiley & Sons Inc Meshing, Geometric Modeling and Numerical
Book SynopsisTriangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena. In numerical simulations, the functional spaces of approximation used to search for solutions are defined from meshes, and in this sense these meshes play a fundamental role. This strong link between the meshes and functional spaces leads us to consider advanced simulation methods in which the meshes are adapted to the behaviors of the underlying physical phenomena. This book presents the basic elements of this meshing vision.Table of ContentsForeword 9 Introduction 11 Chapter 1 Finite Elements and Shape Functions 15 1.1. Basic concepts 15 1.2. Shape functions, complete elements 18 1.2.1. Generic expression of shape functions 18 1.2.2. Explicit expression for degrees 1–3 22 1.3. Shape functions, reduced elements 26 1.3.1. Simplices, triangles and tetrahedra 27 1.3.2. Tensor elements, quadrilateral and hexahedral elements 31 1.3.3. Other elements, prisms and pyramids 48 1.4. Shape functions, rational elements 49 1.4.1. Rational triangle with a degree of 2 or arbitrary degree 49 1.4.2. Rational quadrilateral of an arbitrary degree 50 1.4.3. General case, B-splines or Nurbs elements 50 Chapter 2 Lagrange and Bézier Interpolants 53 2.1. Lagrange–Bézier analogy 54 2.2. Lagrange functions expressed in Bézier forms 55 2.2.1. The case of tensors, natural coordinates 55 2.2.2. Simplicial case, barycentric coordinates 63 2.3. Bézier polynomials expressed in Lagrangian form 66 2.4. Application to curves 66 2.4.1. Bézier expression for a Lagrange curve 67 2.4.2. Lagrangian expression for a Bézier curve 70 2.5. Application to patches 71 2.5.1. Bézier expression for a patch in Lagrangian form 71 2.5.2. Lagrangian expression for a patch in Bézier form 73 2.6. Reduced elements 74 2.6.1. The tensor case, Bézier expression for a reduced Lagrangian patch 74 2.6.2. The tensor case, definition of reduced Bézier patches 82 2.6.3. The tensor case, Lagrangian expression of a reduced Bézier patch 90 2.6.4. The case of simplices 92 Chapter 3 Geometric Elements and Geometric Validity 95 3.1. Two-dimensional elements 96 3.2. Surface elements 105 3.3. Volumetric elements 105 3.4. Control points based on nodes 111 3.5. Reduced elements 115 3.5.1. Simplices, triangles and tetrahedra 115 3.5.2. Tensor elements, quadrilaterals and hexahedra 116 3.5.3. Other elements, prisms and pyramids 120 3.6. Rational elements 121 3.6.1. Shift from Lagrange rationals to Bézier rationals 121 3.6.2. Degree 2, working on the (arc of a) circle 121 3.6.3. Application to the analysis of rational elements 123 3.6.4. On the use of rational elements or more 138 Chapter 4 Triangulation 141 4.1. Triangulation, definitions, basic concepts and natural entities 142 4.1.1. Definitions and basic concepts 142 4.1.2. Natural entities 145 4.1.3. A ball (topological) of a vertex 145 4.1.4 A shell of a k-face 145 4.1.5 The ring of a k-face 146 4.2. Topology and local topological modifications 146 4.2.1. Flipping an edge in two dimensions 148 4.2.2. Flipping a face in three dimensions 148 4.2.3. Flipping an edge in three dimensions 148 4.2.4. Other flips? 150 4.3. Enriched data structures 151 4.3.1. Minimal structure 151 4.3.2. Enriched structure 152 4.4. Construction of natural entities 153 4.5. Triangulation, construction methods 156 4.6. The incremental method, a generic method 159 4.6.1. Naive triangulation 160 4.6.2. Delaunay triangulation 163 Chapter 5 Delaunay Triangulation 165 5.1. History 166 5.2. Definitions and properties 168 5.3. The incremental method for Delaunay 175 5.4. Other methods of construction 181 5.5. Variants 186 5.6. Anisotropy 188 Chapter 6 Triangulation and Constraints 193 6.1. Triangulation of a domain 194 6.1.1. Triangulation of a domain in two dimensions 195 6.1.2. Triangulation of a domain in three dimensions 202 6.2. Delaunay Triangulation “Delaunay admissibility” 214 6.3. Triangulation of a variety 219 6.4. Topological invariants (triangles and tetrahedra) 222 Chapter 7 Geometric Modeling: Methods 233 7.1. Implicit or explicit form (CAD), starting from an analytical definition 234 7.1.1. Modeling an implicit curve, continuous → discrete 234 7.1.2. Modeling a parametric curve 237 7.1.3. Modeling an implicit surface 238 7.1.4. Modeling of a parametric surface 242 7.2. Starting from a discretization or triangulation, discrete → continuous 246 7.2.1. Case of a curve 247 7.2.2. The case of a surface 253 7.3. Starting from a point cloud, discrete → discrete 278 7.3.1. The case of a curve in two dimensions 278 7.3.2. The case of a surface 283 7.4. Extraction of characteristic points and characteristic lines 302 Chapter 8 Geometric Modeling: Examples 305 8.1. Geometric modeling of parametric patches 306 8.2. Characteristic lines of a discrete surface 311 8.3. Parametrization of a surface patch through unfolding 311 8.4. Geometric simplification of a surface triangulation 324 8.5. Geometric support for a discrete surface 325 8.6. Discrete reconstruction of a digitized object or environment 330 Chapter 9 A Few Basic Algorithms and Formulae 343 9.1. Subdivision of an entity (De Casteljau) 344 9.1.1. Subdivision of a curve 344 9.1.2. Subdivision of a patch 345 9.2. Computing control coefficients (higher order elements) 348 9.3. Algorithms for the insertion of a point (Delaunay) 351 9.3.1. Classic algorithm 352 9.3.2. Modified algorithms 355 9.4. Construction of neighboring relationships, balls and shells 357 9.4.1. Neighboring relationships 357 9.4.2. Construction of the ball of a vertex 359 9.4.3. Construction of the shell of an edge 361 9.5. Localization problems 363 9.5.1. Triangulations or simplicial meshes 363 9.5.2. Other meshes 367 9.6. Some formulae 367 Conclusions and Perspectives 369 Bibliography 371 Index 377
£125.06
ISTE Ltd and John Wiley & Sons Inc Geometric and Topological Mesh Feature Extraction
Book SynopsisThree-dimensional surface meshes are the most common discrete representation of the exterior of a virtual shape. Extracting relevant geometric or topological features from them can simplify the way objects are looked at, help with their recognition, and facilitate description and categorization according to specific criteria. This book adopts the point of view of discrete mathematics, the aim of which is to propose discrete counterparts to concepts mathematically defined in continuous terms. It explains how standard geometric and topological notions of surfaces can be calculated and computed on a 3D surface mesh, as well as their use for shape analysis. Several applications are also detailed, demonstrating that each of them requires specific adjustments to fit with generic approaches. The book is intended not only for students, researchers and engineers in computer science and shape analysis, but also numerical geologists, anthropologists, biologists and other scientists looking for practical solutions to their shape analysis, understanding or recognition problems.Table of ContentsPreface ix Introduction xi Chapter 1. Geometric Features based on Curvatures 1 1.1. Introduction 1 1.2. Some mathematical reminders of the differential geometry of surfaces 2 1.2.1. Fundamental forms and normal curvature 2 1.2.2. Principal curvatures and shape index 5 1.2.3. Principal directions and lines of curvature 6 1.2.4. Weingarten equations and shape operator 9 1.2.5. Practical computation of differential parameters 12 1.2.6. Euler’s theorem 13 1.2.7. Meusnier’s theorem 15 1.2.8. Local approximation of the surface 16 1.2.9. Focal surfaces 17 1.3. Computation of differential parameters on a discrete 3D mesh 19 1.3.1. Introduction 19 1.3.2. Some notations 19 1.3.3. Computing normal vectors 20 1.3.4. Locally fitting a parametric surface 22 1.3.5. Discrete differential geometry operators 22 1.3.6. Integrating 2D curvatures 28 1.3.7. Tensor of curvature: Taubin’s formula 28 1.3.8. Tensor of curvature based on the normal cycle theory 30 1.3.9. Integral estimators 34 1.3.10. Processing unstructured 3D point clouds 38 1.3.11. Discussion of the methods 38 1.4. Feature line extraction 46 1.4.1. Introduction 46 1.4.2. Lines of curvature 47 1.4.3. Crest/ridge lines 55 1.4.4. Feature lines based on homotopic thinning 79 1.5. Region-based approaches 84 1.5.1. Mesh segmentation 84 1.5.2. Shape description based on graphs 87 1.6. Conclusion 98 Chapter 2. Topological Features 99 2.1. Mathematical background 99 2.1.1. A topological view on surfaces 100 2.1.2. Algebraic topology 103 2.2. Computation of global topological features 106 2.2.1. Connected components and genus 106 2.2.2. Homology groups 107 2.3. Combining geometric and topological features 111 2.3.1. Persistent homology 112 2.3.2. Reeb graph and Morse–Smale complex 115 2.3.3. Homology generators 118 2.3.4. Measuring holes 121 2.4. Conclusion 128 Chapter 3. Applications 131 3.1. Introduction 131 3.2. Medicine: lines of curvature for polyp detection in virtual colonoscopy 131 3.3. Paleo-anthropology: crest/ridge lines for shape analysis of human fossils 133 3.4. Geology: extraction of fracture lines on virtual outcrops 137 3.5. Planetary science: detection of feature lines for the extraction of impact craters on asteroids and rocky planets 140 3.6. Botany: persistent homology to recover the branching structure of plants 143 Conclusion 145 References 149 Index 169
£125.06
ISTE Ltd and John Wiley & Sons Inc Earthquake Statistical Analysis through
Book SynopsisEarthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi-)Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7.Table of ContentsList of Abbreviations ix List of Symbols xi Preface xv Introduction xix Chapter 1. Fundamentals on Stress Changes 1 1.1. Introduction 1 1.2. Stress interaction 4 1.3. Stress changes calculation 12 1.4. Modeling of Coulomb stress changes for different faulting types 15 1.4.1.ΔCS for strike-slip faulting 15 1.4.2.ΔCS for dip-slip faulting 16 1.5. Seismicity triggered by stress transfer 21 1.5.1. Triggering of strong earthquakes 21 1.5.2. Aftershock triggering 23 1.5.3. Triggering of mining seismicity 28 1.6. Discussion on stress interaction 31 Chapter 2. Hidden Markov Models 35 2.1. Introduction 35 2.2. Hidden Markov framework 37 2.3. Seismotectonic regime and seismicity data 42 2.4. Application to earthquake occurrences 44 2.4.1. Two hidden states and three observation types 45 2.4.2. Three hidden states and three observation types 48 2.4.3. Model selection and simulation 50 2.4.4. Steps number for the first earthquake occurrence 53 2.5. Conclusion 54 Chapter 3. Hidden Markov Renewal Models 57 3.1. Introduction 57 3.2. Semi-Markov framework 58 3.3. Hidden Markov renewal framework 65 3.4. Modeling earthquakes in Greece 66 3.4.1. Hitting times and earthquake occurrence numbers 69 3.5. Conclusion 73 Chapter 4. Hitting Time Intensity 75 4.1. Introduction 75 4.2. DTIHT for semi-Markov chains 76 4.2.1. Statistical estimation of the DTIHT 78 4.3. DTIHT for hidden Markov renewal chains 83 4.3.1. Statistical estimation of the DTIHT 85 4.4. Conclusion 87 Chapter 5. Models Comparison 89 5.1. Introduction 89 5.2. Markov framework 90 5.2.1. HMM case 92 5.2.2. HMRM case 92 5.3. Markov renewal framework 93 5.3.1. HMM case 95 5.3.2. HMRM case 96 5.4. Conclusion 97 Discussion & Concluding Remarks 99 Appendices 105 Appendix 1 107 Appendix 2 113 Appendix 3 117 References 119 Index 137
£125.06
ISTE Ltd and John Wiley & Sons Inc Advanced Numerical Methods with Matlab 2:
Book SynopsisThe purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing. This last refers to the implementation of appropriate approaches to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or of engineering (mechanics of structures, mechanics of fluids, treatment signal, etc.). Each chapter of this book recalls the essence of the different methods resolution and presents several applications in the field of engineering as well as programs developed under Matlab software.Table of ContentsPreface ix Part 1. Solving Equations 1 Chapter 1. Solving Nonlinear Equations 3 1.1 Introduction 3 1.2 Separating the roots 3 1.3 Approximating a separated root 4 1.3.1 Bisection method (or dichotomy method) 4 1.3.2 Fixed-point method 6 1.3.3 First convergence criterion 7 1.3.4 Iterative stopping criteria.8 1.3.5 Second convergence criterion (local criterion) 9 1.3.6 Newton’s method (or the method of tangents) 10 1.3.7 Secant method 12 1.3.8 Regula falsi method (or false position method) 17 1.4 Order of an iterative process.19 1.5 Using Matlab 19 1.5.1 Finding the roots of polynomials 19 1.5.2 Bisection method 21 1.5.3 Newton’s method 22 Chapter 2. Numerically Solving Differential Equations 25 2.1 Introduction 25 2.2 Cauchy problem and discretization 27 2.3 Euler’s method 30 2.3.1 Interpretation 30 2.3.2 Convergence 30 2.4 One-step Runge–Kutta method 31 2.4.1 Second-order Runge–Kutta method 32 2.4.2 Fourth-order Runge–Kutta method 33 2.5 Multi-step Adams methods 36 2.5.1 Open Adams methods 36 2.5.2 Closed Adams formulas 39 2.6 Predictor–Corrector method.41 2.7 Using Matlab 43 Part 2. Solving PDEs 47 Chapter 3. Finite Difference Methods 49 3.1 Introduction 49 3.2 Presentation of the finite difference method 51 3.2.1 Convergence, consistency and stability 53 3.2.2 Courant–Friedrichs–Lewy condition 56 3.2.3 Von Neumann stability analysis 57 3.3 Hyperbolic equations 58 3.3.1 Key results 59 3.3.2 Numerical schemes for solving the transport equation 63 3.3.3 Wave equation 66 3.3.4 Burgers equation 68 3.4 Elliptic equations 72 3.4.1 Poisson equation 72 3.5 Parabolic equations 74 3.5.1 Heat equation 74 3.6 Using Matlab 76 Chapter 4. Finite Element Method 83 4.1 Introduction 83 4.2 One-dimensional finite element methods 83 4.3 Two-dimensional finite element methods 88 4.4 General procedure of the method 93 4.5 Finite element method for computing elastic structures 93 4.5.1 Linear elasticity 93 4.5.2 Variational formulation of the linear elasticity problem 97 4.5.3 Planar linear elasticity problems 99 4.5.4 Applying the finite element method to planar problems 101 4.5.5 Axisymmetric problems.105 4.5.6 Three-dimensional problems 107 4.6 Using Matlab 107 4.6.1 Solving Poisson’s equation 108 4.6.2 Solving the heat equation.111 4.6.3 Computing structures 112 Chapter 5. Finite Volume Methods 117 5.1 Introduction 117 5.2 Finite volume method (FVM) 118 5.2.1 Conservation properties of the method 118 5.2.2 The stages of the method.119 5.2.3 Convergence 120 5.2.4 Consistency 120 5.2.5 Stability 120 5.3 Advection schemes 121 5.3.1 Two-dimensional FVM. 126 5.3.2 Convection-diffusion equation 129 5.3.3 Central differencing scheme 131 5.3.4 Upwind (decentered) scheme 133 5.3.5 Hybrid scheme 136 5.3.6 Power-law scheme 136 5.3.7 QUICK scheme 137 5.3.8 Higher-order schemes 139 5.3.9 Unsteady one-dimensional convection-diffusion Equation 140 5.3.10 Explicit scheme 142 5.3.11 Crank–Nicolson scheme.142 5.3.12 Implicit scheme 143 5.4 Using Matlab 144 Chapter 6. Meshless Methods. 147 6.1 Introduction 147 6.2 Limitations of the FEM and motivation of meshless methods 148 6.3 Examples of meshless methods148 6.3.1 Advantages of meshless methods 149 6.3.2 Disadvantages of meshless methods150 6.3.3 Comparison of the finite element method and meshless methods 151 6.4 Basis of meshless methods 151 6.4.1 Approximations 151 6.4.2 Kernel (weight) functions.152 6.4.3 Completeness 152 6.4.4 Partition of unity 152 6.5 Meshless method (EFG) 153 6.5.1 Theory 153 6.5.2 Moving Least-Squares Approximation 153 6.6 Application of the meshless method to elasticity 163 6.6.1 Formulation of static linear elasticity 163 6.6.2 Imposing essential boundary conditions 165 6.7 Numerical examples 170 6.7.1 Fixed-free beam 170 6.7.2 Compressed block 171 6.8 Using Matlab 173 Part 3. Appendices 179 Appendix 1181 Appendix 2189 Bibliography 195 Index 199
£125.06
ISTE Ltd and John Wiley & Sons Inc Numerical Methods for Inverse Problems
Book SynopsisThis book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.Trade Review"The book is very carefully written, in a reader-friendly style. It can be considered as an introductory textbook for the theory of ill-posed problems and their numerical solution." (Mathematical Reviews/MathSciNet 11/05/2017)Table of ContentsPreface ix Part 1. Introduction and Examples 1 Chapter 1. Overview of Inverse Problems 3 1.1. Direct and inverse problems 3 1.2. Well-posed and ill-posed problems 4 Chapter 2. Examples of Inverse Problems 9 2.1. Inverse problems in heat transfer 10 2.2. Inverse problems in hydrogeology 13 2.3. Inverse problems in seismic exploration 16 2.4. Medical imaging 21 2.5. Other examples 25 Part 2. Linear Inverse Problems 29 Chapter 3. Integral Operators and Integral Equations 31 3.1. Definition and first properties 31 3.2. Discretization of integral equations 36 3.2.1. Discretization by quadrature–collocation 36 3.2.2. Discretization by the Galerkin method 39 3.3. Exercises 42 Chapter 4. Linear Least Squares Problems – Singular Value Decomposition 45 4.1. Mathematical properties of least squares problems 45 4.1.1. Finite dimensional case 50 4.2. Singular value decomposition for matrices 52 4.3. Singular value expansion for compact operators 57 4.4. Applications of the SVD to least squares problems 60 4.4.1. The matrix case 60 4.4.2. The operator case 63 4.5. Exercises 65 Chapter 5. Regularization of Linear Inverse Problems 71 5.1. Tikhonov’s method 72 5.1.1. Presentation 72 5.1.2. Convergence 73 5.1.3. The L-curve 81 5.2. Applications of the SVE 83 5.2.1. SVE and Tikhonov’s method 84 5.2.2. Regularization by truncated SVE 85 5.3. Choice of the regularization parameter 88 5.3.1. Morozov’s discrepancy principle 88 5.3.2. The L-curve 91 5.3.3. Numerical methods 92 5.4. Iterative methods 94 5.5. Exercises 98 Part 3. Nonlinear Inverse Problems 103 Chapter 6. Nonlinear Inverse Problems – Generalities 105 6.1. The three fundamental spaces 106 6.2. Least squares formulation 111 6.2.1. Difficulties of inverse problems 114 6.2.2. Optimization, parametrization, discretization 114 6.3. Methods for computing the gradient – the adjoint state method 116 6.3.1. The finite difference method 116 6.3.2. Sensitivity functions 118 6.3.3. The adjoint state method 119 6.3.4. Computation of the adjoint state by the Lagrangian 120 6.3.5. The inner product test 123 6.4. Parametrization and general organization 123 6.5. Exercises 125 Chapter 7. Some Parameter Estimation Examples 127 7.1. Elliptic equation in one dimension 127 7.1.1. Computation of the gradient 128 7.2. Stationary diffusion: elliptic equation in two dimensions 129 7.2.1. Computation of the gradient: application of the general method 132 7.2.2. Computation of the gradient by the Lagrangian 134 7.2.3. The inner product test 135 7.2.4. Multiscale parametrization 135 7.2.5. Example 136 7.3. Ordinary differential equations 137 7.3.1. An application example 144 7.4. Transient diffusion: heat equation 147 7.5. Exercises 152 Chapter 8. Further Information 155 8.1. Regularization in other norms 155 8.1.1. Sobolev semi-norms 155 8.1.2. Bounded variation regularization norm 157 8.2. Statistical approach: Bayesian inversion 157 8.2.1. Least squares and statistics 158 8.2.2. Bayesian inversion 160 8.3. Other topics 163 8.3.1. Theoretical aspects: identifiability 163 8.3.2. Algorithmic differentiation . 163 8.3.3. Iterative methods and large-scale problems 164 8.3.4. Software 164 Appendices 167 Appendix 1 169 Appendix 2 183 Appendix 3 193 Bibliography 205 Index 213
£125.06
Springer Nature Switzerland AG Approximation Theory and Algorithms for Data
Book SynopsisThis textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.Trade Review“This book is an excellent first course in approximation theory, covering all the aspects from theoretical results to practical methods, from discrete to continuous approximation, from univariate to multivariate. … The book is an excellent text for an undergraduate course in approximation methods. … this book is a very important textbook on approximation theory and its methods.” (Ana Cristina Matos, Mathematical Reviews, August, 2019)Table of Contents1 Introduction.- 2 Basic Methods and Numerical Analysis.- 3 Best Approximations.- 4 Euclidean Approximations.- 5 Chebyshev Approximations.- 6 Asymptotic Results.- 7 Basic Concepts of Signal Approximation.- 8 Kernel-Based Approximation.- 9 Computational Topology.- References.- Subject Index.- Name Index.
£41.24
Springer Nature Switzerland AG Differential Geometry and Lie Groups: A
Book SynopsisThis textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications.Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry.Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics.Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.Trade Review“The book … is intended ‘for a wide audience ranging from upper undergraduate to advanced graduate students in mathematics, physics, and more broadly engineering students, especially in computer science.’ … The text’s coverage is extensive, its exposition clear throughout, and the color illustrations helpful. The authors are also familiar with many texts at a comparable level and have drawn on them in several places to include some of the most insightful proofs already in the literature.” (Jer-Chin Chuang, MAA Reviews, October 4, 2021)“The book is intended for incremental study and covers both basic concepts and more advanced ones. The former are thoroughly supported with theory and examples, and the latter are backed up with extensive reading lists and references. … Thanks to its design and approach style this is a timely and much needed addition that enables interdisciplinary bridges and the discovery of new applications for differential geometry.” (Corina Mohorian, zbMATH 1453.53001, 2021)Table of Contents1. The Matrix Exponential; Some Matrix Lie Groups.- 2. Adjoint Representations and the Derivative of exp.- 3. Introduction to Manifolds and Lie Groups.- 4. Groups and Group Actions.- 5. The Lorentz Groups ⊛.- 6. The Structure of O(p,q) and SO(p, q).- 7. Manifolds, Tangent Spaces, Cotangent Spaces.- 8. Construction of Manifolds From Gluing Data ⊛.- 9. Vector Fields, Integral Curves, Flows.- 10. Partitions of Unity, Covering Maps ⊛.- 11. Basic Analysis: Review of Series and Derivatives.- 12. A Review of Point Set Topology.-13. Riemannian Metrics, Riemannian Manifolds.- 14. Connections on Manifolds.- 15. Geodesics on Riemannian Manifolds.- 16. Curvature in Riemannian Manifolds.- 17. Isometries, Submersions, Killing Vector Fields.- 18. Lie Groups, Lie Algebra, Exponential Map.- 19. The Derivative of exp and Dynkin's Formula ⊛.- 20. Metrics, Connections, and Curvature of Lie Groups.- 21. The Log-Euclidean Framework.- 22. Manifolds Arising from Group Actions.
£55.24
Springer Nature Switzerland AG Mathematical Descriptions of Traffic Flow: Micro,
Book SynopsisThe book originates from the mini-symposium "Mathematical descriptions of traffic flow: micro, macro and kinetic models" organised by the editors within the ICIAM 2019 Congress held in Valencia, Spain, in July 2019. The book is composed of five chapters, which address new research lines in the mathematical modelling of vehicular traffic, at the cutting edge of contemporary research, including traffic automation by means of autonomous vehicles. The contributions span the three most representative scales of mathematical modelling: the microscopic scale of particles, the mesoscopic scale of statistical kinetic description and the macroscopic scale of partial differential equations.The work is addressed to researchers in the field.Table of ContentsM. Herty et al., Reconstruction of traffic speed distributions from kinetic models with uncertainties.- M. Herty et al., From kinetic to macroscopic models and back.- R. Ramadan et al., Structural Properties of the Stability of Jamitons.- C. Balzotti and E. Iacomini, Stop-and-go waves: A Microscopic and a Macroscopic Description.- F. A. Chiarello, An overview of non-local traffic flow models.
£87.99
Springer Nature Switzerland AG Parallel-in-Time Integration Methods: 9th
Book SynopsisThis volume includes contributions from the 9th Parallel-in-Time (PinT) workshop, an annual gathering devoted to the field of time-parallel methods, aiming to adapt existing computer models to next-generation machines by adding a new dimension of scalability. As the latest supercomputers advance in microprocessing ability, they require new mathematical algorithms in order to fully realize their potential for complex systems. The use of parallel-in-time methods will provide dramatically faster simulations in many important areas, including biomedical (e.g., heart modeling), computational fluid dynamics (e.g., aerodynamics and weather prediction), and machine learning applications. Computational and applied mathematics is crucial to this progress, as it requires advanced methodologies from the theory of partial differential equations in a functional analytic setting, numerical discretization and integration, convergence analyses of iterative methods, and the development and implementation of new parallel algorithms. Therefore, the workshop seeks to bring together an interdisciplinary group of experts across these fields to disseminate cutting-edge research and facilitate discussions on parallel time integration methods. Table of ContentsTight two-level convergence of linear Parareal and MGRIT: Extensions and implications in practice (Southworth et al.).- A Parallel algorithm for solving linear parabolic evolution equations (van Venetië et al.).- Using performance analysis tools for a parallel-in-time integrator (Speck et al.).- Twelve Ways to Fool the Masses When Giving Parallel-In-Time Results (Götschel et al.).- IMEX Runge-Kutta Parareal for Non-Diffusive Equations (Buvoli et al.).
£111.99
Springer Nature Switzerland AG Hybrid High-Order Methods: A Primer with
Book SynopsisThis book provides a comprehensive coverage of hybrid high-order methods for computational mechanics. The first three chapters offer a gentle introduction to the method and its mathematical foundations for the diffusion problem. The next four chapters address applications of increasing complexity in the field of computational mechanics: linear elasticity, hyperelasticity, wave propagation, contact, friction, and plasticity. The last chapter provides an overview of the main implementation aspects including some examples of Matlab code. The book is primarily intended for graduate students, researchers, and engineers working in related fields of application, and it can also be used as a support for graduate and doctoral lectures.Table of Contents1.Getting Started: Linear Diffusion.- 2.Mathematical Aspects.- 3.Some Variants.- 4.Linear Elasticity and Hyperelasticity.- 5.Elastodynamics.- 6.Contact and Friction.- 7.Plasticity.- 8.Implementaion Aspects.- References.
£41.24
Springer Nature Switzerland AG Recent Advances in Kinetic Equations and
Book SynopsisThe volume covers most of the topics addressed and discussed during the Workshop INdAM "Recent advances in kinetic equations and applications", which took place in Rome (Italy), from November 11th to November 15th, 2019. The volume contains results on kinetic equations for reactive and nonreactive mixtures and on collisional and noncollisional Vlasov equations for plasmas. Some contributions are devoted to the study of phase transition phenomena, kinetic problems with nontrivial boundary conditions and hierarchies of models. The book, addressed to researchers interested in the mathematical and numerical study of kinetic equations, provides an overview of recent advances in the field and future research directions.Table of Contents- Sharpening of Decay Rates in Fourier Based Hypocoercivity Methods. - Quantum Drift-Diffusion Equations for a Two-Dimensional Electron Gas with Spin-Orbit Interaction. - A Kinetic BGK Relaxation Model for a Reacting Mixture of Polyatomic Gases. - On Some Recent Progress in the Vlasov–Poisson–Boltzmann System with Diffuse Reflection Boundary. - The Vlasov Equation with Infinite Mass. - Mathematical and Numerical Study of a Dusty Knudsen Gas Mixture: Extension to Non-spherical Dust Particles. - Body-Attitude Alignment: First Order Phase Transition, Link with Rodlike Polymers Through Quaternions, and Stability. - The Half-Space Problem for the Boltzmann Equation with Phase Transition at the Boundary. - Recent Developments on Quasineutral Limits for Vlasov-Type Equations. - A Note on Acoustic Limit for the Boltzmann Equation. - Thermal Boundaries in Kinetic and Hydrodynamic Limits. - Control of Collective Dynamics with Time-Varying Weights. - Kinetic Modelling of Autoimmune Diseases. - A Generalized Slip-Flow Theory for a Slightly Rarefied Gas Flow Induced by Discontinuous Wall Temperature. - A Revisit to the Cercignani–Lampis Model: Langevin Picture and Its Numerical Simulation. - On the Accuracy of Gyrokinetic Equations in Fusion Applications.
£127.99
Springer Nature Switzerland AG Recent Advances in Industrial and Applied
Book SynopsisThis open access book contains review papers authored by thirteen plenary invited speakers to the 9th International Congress on Industrial and Applied Mathematics (Valencia, July 15-19, 2019). Written by top-level scientists recognized worldwide, the scientific contributions cover a wide range of cutting-edge topics of industrial and applied mathematics: mathematical modeling, industrial and environmental mathematics, mathematical biology and medicine, reduced-order modeling and cryptography. The book also includes an introductory chapter summarizing the main features of the congress. This is the first volume of a thematic series dedicated to research results presented at ICIAM 2019-Valencia Congress.Table of Contents1 M. Berger, Asteroid-Generated Tsunamis: A Review.- 2 A. Bermúdez, Some Case Studies in Environmental and Industrial Mathematics.- 3 Z. Cai et al., Hyperbolic Model Reduction for Kinetic Equations.- 4 A. Cohen et al., State Estimation - The Role of Reduced Models.- 5 C. Conca, Modelling Our Sense Of Smell.- 6 L. Edelstein-Keshet, Pattern formation inside living cells.- 7 M. Garzon et al., Efficient Algorithms for Tracking Moving Interfaces.- 8 K. Lauter, Private AI: Machine Learning on Encrypted Data.- 9 C. Le Bris, Mathematical approaches for contemporary materials science: Addressing defects in the microstructure.- 10 H. Leng et al., An iterative thresholding method for topology optimization for the Navier-Stokes flow.- 11 K. Sako, Cryptography and Digital Transformation.- 12 H. Suito et al., Numerical Study for Blood Flows in Thoracic Aorta.- 13 J.A.C. Weideman, Dynamics of Complex Singularities of Nonlinear PDEs: Analysis and Computation.
£35.99
Springer Nature Switzerland AG Mesh Methods for Boundary-Value Problems and
Book SynopsisThis book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.Table of ContentsTheory of the mesh methods for the boundary-value problems in Mathematical Physics.- Non-linear mathematical models in mechanics and physics.- Algorithms for solving variational inequalities.- Computing Science and educational systems.
£97.49
Springer Nature Switzerland AG Mathematical Modeling and Simulation of Systems:
Book SynopsisThis book contains works on mathematical and simulation modeling of processes in various domains: ecology and geographic information systems, IT, industry, and project management. The development of complex multicomponent systems requires an increase in accuracy, efficiency, and adequacy while reducing the cost of their creation. The studies presented in the book are useful to specialists who involved in the development of real events models-analog, management and decision-making models, production models, and software products. Scientists can get acquainted with the latest research in various decisions proposed by leading scholars and identify promising directions for solving complex scientific and practical problems. The chapters of this book contain the contributions presented on the 16th International Scientific-practical Conference, MODS, June 28–July 01, 2021, Chernihiv, Ukraine.Table of ContentsMathematical Modeling of Information System Designing Master Plan of the Building Territory Based on OLAP Technology.- Models and information technologies of coverage of the territory by sensors with energy consumption optimization.- Transport of Reactive Tracer in Compacting Multi-fraction Bottom Sediments.- Pillars for establishing a durable and future-proof IT architecture maturing along with the NSC: Approaches from Continuous Integration to Service Mesh.- Optimal Control of Buried Point Sources in a Two-Dimensional Richards-Klute Equation.
£179.99
Springer Nature Switzerland AG Elements of the General Theory of Optimal
Book SynopsisIn this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T-efficient algorithms for computing ε-solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.Table of Contents-Preface.- Introduction.- List of symbols and abbreviations.- 1. Elements of the computing theory.- 2. Theories of computational complexity.- 3. Interlination of functions.- 4. Interflatation of functions.- 5. Cubature formulae using interlanation functions.- 6. Testing the quality of algorithm programs.- 7. Computer technologies of solving problems of computational and applied mathematics with fixed values of quality characteristics.- Bilbiography.- Index.- About the Authors.
£87.99
Springer Nature Switzerland AG Mesh Generation and Adaptation: Cutting-Edge
Book SynopsisThe developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.Table of Contents1 Carolyn Woeber, Advances in H-P Mesh Adaptation for Finite Element Methods.- 2 Chiara Nardoni, Remeshing techniques in shape and topology optimization.- 3 Dimitrios Papadimitrakis, Building direction fields on the medial object to generate 3D domain decompositions for hexahedral meshing.- 4 Franck Ledoux, Interecode hexahedral meshing from Eulerian to Lagrangian simulations.- 5 Jean-Francois Remacle, A robust approach for mesh generation of surfaces with irregular/singular parametrizations.6 Jens Lang, Sample Adaptive Multilevel Stochastic Collocation Schemes in Uncertainty Quantification of Gas Transport in Networks.- 7 Jessica Zhang, Hexahedral dominant mesh generation and spline modeling for isogeometric analysis.- 8 Juan José Ródenas, Mesh adaptivity in the framework of the Cartesian grid finite element method, cgFEM.- 9 Mario Ricchiuto, h- and r-adaptation on simplicial meshes: implementation and applications.- 10 Onkar Sahni, Geometry and Adaptive Mesh Update Procedures for Ballistics Simulations.- 11 Per-Olof Persson, HOIST: High-Order Implicit Shock Tracking using an optimization-based discontinuous Galerkin method.- 12 Rainald Lohner, Breakthrough ‘workarounds’ in unstructured mesh generation.- 13 Simone Appella, An adaptive moving mesh method with conservative interpolation based on local projection.- 14 Suzanne Shontz, Global optimization strategies for automated edge grid generation.
£93.49
Springer Nature Switzerland AG Convex Analysis and Beyond: Volume I: Basic
Book SynopsisThis book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.Trade Review“Each chapter ends with an exercise section … . While primarily addressed to researchers, the book can be used for graduate courses in optimization, by undergraduate and graduate students for theses and projects as well as by researchers and practitioners from other fields where tools from convex analysis, variational analysis and optimization play a role. All in one, the reviewer warmly recommends this book to anyone interested.” (Sorin-Mihai Grad, zbMATH 1506.90001, 2023)“This outstanding book will certainly be useful to anyone interested to learn convex analysis, in particular to graduate students and researchers in the field. Most parts of it can also serve as the basis of advanced courses on a variety of topics. In view of the excellence of this first volume, one can expect the best of the announced second one, which will deal with applications of convex analysis.” (Juan Enrique Martínez-Legaz, Mathematical Reviews, February, 2023)“Every chapter of the book has one section of exercises and one section of commentaries. These sections provide the reader with a lot of information and give him/her great benefits in self-learning. … The book under review has many things to offer and, surely, it will play an important role in the development of convex analysis … . The book is very useful for theoretical research and practical use. Thanks to the art of writing of the authors … .” (Nguyen Dong Yen, Journal of Global Optimization, Vol. 85, 2023)Table of ContentsFundamentals.- Basic theory of convexity.- Convex generalized differentiation.- Enhanced calculus and fenchel duality.- Variational techniques and further subgradient study.- Miscellaneous topics on convexity.- Convexified Lipschitzian analysis.- List of Figures.- Glossary of Notation and Acronyms.- Subject Index.
£42.49
Springer Nature Switzerland AG Realization and Model Reduction of Dynamical
Book SynopsisThis book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications. Table of ContentsPart I: Linear Dynamical Systems: B. Joseph, The rational interpolation problem: Grassmannian and Loewner-matrix approaches.- B. Jean-Paul, The conditioning of a linear barycentric rational interpolant.- D. Zlatko, Learning low-dimensional dynamical-system models from noisy frequency-response data with Loewner rational interpolation.- E. Mark, Pseudospectra of Loewner Matrix Pencils.- R. Paolo, A Loewner matrix approach to the identification of linear time-varying systems.- V. D. Paul, Linear System Matrices of Rational Transfer Functions.- Part II: Nonlinear Dynamical Systems: C. Xingang, Interpolation-based Model Order Reduction for Quadratic-Bilinear Systems and H2 Optimal Approximation.- C. Sridhar, An Adaptive Sampling Approach for the reduced basis method.- K. Boris, Balanced Truncation Model Reduction for Lifted Nonlinear Systems.- L. Sanda, Modeling the buck converter from measurements of its Harmonic Transfer Function.- P. Mihaly, Model reduction and realization theory of linear switched systems.- Part III: Structured Dynamical Systems: F. F. Damasceno, Developments in the Computation of Reduced Order Models with the Use of Dominant Spectral Zeros.- M. Volker, Structure-preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems.- P. D. Igor, Data-Driven Identification of Rayleigh-Damped Second-Order Systems.- S. Tatjana, Balanced truncation model reduction for 3D linear magneto-quasistatic field problems.- Van der S. Arjan, Structure-preserving model reduction of physical network systems.- Part IV: Model Reduction for Control: B. Tobias, H2-gap model reduction for stabilizable and detactable systems.- H. Matthias, Reduced Order Model Hessian Approximations in Newton Methods for Optimal Control.- P.-V. Charles, Interpolation-based irrational model control design and stabilty analysis.- Part V: Applications: D. Clifford, Oscillations in Biology: G. Eduardo, Model-Order Reduction for Coupled Flow and Linear Thermal-Poroplasticity with Applications to Unconventional Reservoirs.- I. Roxana, Challenges in model reduction for real-time simulation of traction chain systems.- N. Masaaki, Sparse Representation for Sampled-data Hinf Filter.- S. Eduardo, Analysis of a reduced model of epithelial–mesenchymal fate determination in cancer metastasis as a singularly-perturbed monotone system.
£87.99
Springer Nature Switzerland AG Modeling, Simulation and Optimization in the
Book SynopsisThis volume is addressed to people who are interested in modern mathematical solutions for real life applications. In particular, mathematical modeling, simulation and optimization is nowadays successfully used in various fields of application, like the energy- or health-sector. Here, mathematics is often the driving force for new innovations and most relevant for the success of many interdisciplinary projects. The presented chapters demonstrate the power of this emerging research field and show how society can benefit from applied mathematics.Table of ContentsPart I Prognostic MR Thermometry for Thermal Ablation of Liver Tumours.- 1 Sebastian Blauth et al., Mathematical Modeling and Simulation of Laser-Induced Thermotherapy for the Treatment of Liver Tumors.- 2 Matthias Andres and René Pinnau, The Cattaneo Model for Laser-Induced Thermotherapy: Identification of the Blood-Perfusion Rate.- 3 Kevin Tolle and Nicole Marheineke, On Online Parameter Identification in Laser-Induced Thermotherapy.- Part II Energy-efficient High Temperature Processes via Shape Optimisation.- 4 Robert Feßler at al., Feasibility Study on Simulating a 3D Furnace Including the Effects of Reactions and Vaporization.- 5 Thomas Marx et al., Shape Optimization for the SP1–Model for Convective Radiative Heat Transfer- 6 Nicolas Dietrich et al., Diffusive Radiation Models for Optimal Shape Design in Phosphate Production.- 7 Ruben Sanchez at al., Adjoint-based sensitivity analysis in high-temperature fluid flows with participating media.
£82.49
Springer International Publishing AG Numerical Methods for Solving Discrete Event
Book SynopsisThis graduate textbook provides an alternative to discrete event simulation. It describes how to formulate discrete event systems, how to convert them into Markov chains, and how to calculate their transient and equilibrium probabilities. The most appropriate methods for finding these probabilities are described in some detail, and templates for efficient algorithms are provided. These algorithms can be executed on any laptop, even in cases where the Markov chain has hundreds of thousands of states. This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods.The material provided should aid practitioners significantly to solve their problems. This book also provides an interesting approach to teaching courses of stochastic processes. Trade Review“This monograph is an exciting addition to the queueing/stochastic processes literature, written by two highly respected senior researchers. … The writing is precise and clear. Well-known models are used as examples to illustrate the methods presented. … It has a huge number of powerful techniques that are not given sufficient focus elsewhere. This may be one of the best books to introduce graduate students … . This monograph is essential for the bookshelf … of every serious queueing theorist.” (Myron Hlynka, Mathematical Reviews, December, 2023)Table of ContentsBasic Concepts and Definitions.- Systems with Events Generated by Poisson or by Binomial Processes.- Generating the Transition Matrix.- Systems with Events Created by Renewal Processes.- Systems with Events Created by Phase-type Processes.- Computational Complexity and Rounding and Truncation Errors.- Transient Solutions of Markov Chains.- Moving Toward the Statistical Equilibrium.- Equilibrium Solutions of Markov Chains and Related Topics.- Reducing the State Space Through Censoring and Embedding.- Systems with Independent or Almost Independent Components.- Infinite-State Markov Chains and Matrix Analytic Methods.
£56.24
Springer International Publishing AG Optimal Surface Fitting of Point Clouds Using
Book SynopsisThis open access book provides insights into the novel Locally Refined B-spline (LR B-spline) surface format, which is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline surface has an overall smooth behavior and allows the modeling of local details with only a limited growth in data volume. In regions where many data points belong to the same smooth area, LR B-splines allow a very lean representation of the shape by locally adapting the resolution of the spline space to the size and local shape variations of the region. The iterative method can be modified to improve the accuracy in particular domains of a point cloud. The use of statistical information criterion can help determining the optimal threshold, the number of iterations to perform as well as some parameters of the underlying mathematical functions (degree of the splines, parameter representation). The resulting surfaces are well suited for analysis and computing secondary information such as contour curves and minimum and maximum points. Also deformation analysis are potential applications of fitting point clouds with LR B-splines.Table of ContentsIntroduction.- Locally Refined Splines.- Adaptive surface Fitting with Local Refinement: LR B-spline Surfaces.- A Statistical Criterion to Judge the Goodness of Fit of LR B-splines Surface Approximation.- LR B-splines for Representation of Terrain and Seabed: Data Fusion, Outliers, and Voids.- LR B-spline Surfaces and Volumes for Deformation Analysis of Terrain Data.- Conclusion.
£23.74
Springer International Publishing AG High Performance Computing in Science and
Book SynopsisThis book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2021. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance.The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.Table of ContentsPart I Physics.- Part II Molecules, Interfaces, and Solids.- Part III Reactive Flows.- Part IV Computational Fluid Dynamics.- Part V Transport and Climate.- Part VI Computer Science.- Part VII Miscellaneous Topics.
£159.99
Springer International Publishing AG Learning and Intelligent Optimization: 16th
Book SynopsisThis book constitutes the refereed proceedings of the 16th International Conference on Learning and Intelligent Optimization, LION 16, which took place in Milos Island, Greece, in June 2022.The 36 full papers and 3 short papers presented in this volume were carefully reviewed and selected from 60 submissions. LION deals with automatic solver configuration, parallel methods, intelligent optimization, nature-inspired algorithms, hard combinatorial optimization problems, DC learning, computational intelligence, and others. The contributions were organized in topical sections as follows: Invited Papers; Contributed Papers.Table of ContentsInvited Papers.- Optimal Scheduling of the Leaves of a Tree and the SVO Frequencies of Languages.- From Design of Experiments to Combinatorics of Disasters: A Conceptual Framework for Disaster Exercises.- Separating two polyhedra utilizing alternative theorems and penalty function.- Contributed Papers. -A Composite Index Method for Optimization Benchmarking.- Optimal Energy Management of Microgrid Using Multi-objective Optimisation Approach.- A Stochastic Alternating Balance k-Means Algorithm for Fair Clustering.- Binary Black Widow Optimization Algorithm for Feature Selection Problems.- Learning to Solve a Stochastic Orienteering Problem with Time Windows.- ML-based approach for accelerating global search algorithm for solving multicriteria problems .- The Skewed Kruskal algorithm.- Bounds for sparse solutions of K-SVCR multi-class classification model.- Integer Linear Programming in Solving an Optimization Problem at the Mixing Department of the Metallurgical Production.- Realtime Gray-Box Algorithm Configuration.- Dynamic urban solid waste management system for smart cities.- Single MCMC Chain Parallelisation on Decision Trees.- Single MCMC Chain Parallelisation on Decision Trees.- Competitive supply allocation in a distribution network under overproduction.- Safe-exploration of control policies from safe-experience via Gaussian Processes.- Bayesian Optimization in Wasserstein Spaces.- Network Vulnerability Analysis in Wasserstein Spaces.- BERT Self-Learning Approach with Limited Labels for Document Classification.- Autonomous Learning Optimization for Deep Learning.- Optimizing Data Augmentation Policy through Random Unidimensional Search.- Evaluating Student Behaviour on the MathE Platform - Clustering Algorithms Approaches.- Unsupervised Training for Neural TSP Solver.- Comparing surrogate models for tuning optimization algorithms.- Search and Score-based Waterfall Auction Optimization.- Survey on KNN Methods in Data Science.- Constrained Shortest Path and Hierarchical Structures.- Investigation of Graph Neural Networks for Instance Segmentation of Industrial Point Cloud Data.- Fitness landscape ruggedness impact on PSO in dealing with three variants of the travelling salesman problem.- A Multi-UAVs’ Provider Model for the provision of 5G Service Chains: a game theoretic approach.- Metabolic Syndrome Risk Forecasting on Elderly with ML Techniques.- Airport Digital Twins for Resilient Disaster Management Response.- Strategies for Surviving Aggressive Multiparty Repeated Standoffs.- A Hybridization of GRASP and UTASTAR for Solving the Vehicle Routing Problem with Pickups and Deliveries and 3D Loading Constraints.- Packing hypertrees and the k-cut problem in Hypergraphs.- Maximizing the Eigenvalue-Gap and Promoting Sparsity of Doubly Stochastic Matrices with PSO.- Value of Information in the Mean-Square Case and its Application to the Analysis of Financial Time-Series Forecast.
£66.49
Springer International Publishing AG Sixty Shades of Generalized Continua: Dedicated
Book SynopsisIn this book, well-known scientists discuss modern aspects of generalized continua, in order to better understand modern materials and advanced structures. They possess complicated internal structure, and it requires the development of new approaches to model such structures and new effects caused by it. This book combines fundamental contributions in honor of Victor Eremeyev and his 60th birthday.Table of Contents1 Effects of 3-D Printing Infill Density Parameter on the Mechanical Properties of PLA Polymer Reza Afshar, Simon Jeanne, and Bilen Emek Abali1.1 Introduction 1.2 Additive Manufacturing 1.3 Materials and Methods 1.3.1 Fused Deposition Modeling (FDM) 1.3.2 Unidirectional Tensile Tests 1.3.3 Digital Image Correlation Method 1.4 Results and Discussions 1.5 Conclusions References 2 Advance Approximate Analytical Solutions of the Contact Problem for an Inhomogeneous Layer Sergei M. Aizikovich, Polina A. Lapina, and Sergei S. Volkov2.1 Introduction 2.2 Statement of the Problem of a Shear of the Surface of an Inhomogeneous Layer 2.3 Integral Equations of Contact Problems 2.4 Numerical Analysis 2.5 Closure References 3 The Direct Approach for Plates Considering Hygrothermal Loading and Residual Kinetics Marcus Aßmus, Zia Javanbakht, and Holm Altenbach3.1 Introduction 3.2 Frame of Reference 3.3 Thermal Effects and Hygroscopic Impact 3.4 Residual Kinetics 3.5 Conclusion References 4 A Technique for Determining True Deformation Diagrams Under Dynamic Tension Using DIC Artem V. Basalin, Anatoly M. Bragov, Aleksandr Yu. Konstantinov,and Andrey R. Filippov4.1 Introduction 4.2 Pneumatic Dynamic Installation for Testing Materials at a Deformation Rate of the Order of 10-100 s−1 4.2.1 Installation Scheme 4.2.2 Methods of Obtaining and Processing Information in the Experiment 4.3 Test Results of Sheet (3 mm) Steel 09G2S in a Wide Range of Strain Rates 4.4 Conclusion References 5 Strain Gradient Elasticity and Dual Internal Variables Arkadi Berezovski5.1 Introduction 5.2 Dual Internal Variables 5.2.1 Evolution Equations 5.2.2 Quadratic Free Energy 5.3 Concluding Remarks References 6 On the Coercivity of Strain Energy Functions in Generalized Models of 6-Parameter Shells Mircea Bîrsan and Patrizio Neff6.1 Introduction 6.2 General 6-Parameter Elastic Shells. Governing Equations 6.3 The Order ℎ3 Model of 6-Parameter Shells made of Cosserat Material 6.3.1 Coercivity Results for the Model of Order ����(ℎ3) 6.3.2 Existence of Minimizers 6.4 The Higher Order Model of Cosserat 6-Parameter Shells References 7 Solving the Equations of Nonlinear Model of Crystalline Media with Complex Lattice and Some Structures of Plane Deformation Anatolii N. Bulygin and Yuri V. Pavlov7.1 Introduction 7.2 Nonlinear Model of Deformation of Crystal Media 7.3 General Solution of Dynamic Equations of Plane Deformation of the Nonlinear Model 7.4 Solving the Micro-Field Equations 7.5 Conclusion References 8 Modal Analysis of a Second-Gradient Annular Plate made of an Orthogonal Network of Logarithmic Spiral Fibers Alessandro Ciallella, Francesco D’Annibale, Francesco dell’Isola,Dionisio Del Vescovo, and Ivan Giorgio8.1 Introduction 8.2 The Model for a Fiber Net Arranged in Logarithmic Spirals 8.3 Modal Analysis 8.4 Conclusions and Future Perspectives References 9 Non-Linear Simplest Reduced Kelvin’s Medium in the Vicinity of the Spherical Stress State: Waves and Instabilities Mikhail A. Drepin and Elena F. Grekova9.1 Introduction and Notation9.2 Basic Equations for the Isotropic Elastic Reduced Kelvin’s Medium in the Vicinity of a Preliminary Stress State 9.2.1 Dynamic Laws of a Nonlinear Reduced Kelvin Medium 9.2.2 Constitutive Relations for a Nonlinear Reduced Kelvin Medium9.2.3 The Simplest Nonlinear Reduced Kelvin Medium. Strain Energy9.2.4 Medium in the Vicinity of a Homogeneous Nonlinear Spherical Deformation State 9.3 Dispersion Relations of the Simplest Elastic Reduced Kelvin Medium in the Vicinity of Preliminary Spherical Strain State for Special Directions of Perturbation Propagation. Waves and Stability9.3.1 Harmonic Waves 9.3.2 Propagation of Harmonic Waves Along the Body Point Axis (ˆ������������ = ±������������0) 9.3.3 Propagation of Harmonic Waves in the Direction Orthogonal to the Body Point Axis (ˆ������������⊥������������0) 9.4 Conclusion References 10 On the Spectrum of Relaxation Times of Coupled Diffusion and Rheological Processes in Media with Microstructure Dmitrii S. Dudin and Ilya E. Keller10.1 Introduction 10.2 Deformations 10.3 Balance Equations 10.4 The Helmholtz Free Energy 10.5 Thermodynamic Inequality 10.6 Constitutive Equations 10.7 Model Problem and its Equations 10.8 Diffusion Coefficients in Coupled System 10.9 Conclusion References 11 Representative Volume Element Size and Length Scale Identification in Generalised Magneto-Elasticity Sinan Eraslan, Inna M. Gitman, Mingxiu Xu, Harm Askes, and René de Borst11.1 Introduction 11.2 Formulation 11.2.1 Homogenisation and Macroscopic Characteristic Length Scale Parameters11.2.2 Determination of RVE Sizes and Identification of Characteristic Length Scale Parameters 11.3 Numerical Results and Discussion11.4 Conclusions References 12 Rayleigh Waves in the Cosserat Half-Space (Reduced Model) and Half-Space of Damaged Material Vladimir Erofeev, Artem Antonov, Anna Leonteva, and Alexey Malkhanov12.1 Introduction 12.2 Rayleigh Waves in the Cosserat Half-space (Reduced Model) 12.3 Rayleigh Waves in the Half-space of Damaged Material 12.4 Conclusion References 13 Validation of a Hemi-Variational Block-Based Approach to the Modelling of Common In-plane Failures in Masonry Structures José Manuel Torres Espino, Jaime Heman Espinoza Sandoval, Chuong Anthony Tran, Roberto Fedele, Emilio Turco, Francesco dell’Isola, LucaPlacidi, Anil Misra, Francisco James León Trujillo, and Emilio Barchiesi13.1 Introduction 13.2 Mathematical Formulation 13.2.1 Vertex Springs and Stiffnesses 13.2.2 Deformation Energy and Impenetrability Potential 13.2.3 Damage Laws 13.2.4 Principle of Minimum Potential Energy 13.2.5 Numerical Model 13.2.6 Stiffness Matrix13.2.7 Algorithm 13.3 Results 13.3.1 Comparative Result 13.3.2 Influence of Mortar Thickness on Masonry Performance 13.3.3 Bending and Shear Sliding 13.3.4 Rocking 13.4 Conclusions and Future Challenges References 14 Size Effects in Cosserat Crystal Plasticity Samuel Forest and Flavien Ghiglione14.1 Introduction 14.2 Problem Setting 14.2.1 Field Equations 14.2.2 Constitutive Equations14.2.3 Studied Boundary Value Problem 14.3 Cosserat Elastoplasticity Based on a Quadratic Potential14.3.1 Simple Glide in Isotropic Elasticity 14.3.2 Crystal Plasticity Based on the Full Stress Tensor 14.3.3 Schmid Law Limited to the Symmetric Part of the Stress Tensor 14.3.4 Comparison with the Curl ���� ���� Model 14.4 Rank One Energy Potential 14.4.1 Elasticity Solution14.4.2 Crystal Plasticity 14.4.3 Comparison with the Curl ���� ���� Model14.5 Combined Potential 14.6 Application to Grain Boundary Behaviour 14.6.1 Cosserat-Phase Field Model of Grain Boundaries 14.6.2 Analytical Solution of a Single Flat Grain Boundary 14.6.3 Grain Boundary Energy References 15. On the Influence of Poisson’s Ratio on Phase Transformations Limiting Surfaces Alexander B. Freidin and Leah L. Sharipova15.1 Introduction15.2 Phase Equilibrium and Phase Transition Zones for Phases with Positive and Negative Poisson’s Ratios15.3 Optimal Laminates and Phase Transformations Limiting Surfaces15.4 Results 15.5 Conclusions References 16. Application of Nonlocal Fick’s Law Within Micropolar Approach Ksenia Frolova, Nikolay Bessonov, and Elena Vilchevskaya16.1 Introduction 16.2 Diffusion in Media Modeled by Micropolar Continuum 16.3 Axially Symmetric Problem 16.4 Results and Discussion 16.5 Conclusions Appendix. Some Remarks on Numerical Approximation References 17 Geometrically Nonlinear Cosserat Elasticity with Chiral Effects Based upon Granular Micromechanics Ivan Giorgio, Anil Misra, and Luca Placidi17.1 Introduction 17.2 Discrete and Continuous Models for Granular Systems 17.2.1 Identification via Piola’s Ansatz 17.2.2 Relative Intergranular Displacement and Related Continuum Deformation Measures 17.2.3 On the Objective (Macro and Micro-macro)Displacement Vectors 17.2.4 On the Objective Tensor 17.2.5 The Objective Scalar Deformation Measures17.3 Elastic Energy Function 17.4 Identification of the Undamaged Isotropic Case 17.4.1 Characterization of the Undamaged Isotropic Case 17.4.2 Macroscopic Isotropic Stiffness Matrices 17.4.3 Identification of the Macroscopic Isotropic Stiffness Matrices 17.5 Conclusion References 18 Study of the Dynamic Properties of Reinforced Concrete Under High-Speed Compression Mikhail E. Gonov, Vladimir V. Balandin, Anatoly M. Bragov,and Aleksandr Yu. Konstantinov18.1 Introduction 18.2 Test Method 18.3 Characteristics of the Tested Materials 18.4 Results of Dynamic Tests for Uniaxial Compression 18.5 Conclusion References19 Multistability of Convective Flows in a Porous Enclosure Vasily Govorukhin, Mezhlum Sumbatyan, and Vyacheslav Tsybulin19.1 Introduction 19.2 Mathematical Formulation of the Problem19.3 Numerical Methods and Extreme Multistability 19.3.1 Spectral Global Galerkin Method 19.3.2 Cosymmetry Preserving Finite-Difference Approximations19.3.3 Continuation on the Hidden Parameter Method 19.4 Multistability References 20 Hydrogen Transport in Framework of Linear Non-Equilibrium Thermodynamics Approach Polina M. Grigoreva and Vladimir A. Polyanskiy20.1 Introduction 20.2 Problem Statement and Governing Equations 20.3 Plane Boundary Value Problem 20.4 ConclusionReferences 21 Classical and Non-Classical Models of Changes in the Young Modulus of Geomaterials Under Alternating Loads Mikhail A. Guzev, Evgenii P. Riabokon, Mikhail S. Turbakov,Vladimir V. Poplygin, Evgenii V. Kozhevnikov, and Evgenii A. Gladkikh21.1 Introduction 21.2 Experimental Studies 21.3 Classical Model of Changes in the Young Modulus Under an Alternating Load 21.4 Non-classical Model of Change in the Young Modulus Under the Alternating Load 21.4.1 Formulation of the Non-classical Model 21.4.2 Building the Solution 21.5 Conclusion References22 Two Approaches to Modeling Viscoelastic Cosserat Continua Elena A. Ivanova22.1 Introduction 22.2 Kinematics and Balance Equations 22.3 Differential Equations Relating the Strain Tensors to the Velocity Vector and the Angular Velocity Vector 22.4 The Reduced Energy Balance Equation and the Heat Conduction Equation: Zhilin’s Method 22.5 Integral Equations Relating the Strain Tensors to the Velocity Vector and the Angular Velocity Vector 22.6 Source Terms in the Strain Balance Equations22.7 The Reduced Energy Balance Equation and the Heat Conduction Equation: A new Method 22.8 A Comparison of two Approaches 22.9 Discussion References 23 Porous Media Models Based on Generalized State Equations with Simple Examples Anna Knyazeva and Nelli Nazarenko23.1 Introduction 23.2 Definitions and General Relationships 23.3 Thermodynamical Relations 23.4 Examples of Particular Problems 23.4.1 Compressible Nonviscous Gas 23.4.2 Compressible Fluid with Bulk Viscosity 23.4.3 Non-ideal Gas Under Non-isothermal Conditions 23.4.4 Binary Non-viscous Imperfect Mixture 23.4.5 Diffusion and Filtration in Media with Double Porosity 23.4.6 Viscous Two-component Fluid in Media with DoublePorosity23.4.7 Nonviscous Two-component Fluid in Porous media with Nano- and Micro-pores 23.5 Conclusion References 24 Ball Indentation of Perforated Circular Hyperelastic Membranes Alexey M. Kolesnikov24.1 Introduction 24.2 Mathematical Model 24.2.1 Axisymmetric Problem of Non-linear Elastic Membranes 24.2.2 Ball Indentation of Perforated Circular Hyperelastic Membranes 24.3 Numerical Results 24.4 Conclusions References25 Integrated Asymptotic Approach to the Structural Mechanics Models Alexander G. Kolpakov and Sergey I. Rakin25.1 Motivation of the Research 25.2 Modern State of Structural Mechanics 25.2.1 Deformation of the “Main” Part of Frame 25.2.2 Deformation of Connecting Units of Frame 25.2.3 “Infinite Rigidity” of Connecting Units 25.2.4 Structural Mechanics Achievements and Limitations 25.3 Integrated Approach to the Computation of Thin-walled Structures 25.3.1 Displacements in the “Main” Part of the Beams 25.3.2 “Rigid” Displacements of the Connecting Unit 25.3.3 Conjugation of the Displacements in the Main Part of a Beam with the “Rigid Body” Displacements of the Connecting Unit 25.3.4 Assembling the Single-beam Domain Functions into the Function in 2-D Frame 25.3.5 Supplement of the Functions (25.5) with the Local Perturbations 25.4 Local Stress-strain State in the Connecting Units 25.5 Representative Fragment of Joint 25.6 Integrated Procedure for Computation of Framework 25.7 Actual Problems 25.8 Conclusions References 26 The Homogenized Delamination Criterion for Fiber-reinforced Plate Alexander G. Kolpakov, Sergey I. Rakin, and Igor V. Andrianov26.1 Introduction 26.2 Boundary Layer 26.3 Numerical Computation Results 26.3.1 Extension Along ��������- or ��������-axis 26.3.2 Shift in ��������2����3-plane 26.4 The Asymptotic Homogenized Strength Criterion of the Interface Zone 26.5 Constructing the Delaminating Strength Criterion26.6 Conclusions References 27 Lightly Loaded Hydrodynamic Thrust Bearing Lubricated by a Non-Newtonian Fluid Ilya I. Kudish, Sergei S. Volkov, and Andrey S. Vasiliev27.1 Introduction 27.2 Formulation of the Lubrication Problem 27.3 Asymptotic Analysis of the Rheological and Motion Equations 27.4 Examples of Some Specific Lubrication Problem Solutions and Discussion 27.5 Closure References 28 The Idea of Using Adhesive Bonds in Shaping of Cold-formed Thin-walled Beam-columnsMarcin Kujawa, Antonio Cazzani, Lukasz Smakosz, ViolettaKonopińska-Zmysłowska, Karol Winkelmann, Faizullah Jan, andCzesław Szymczak28.1 Introduction 28.2 State of the Art28.2.1 Static, Dynamics, and Stability Analysis of Thin-walled Members 28.2.2 Influence of Imperfections 28.2.3 Failure Analysis with Attention to Creep in Adhesive Bonded Metal Members/Structures 28.3 The Rationale for Addressing the Research Problem 28.4 Conclusions References 29 Dissipative Mechano-Electro-Magnetism Simulations in Electronic Components Yiming Liu, Wolfgang H. Müller, and Bilen Emek Abali29.1 Introduction29.2 Governing Equations 29.3 Constitutive Equations 29.4 Generating Weak Forms 29.5 Implementation and Results 29.6 Conclusion References 30 On Possible Reduction of Gradient Theories of Elasticity Sergey A. Lurie, Petr A. Belov, and Yury O. Solyaev30.1 Introduction30.2 Variational Formulation of Gradient Theories 30.3 Structure of Sixth Rank Tensors 30.4 Special Structure of Gradient Part of Potential Energy. Hypothesis on Absence of Divergent Terms30.5 Features of Variational Formulation of Vector-Type Gradient Models 30.6 System of Governing Equilibrium Equations 30.7 On Uniqueness of Reduced Vector-Type Models 30.8 Conclusions References 31 Dynamics of a Rectangular Rigid Body on a Movable Base Vladimir S. Metrikin, Leonid A. Igumnov, and Elena I. Komarova31.1 Introduction 31.2 Mathematical Model31.3 Construction of a Point Mapping of the Poincaré Surface 31.3.1 The Coordinates of the Fixed Point Corresponding to the Symmetrical Periodic Motion. Sustainability 31.3.2 Equations for Determining the Coordinates of a Fixed Point Corresponding to Asymmetric Periodic Motions.Sustainability 31.4 Numerical Results for ¥����(����) = ����sin(��������) 31.5 Numerical Results 31.6 Conclusion References 32 Asymptotically Correct Analytical Model for Flexural Response of a Two-Layer Strip with Contrast Elastic Constants Gennadi Mikhasev and Nguyen Le32.1 Introduction 32.2 Statement of the Problem 32.3 Bernoulli-Euler Type Model for Strip Consisting of Layers with Close Material Constants 32.4 Timoshenko-Reissner Type Model for Strip Consisting of Layers with High-Contrast Elastic Properties 32.4.1 Leading Approximation 32.4.2 First-Order Approximation 32.4.3 One-Dimensional Governing Equation32.5 Free Vibrations 32.6 ConclusionsReferences 33 On Analytical Modeling of Tension-Assisted Winding of Flexible Sheets Aleksandr Morozov, Wilhelm Rickert, and Sergei Shubin33.1 Introduction 33.2 General Assumptions for the Winding Problem 33.3 Winding the First Layer 33.4 Winding the Subsequent Layers 33.5 Conclusions References 34 On Using Rotations as Primary Variables in the Nonlinear Theory of Thin Elastic Shells Wojciech Pietraszkiewicz34.1 Introduction 34.2 Geometry and Deformation of the Reference Surface 34.3 Equilibrium Conditions 34.4 Boundary Value Problem with Independent Rotations 34.5 Constitutive Equations of Rubber-Like Shells References 35 Continuum Description of Extended Mass-in-Mass Metamaterial Models Alexey V. Porubov35.1 Introduction 35.2 Classic Mass-in-Mass Chain 35.3 Chain with Extra Attached Masses35.4 Chain with Extra Internal Attached Masses 35.5 Attached Masses Through one Element of the Main Chain 35.6 Conclusions References 36 Multi-Element Metamaterial’s Design Through the Relaxed Micromorphic Model Leonardo A. Perez Ramirez, Gianluca Rizzi, and Angela Madeo36.1 Introduction 36.2 The Relaxed Micromorphic Model: Constitutive laws,Equilibrium Equations, and Boundary Conditions 36.2.1 Equilibrium Equations 36.2.2 Boundary and Interface Conditions 36.2.3 Numerical Results 36.3 Parametric Study on the Thickness of a Shielding Device: Capability Limit for the Relaxed Micromorphic Model 36.4 Design of a Double Shield Device 36.5 Multiple-Shields Optimization 36.6 Conclusions References37 On Magnetically Induced Motion of Micropolar FerrofluidsWilhelm Rickert, Margarita Dementeva, Gregor Ganzosch, Elena N.Vilchevskaya, and Wolfgang H. Müller37.1 Introduction 37.2 A Flow Problem Coupled to Electromagnetism 37.3 Simplifications and Normalization 37.4 Electromagnetic Force Density 37.5 Initial Values, Boundary Conditions and Implementation 37.6 Results 37.6.1 Slip 37.6.2 No Slip 37.6.3 Homogeneous Magnetic Field 37.7 Summary References 38 Manufacturing Quality Evaluation of Photopolymer Resin 3D-Printed Scaffolds Using Microtomography Evgeniy V. Sadyrin, Andrey L. Nikolaev, Sergei V. Chapek, Dmitry V.Nazarenko, Sergei M. Aizikovich, and Yun-Che Wang38.1 Introduction 38.2 Materials and Methods 38.3 Results and Discussion 38.4 Conclusion References 39 Comparison of Homogenization Techniques in Strain Gradient Elasticity for Determining Material Parameters Bekir Cagri Sarar, M. Erden Yildizdag, and Bilen Emek Abali39.1 Introduction 39.2 Determining Strain Gradient Parameters 39.3 Microscale Structure 39.4 Results and Discussion 39.5 Conclusion References 40 Buckling of Rectangular Micropolar Plate with Prestressed Coatings Denis N. Sheydakov40.1 Introduction 40.2 Micropolar Plate with Prestressed Coatings40.3 Equations of Neutral Equilibrium 40.4 Micropolar Plate with Identical Coatings 40.5 Conclusion References 41 A Cosserat Model for Fiber-Reinforced Elastic Plates David J. Steigmann, Mircea Bîrsan, and Milad Shirani41.1 Introduction 41.2 The Three-Dimensional Cosserat Model for Fiber-Reinforced Elastic Solids 41.2.1 Kinematical Variables and Strain Measures in Cosserat Elasticity 41.2.2 Fiber-Reinforced Materials 41.2.3 Equilibrium and Constitutive Equations 41.3 Plate Theory for Fiber-Reinforced Laminae41.4 Specific Constitutive Assumptions 41.4.1 Coercivity 41.4.2 Minimum Property Appendix References 42 On the Structure of Solutions in the Vicinity of Discontinuity of Boundary Conditions for Gradient ModelsAlexander O. Vatulyan, Sergey A. Nesterov, Victor O. Yurov, and OksanaV. Yavruyan42.1 Introduction 42.2 Constitutive Relations of the Gradient Theory of Elasticity and Electroelasticity 42.3 Problem for a Strip with Delamination 42.4 Problem for an Electroelastic Strip with a Surface Electrode42.5 Conclusion References 43 A Damaged Medium Model for Assessing Life Characteristics of Polycrystalline Structural Alloys with Joint Mechanical Fatigue and Long-Term Strength of Material Ivan A. Volkov, Leonid A. Igumnov, Aleksandr A. Belov, and Andrey I.Volkov43.1 Introduction43.2 Constitutive Relations of the Mathematical Model of Mechanics of Damaged Medium 43.2.1 Constitutive Relations of Thermoviscoplasticity 43.2.2 Evolutionary Equations for Damage Accumulation43.3 Numerical Results 43.4 ConclusionReferences44 Bandgap Properties of a Class of Chiral and Achiral Metamaterials Yun-Che Wang, Tse-Chun Liao, Kai-Wen Tan, and Sergey M. Aizikovich44.1 Introduction 44.2 Theoretical Considerations 44.3 Numerical Considerations 44.4 Results and Discussion 44.5 Conclusions References45 Large Strains of a Spherical Shell with Distributed Dislocations and Disclinations Leonid M. Zubov and Mikhail I. Karyakin45.1 Introduction 45.2 The Model of a Nonlinear Elastic Micropolar Shell 45.3 Continuously Distributed Dislocations in an Elastic MicropolarShell 45.4 Transformation of Incompatibility Equations and EquilibriumEquations 45.5 Equilibrium of a Closed Spherical Shell with DistributedDislocations and Disclinations 45.6 Numerical Results 45.7 Conclusions References
£123.49
Springer International Publishing AG Intelligence for Future Cities: Planning Through
Book SynopsisThis book contains a selection of the best papers presented at the Computational Urban Planning and Urban Management (CUPUM) conference, held in June 2023 at McGill University in Montreal, Quebec. Major themes of this book are smart cities, urban big data, and shared mobility. This book also contains chapters with cutting-edge research on urban modeling, walkability and bikeability analysis, and planning support systems (PSS).Table of ContentsIntroduction.- Part 1: Digital cities.- Hybrid smartness: Seeking a balance between top-down and bottom-up smart city approaches.- Interpreting the smart city through topic modelling.- The venue code: digital surveillance, spatial (re)organization, and infrastructural power during the COVID pandemic in China.- The platformization of public participation: Considerations for urban planners navigating new engagement tools.- Part 2: Mobility futures.- Shared micro-mobility: A panacea or a patch for our urban transport problems?- Understanding bikeability: Insight into the cycling–city relationship using massive dockless bike-sharing records in Beijing.- Disclosing the impact of micro-level environmental characteristics on dockless bikeshare trip volume: A case study of Ithaca.- A planning support system for boosting bikeability in Seoul.- Integrating big data and a travel survey to understand the gender gap in ride-hailing usage: evidence from Chengdu, China.- Urban airspace route planning for advanced air mobility operations.- Part 3: Fine-scale urban analysis.- “Eyes on the Street”: Estimating natural surveillance along Amsterdam’s city streets using street-level imagery.- Automatic evaluation of street-level walkability based on computer vision techniques and urban big data: A case study of Kowloon West, Hong Kong.- Promoting sustainable travel through a web-based tourism support system.- Applying the Aurin walkability index at the metropolitan and local levels by sex and age in Australia.- Predicting urban heat island mitigation with random forest regression in Belgian cities.- A framework to probe the uncertainties in urban cellular automata modeling with multilevel density for the Wallonia region, Belgium.
£189.99
Springer International Publishing AG Numerical Methods and Applications: 10th
Book SynopsisThis book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Numerical Methods and Applications, NMA 2022, held in Borovets, Bulgaria, in August 2022.The 30 revised regular papers presented were carefully reviewed and selected from 38 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.Table of ContentsSUSHI for a Bingham Flow.- Two-Phase Algorithm For Solving Vehicle Routing Problem with Time Windows.- Topological dynamic consistency of numerical methods for dynamical models in biosciences?.- Parameter Estimation Inspired by Temperature Measurements for a Chemotactic Model of Honeybee Thermoregulation.- On the Consistency and Convergence of Repeated Richardson Extrapolation.- Convergence Analysis of a Finite Volume Scheme for a Distributed Order Diffusion Equation.- SUSHI for a Non-Linear Time Fractional Diffusion Equation with a Time Independent Delay.- On the Numerical Simulation of Exponential Decay and Outbreak Data Sets Involving Uncertainties.- Rational approximation preconditioners for multiphysics problems.- Rational approximation preconditioners for multiphysics problems.- Analysis of Effective Properties of Poroelastic Composites with Surface Effects Depending on Boundary Conditions in Homogenization Problems.- Ant Algorithm for GPS Surveying Problem with Fuzzy Pheromone Updating.- Covering a set of points with a minimum number of equal disks via simulated annealing.- Mathematical modelling of nonlinear heat conduction with relaxing boundary conditions.- Random Sequences in Vehicle Routing Problem.- A database of high precision trivial choreographies for the planar three-body problem.- Evaluation of the Effective Material Properties of Media with Voids Based on Numerical Homogenization and Microstructure Data.- Variable Neighborhood Search Approach to Community Detection Problem.- Simulation Investigations of Pyramidal Cells Layer Effect on Conscious Visual Perception.- On Decision Making Under Uncertainty.- An Inequality for Polynomials on the Standard Simplex.- A Theoretical Analysis on the Bound Violation Probability in Differential Evolution Algorithm.- On the Extreme Zeros of Jacobi Polynomials.- Sensitivity Analysis of an Air Pollution Model Using Innovative Monte Carlo Methods in Calculating Multidimensional Integrals.- Demanded scale for modern numerical optimisation.- RMSD Calculations For Comparing Protein Three-Dimensional Structures.- On the Application of a Hierarchically Semi-Separable Compression for Space-Fractional Parabolic Problems with Varying Time Steps.- Optimized Stochastic Approaches Based on Sobol Quasirandom Sequences for Fredholm Integral Equations of the Second Kind.- Intuitionistic Fuzzy Knapsack Problem trough the Index Matrices Prism.- Simulation of the Mechanical Wave Propagation in a Viscoelastic Media with and without Stiff Inclusions.
£56.99
Springer International Publishing AG Introduction to Applications of Modular Forms:
Book SynopsisThis book is a self-contained treatment for those who study or work on the computational aspects of classical modular forms. The author describes the theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the theory in context and make new conjectures. Table of ContentsDirichlet Characters.- Modular Forms: Definition and Some Properties.- Application: Quadratic Forms.- Application: Eta Quotients.- Various Applications.
£66.49
Springer International Publishing AG Integer Programming and Combinatorial
Book SynopsisThis book constitutes the refereed proceedings of the 24th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2023, held in Madison, WI, USA, during June 21–23, 2023. The 33 full papers presented were carefully reviewed and selected from 119 submissions. IPCO is under the auspices of the Mathematical Optimization Society, and it is an important forum for presenting present recent developments in theory, computation, and applications. The scope of IPCO is viewed in a broad sense, to include algorithmic and structural results in integer programming and combinatorial optimization as well as revealing computational studies and novel applications of discrete optimization to practical problems.
£61.74
Springer International Publishing AG Monte Carlo Simulations Using Microsoft EXCEL
Book SynopsisMonte Carlo simulation has been a powerful computational tool for physics models, and when combined with the programming language Excel, this book is a valuable resource for readers who wish to acquire knowledge that can be applied to more complex systems.
£49.49
Springer International Publishing AG A³N²M: Approximation, Applications, and Analysis
Book SynopsisThis volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.Table of ContentsCTRW approximations for fractional equations with variable order (Kolokoltsov).- Fractional Elliptic Problems on Lipschitz Domains: Regularity and Approximation (Borthagaray).- Regularity estimates and open problems in kinetic equations (Silvestre).- An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions (Littlewood).- Nonlocal diffusion models with consistent local and fractional limits (Du).- A one-dimensional symmetric force-based blending method for atomistic-to-continuum coupling (Li).- A note on estimates of level sets and their role in demonstrating regularity of solutions to nonlocal double phase equations (Mengesha).- An overview of Almost Minimizers of Bernoulli-Type Functionals (Garcia).
£87.99
Springer International Publishing AG Frontiers of Algorithmics: 17th International
Book SynopsisThis book constitutes the refereed proceedings of the 17th International Joint Conference on Theoretical Computer Science-Frontier of Algorithmic Wisdom (IJTCS-FAW 2023), consisting of the 17th International Conference on Frontier of Algorithmic Wisdom (FAW) and the 4th International Joint Conference on Theoretical Computer Science (IJTCS), held in Macau, China, during August 14–18, 2023.FAW started as the Frontiers of Algorithmic Workshop in 2007 at Lanzhou, China, and was held annually from 2007 to 2021 and published archival proceedings. IJTCS, the International joint theoretical Computer Science Conference, started in 2020, aimed to bring in presentations covering active topics in selected tracks in theoretical computer science. To accommodate the diversified new research directions in theoretical computer science, FAW and IJTCS joined their forces together to organize an event for information exchange of new findings and work of enduring value in the field. The 21 full papers included in this book were carefully reviewed and selected from 34 submissions. They were organized in topical sections as follows: algorithmic game theory; algorithms and data structures; combinatorial optimization; and computational economics.Table of ContentsUnderstanding the Relationship Between Core Constraints and Core-Selecting Payment Rules in Combinatorial Auctions.- An Improved Analysis of the Greedy+Singleton Algorithm for k-Submodular Knapsack Maximization.- Generalized Sorting with Predictions Revisited.- Eliciting Truthful Reports with Partial Signals in Repeated Games.- On the NP-hardness of two scheduling problems under linear constraints.- On the Matching Number of k-Uniform Connected Hypergraphs with Maximum Degree.- Max-Min Greedy Matching Problem: Hardness for the Adversary and Fractional Variant.- Approximate Core Allocations for Edge Cover Games.- Random Approximation Algorithms for Monotone k-Submodular Function Maximization with Size Constraints.- Additive Approximation Algorithms for Sliding Puzzle.- Differential Game Analysis for Cooperation Models in Automotive Supply Chain under Low-Carbon Emission Reduction Policies.- Adaptivity Gap for Influence Maximization with Linear Threshold Model on Trees.- Physically Verifying the First Nonzero Term in a Sequence: Physical ZKPs for ABC End View and Goishi Hiroi.- Mechanism Design in Fair Sequencing.- Red-Blue Rectangular Annulus Cover Problem.- Applying Johnson's Rule in Scheduling Multiple Parallel Two-Stage Flowshops.- The Fair k-Center with Outliers Problem: FPT and Polynomial Approximations.- Constrained Graph Searching on Trees.- EFX Allocations Exist for Binary Valuations.- Maximize Egalitarian Welfare for Cake Cutting.- Stackelberg Strategies on Epidemic Containment Games.
£56.99
Springer International Publishing AG Sustained Simulation Performance 2022
Book SynopsisThis book presents the state of the art in High-Performance Computing on modern supercomputer architectures.
£104.99
Springer International Publishing AG Artificial Evolution: 15th International
Book SynopsisThis book constitutes the refereed post-conference proceedings of the 15th International Conference, Évolution Artificielle, EA 2022, held in Exeter, UK, during October 31–November 2, 2022.The 15 full papers were carefully reviewed and selected from 18 submissions. The papers cover a wide range of topics in the field of artificial evolution, including, but not limited to: evolutionary computation, evolutionary optimization, coevolution, artificial life, population dynamics, theory, algorithmic and modeling, implementations.Table of ContentsOn the Active Use of an ND-Tree-Based Archive for Multi-Objective Optimisation.- HyTEA: Hybrid Tree Evolutionary Algorithm.- A Game Theoretic Decision Tree for Binary Classification.- Evaluating a New Genetic Algorithm for Automated Machine Learning in Positive-Unlabelled Learning.- Neural Network-based Virtual Analog Modeling.- Defining a Quality Measure Within Crossover: An Electric Bus Scheduling Case Study.- Maximizing the Number of Satisfied Charging Demands in Electric Vehicle Charging Scheduling Problem.- Fine-Grained Cooperative Coevolution in a Single Population: Between Evolution and Swarm Intelligence.- One-Class Ant-Miner: Selection of Majority Class Rules for Binary Rule-based Classification.- Towards a Many-Objective Optimiser for University Course Timetabling.- Empirical Investigation of MOEAs for Multi-objective Design of Experiments.- Evolutionary Continuous Optimization of Hybrid Gene Regulatory Networks.- Designing Attention based Convolutional Neural Network (CNN) Architectures for Medical Image Classification using Genetic Algorithm based on Variable Length-encoding Scheme.- A Multi-objective 3D Offline UAV Path Planning Problem with Variable Flying Altitude.- An Elitist Non-dominated Heuristic Resolution for the Dynamic Asset Protection Problem.
£47.49
