Numerical analysis Books

Book SynopsisThis book presents in comprehensive detail numerical solutions to boundary value problems of a number of differential equations using the so-called Shooting Method. 4th order Runge-Kutta method, Newton's forward difference interpolation method and bisection method for root finding have been employed in this regard. Programs in Mathematica 6.0 were written to obtain the numerical solutions. This monograph on Shooting Method is the only available detailed resource of the topic.Table of ContentsPreface; Introduction; Differential Equations of Some Elementary Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method; Differential Equations of Special Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method; Differential Equation of Airy Functions: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method; Differential Equation of Stationary Localized Wavepacket: Numerical Solutions of Boundary Value Problems with So-Called Shooting Method; Differential Equation for Motion under Gravitational Interaction: Numerical Solution of Boundary Value Problem with So-Called Shooting Method; Conclusion; References; Index.

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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

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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

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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

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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

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Book SynopsisThis book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences.The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus.The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.Table of ContentsIntroduction 1 0.1 The finite element method 1 0.1.1 General remarks 1 0.1.2 Historical evolution of the method 2 0.1.3 State of the art 3 0.2 Object and organization of the book 3 0.2.1 Teaching the finite element method 3 0.2.2 Objectives of the book 4 0.2.3 Organization of the book 4 0.3 Numerical modeling approach 6 0.3.1 General aspects 6 0.3.2 Physical model 7 0.3.3 Mathematical model 9 0.3.4 Numerical model 10 0.3.5 Computer model 13 Bibliography 16 Conference proceedings 17 Monographs 18 Periodicals 19 Chapter 1. Approximations with finite elements 21 1.0 Introduction 21 1.1 General remarks 21 1.1.1 Nodal approximation 21 1.1.2 Approximations with finite elements 28 1.2 Geometrical definition of the elements 33 1.2.1 Geometrical nodes 33 1.2.2 Rules for the partition of a domain into elements 33 1.2.3 Shapes of some classical elements 35 1.2.4 Reference elements 37 1.2.5 Shapes of some classical reference elements 41 1.2.6 Node and element definition tables 44 1.3 Approximation based on a reference element 45 1.3.1 Expression of the approximate function u(x) 45 1.3.2 Properties of approximate function u(x) 49 1.4 Construction of functions N (ξ ) and N (ξ ) 54 1.4.1 General method of construction 54 1.4.2 Algebraic properties of functions N and N 59 1.5 Transformation of derivation operators 61 1.5.1 General remarks 61 1.5.2 First derivatives 62 1.5.3 Second derivatives 65 1.5.4 Singularity of the Jacobian matrix 68 1.6 Computation of functions N, their derivatives and the Jacobian matrix 72 1.6.1 General remarks 72 1.6.2 Explicit forms for N 73 1.7 Approximation errors on an element 75 1.7.1 Notions of approximation errors 75 1.7.2 Error evaluation technique 80 1.7.3 Improving the precision of approximation 83 1.8 Example of application: rainfall problem 89 Bibliography 95 Chapter 2. Various types of elements 97 2.0 Introduction 97 2.1 List of the elements presented in this chapter 97 2.2 One-dimensional elements 99 2.2.1 Linear element (two nodes, C0) 99 2.2.2 High-precision Lagrangian elements: (continuity C0) 101 2.2.3 High-precision Hermite elements 105 2.2.4 General elements 109 2.3 Triangular elements (two dimensions) 111 2.3.1 Systems of coordinates 111 2.3.2 Linear element (triangle, three nodes, C0) 113 2.3.3 High-precision Lagrangian elements (continuity C0) 115 2.3.4 High-precision Hermite elements 123 2.4 Quadrilateral elements (two dimensions) 127 2.4.1 Systems of coordinates 127 2.4.2 Bilinear element (quadrilateral, 4 nodes, C0) 128 2.4.3 High-precision Lagrangian elements 129 2.4.4 High-precision Hermite element 134 2.5 Tetrahedral elements (three dimensions) 137 2.5.1 Systems of coordinates 137 2.5.2 Linear element (tetrahedron, four nodes, C0) 139 2.5.3 High-precision Lagrangian elements (continuity C0) 140 2.5.4 High-precision Hermite elements 142 2.6 Hexahedric elements (three dimensions) 143 2.6.1 Trilinear element (hexahedron, eight nodes, C0) 143 2.6.2 High-precision Lagrangian elements (continuity C0) 144 2.6.3 High-precision Hermite elements 150 2.7 Prismatic elements (three dimensions) 150 2.7.1 Element with six nodes (prism, six nodes, C0) 150 2.7.2 Element with 15 nodes (prism, 15 nodes, C0) 151 2.8 Pyramidal element (three dimensions) 152 2.8.1 Element with five nodes 152 2.9 Other elements 153 2.9.1 Approximation of vectorial values 153 2.9.2 Modifications of the elements 155 2.9.3 Elements with a variable number of nodes 156 2.9.4 Superparametric elements 158 2.9.5 Infinite elements 158 Bibliography 160 Chapter 3. Integral formulation 161 3.0 Introduction 161 3.1 Classification of physical systems 163 3.1.1 Discrete and continuous systems 163 3.1.2 Equilibrium, eigenvalue and propagation problems 164 3.2 Weighted residual method 172 3.2.1 Residuals 172 3.2.2 Integral forms 173 3.3 Integral transformations 174 3.3.1 Integration by parts 174 3.3.2 Weak integral form 177 3.3.3 Construction of additional integral forms 179 3.4 Functionals 182 3.4.1 First variation 182 3.4.2 Functional associated with an integral form 183 3.4.3 Stationarity principle 187 3.4.4 Lagrange multipliers and additional functionals 188 3.5 Discretization of integral forms 194 3.5.1 Discretization of W 194 3.5.2 Approximation of the functions u 197 3.5.3 Choice of the weighting functions ψ 198 3.5.4 Discretization of a functional (Ritz method) 205 3.5.5 Properties of the systems of equations 208 3.6 List of PDEs and weak expressions 209 3.6.1 Scalar field problems 210 3.6.2 Solid mechanics 213 3.6.3 Fluid mechanics 217 Bibliography 229 Chapter 4. Matrix presentation of the finite element method 231 4.0 Introduction 231 4.1 The finite element method 231 4.1.1 Finite element approach 231 4.1.2 Conditions for convergence of the solution 243 4.1.3 Patch test 256 4.2 Discretized elementary integral forms We 264 4.2.1 Matrix expression of We 264 4.2.2 Case of a nonlinear operator L 267 4.2.3 Integral form We on the reference element 269 4.2.4 A few classic forms of We and of elementary matrices 274 4.3 Techniques for calculating elementary matrices 274 4.3.1 Explicit calculation for a triangular element (Poisson’s equation) 274 4.3.2 Explicit calculation for a quadrangular element (Poisson’s equation) 279 4.3.3 Organization of the calculation of the elementary matrices by numerical integration 280 4.3.4 Calculation of the elementary matrices: linear problems 282 4.4 Assembly of the global discretized form W 297 4.4.1 Assembly by expansion of the elementary matrices 298 4.4.2 Assembly in structural mechanics 303 4.5 Technique of assembly 305 4.5.1 Stages of assembly 305 4.5.2 Rules of assembly 305 4.5.3 Example of a subprogram for assembly 307 4.5.4 Construction of the localization table LOCE 308 4.6 Properties of global matrices 310 4.6.1 Band structure 310 4.6.2 Symmetry 314 4.6.3 Storage methods 314 4.7 Global system of equations 318 4.7.1 Expression of the system of equations 318 4.7.2 Introduction of the boundary conditions 318 4.7.3 Reactions 321 4.7.4 Transformation of variables 321 4.7.5 Linear relations between variables 323 4.8 Example of application: Poisson’s equation 324 4.9 Some concepts about convergence, stability and error calculation 329 4.9.1 Notations 329 4.9.2 Properties of the exact solution 330 4.9.3 Properties of the solution obtained by the finite element method 331 4.9.4 Stability and locking 334 4.9.5 One-dimensional exact finite elements 337 Bibliography 343 Chapter 5. Numerical Methods 345 5.0 Introduction 345 5.1 Numerical integration 346 5.1.1 Introduction 346 5.1.2 One-dimensional numerical integration 348 5.1.3 Two-dimensional numerical integration 360 5.1.4 Numerical integration in three dimensions 368 5.1.5 Precision of integration 372 5.1.6 Choice of number of integration points 375 5.1.7 Numerical integration codes 379 5.2 Solving systems of linear equations 384 5.2.1 Introduction 384 5.2.2 Gaussian elimination method 385 5.2.3 Decomposition 391 5.2.4 Adaptation of algorithm (5.44) to the case of a matrix stored by the skyline method 399 5.3 Solution of nonlinear systems 404 5.3.1 Introduction 404 5.3.2 Substitution method 407 5.3.3 Newton–Raphson method 411 5.3.4 Incremental (or step-by-step) method 420 5.3.5 Changing of independent variables 421 5.3.6 Solution strategy 424 5.3.7 Convergence of an iterative method 426 5.4 Resolution of unsteady systems 429 5.4.1 Introduction 429 5.4.2 Direct integration methods for first-order systems 431 5.4.3 Modal superposition method for first-order systems 463 5.4.4 Methods for direct integration of second-order systems 466 5.4.5 Modal superposition method for second-order systems 476 5.5 Methods for calculating the eigenvalues and eigenvectors 480 5.5.1 Introduction 480 5.5.2 Recap of some properties of eigenvalue problems 481 5.5.3 Methods for calculating the eigenvalues 488 Bibliography 502 Chapter 6. Programming technique 505 6.0 Introduction 505 6.1 Functional blocks of a finite element program 506 6.2 Description of a typical problem 507 6.3 General programs 508 6.3.1 Possibilities of general programs 508 6.3.2 Modularity 511 6.4 Description of the finite element code 512 6.4.1 Introduction 512 6.4.2 General organization 513 6.4.3 Description of tables and variables 517 6.5 Library of elementary finite element method programs 521 6.5.1 Functional blocks 521 6.5.2 List of thermal elements 530 6.5.3 List of elastic elements 538 6.5.4 List of elements for fluid mechanics 545 6.6 Examples of application 549 6.6.1 Heat transfer problems 550 6.6.2 Planar elastic problems 558 6.6.3 Fluid flow problems 566 Appendix. Sparse solver 577 7.0 Introduction 577 7.1 Methodology of the sparse solver 578 7.1.1 Assembly of matrices in sparse form: row-by-row format 579 7.1.2 Permutation using the “minimum degree” algorithm 584 7.1.3 Modified column–column storage format 587 7.1.4 Symbolic factorization 589 7.1.5 Numerical factorization 590 7.1.6 Solution of the system by descent/ascent 592 7.2 Numerical examples 593 Bibliography 595 Index 597

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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

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Book SynopsisBiometrics, the science of using physical traits to identify individuals, is playing an increasing role in our security-conscious society and across the globe. Biometric authentication, or bioauthentication, systems are being used to secure everything from amusement parks to bank accounts to military installations. Yet developments in this field have not been matched by an equivalent improvement in the statistical methods for evaluating these systems. Compensating for this need, this unique text/reference provides a basic statistical methodology for practitioners and testers of bioauthentication devices, supplying a set of rigorous statistical methods for evaluating biometric authentication systems. This framework of methods can be extended and generalized for a wide range of applications and tests. This is the first single resource on statistical methods for estimation and comparison of the performance of biometric authentication systems. The book focuses on six common performance metrics: for each metric, statistical methods are derived for a single system that incorporates confidence intervals, hypothesis tests, sample size calculations, power calculations and prediction intervals. These methods are also extended to allow for the statistical comparison and evaluation of multiple systems for both independent and paired data. Topics and features: * Provides a statistical methodology for the most common biometric performance metrics: failure to enroll (FTE), failure to acquire (FTA), false non-match rate (FNMR), false match rate (FMR), and receiver operating characteristic (ROC) curves * Presents methods for the comparison of two or more biometric performance metrics * Introduces a new bootstrap methodology for FMR and ROC curve estimation * Supplies more than 120 examples, using publicly available biometric data where possible * Discusses the addition of prediction intervals to the bioauthentication statistical toolset * Describes sample-size and power calculations for FTE, FTA, FNMR and FMR Researchers, managers and decisions makers needing to compare biometric systems across a variety of metrics will find within this reference an invaluable set of statistical tools. Written for an upper-level undergraduate or master’s level audience with a quantitative background, readers are also expected to have an understanding of the topics in a typical undergraduate statistics course. Dr. Michael E. Schuckers is Associate Professor of Statistics at St. Lawrence University, Canton, NY, and a member of the Center for Identification Technology Research.Table of ContentsPart I: Introduction Introduction Statistical Background Part II: Primary Matching and Classification Measures False Non-Match Rate False Match Rate Receiver Operating Characteristic Curve and Equal Error Rate Part III: Biometric Specific Measures Failure to Enrol Failure to Acquire Part IV: Additional Topics and Appendices Additional Topics and Discussion Tables

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Book SynopsisThis volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text.Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful. Trade Review“The book can be of special interest to mathematicians, STEM students, and engineers working in multidisciplinary industry settings where the insight provided by differential-algebraic equations can be determinant in decision making.” (Andrzej Sokolowski, MAA Reviews, August 11, 2019)Table of ContentsGeneral Nonlinear Differential Algebraic Equations and Tracking Problems: A Robotics Example.- DAE Aspects in Vehicle Dynamics and Mobile Robotics.- Open-loop Control of Underactuated Mechanical Systems Using Servo-constraints: Analysis and Some Examples.- Systems of Differential Algebraic Equations in Computational Electromagnetics.- Gas Network Benchmark Models.- Topological Index Analysis Applied to Coupled Flow Networks.- Nonsmooth DAEs with Applications in Modeling Phase Changes.- Continuous, Semi-Discrete, and Fully Discretized Navier-Stokes Equations.

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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.

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Book SynopsisThis book constitutes the proceedings of the 18th International Conference on Unconventional Computation and Natural Computation, UCNC 2019, held in Tokyo, Japan, in June 2019.The 19 full papers presented were carefully reviewed and selected from 32 submissions. The papers cover topics such as hypercomputation; chaos and dynamical systems based computing; granular, fuzzy and rough computing; mechanical computing; cellular, evolutionary, molecular, neural, and quantum computing; membrane computing; amorphous computing, swarm intelligence; artificial immune systems; physics of computation; chemical computation; evolving hardware; the computational nature of self-assembly, developmental processes, bacterial communication, and brain processes.Table of ContentsInvited Paper.- Co-designing the computational model and the computing substrate.- Contributed Papers.- Generalized Membrane Systems with Dynamical Structure, Petri Nets, and Multiset Approximation Spaces.- Quantum Dual Adversary for Hidden Subgroups and Beyond.- Further Properties of Self-assembly by Hairpin Formation.- The Role of Structure and Complexity on Reservoir Computing Quality.- Lindenmayer Systems and Global Transformations.- Swarm-based multiset rewriting computing models.- DNA Origami Words and Rewriting Systems.- Computational Limitations of Affine Automata.- An Exponentially Growing Nubot System Without State Changes.- Impossibility of Sufficiently Simple Chemical Reaction Network Implementations in DNA Strand Displacement.- Quantum Algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs.- Viewing rate-based neurons as biophysical conductance outputting models.- The Lyapunov Exponents of Reversible Cellular Automata Are Uncomputable.- Geometric Tiles and Powers and Limitations of Geometric Hindrance in Self-Assembly.- DNA Computing Units Based on Fractional Coding.- The role of the representational entity in physical computing.- OIM: Oscillator-based Ising Machines for Solving Combinatorial Optimisation Problems.- Relativizations of Nonuniform Quantum Finite Automata Families.- Self-stabilizing Gellular Automata.

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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.

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Book SynopsisThis volume gathers the latest advances and innovations in the field of flow-induced vibration and noise, as presented by leading international researchers at the 3rd International Symposium on Flow Induced Noise and Vibration Issues and Aspects (FLINOVIA), which was held in Lyon, France, in September 2019. It explores topics such as turbulent boundary layer-induced vibration and noise, tonal noise, noise due to ingested turbulence, fluid-structure interaction problems, and noise control techniques. The authors’ backgrounds represent a mix of academia, government, and industry, and several papers include applications to important problems for underwater vehicles, aerospace structures and commercial transportation. The book offers a valuable reference guide for all those interested in measurement, modelling, simulation and reproduction of the flow excitation and flow induced structural response.Table of ContentsSource Modeling.- Experimental Techniques.- Analytical Developments.- Numerical Methods.

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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.

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Book SynopsisThis book presents a system that combines the expertise of four algorithms, namely Gradient Tree Boosting, Logistic Regression, Random Forest and Support Vector Classifier to trade with several cryptocurrencies. A new method for resampling financial data is presented as alternative to the classical time sampled data commonly used in financial market trading. The new resampling method uses a closing value threshold to resample the data creating a signal better suited for financial trading, thus achieving higher returns without increased risk. The performance of the algorithm with the new resampling method and the classical time sampled data are compared and the advantages of using the system developed in this work are highlighted.Trade Review“The book contains little theory and presents mostly detailed numerical experiments, it reads very engagingly and inspires with many ideas. It is certainly not a reference book but rather a short monograph on a very clearly defined topic. It will be interesting to see whether the trading strategies presented can be transferred from the crypto markets to the presumably more efficient standard stock markets … as published strategies tend to make markets more efficient.” (Volker H. Schulz, SIAM Review, Vol. 64 (3), September, 2022)Table of ContentsChapter 1 - Introduction Chapter 2 - Related work Chapter 3 - Implementation Chapter 4 - Results Chapter 5 - Conclusions and future work

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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.).

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Book SynopsisThis graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization. Table of ContentsIntroduction.- Matrix analysis and differentiation.- Matrix manifolds in MDA.- Principal component analysis (PCA).- Factor analysis (FA).- Procrustes analysis (PA).- Linear discriminant analysis (LDA).- Canonical correlation analysis (CCA).- Common principal components (CPC).- Metric multidimensional scaling (MDS) and related methods.- Data analysis on simplexes.

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Book SynopsisThis text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.Trade Review“This book has a large amount of new exercise problems that are uniformly distributed across the text. … this book is a very nice text which will serve well for the undergraduate as well as graduate students and will also become a ready reference for scholars.” (Murli M. Gupta, Mathematical Reviews, April, 2023)“Many of the SIAM Review readership will be interested in NMEPPDE from the standpoint of self-study or classroom education. … NMEPPDE offers the applied mathematics reader nearly a single point of entry to our broad and challenging area. … a bit of open space on the bookshelf could profitably be well filled with a copy of NMEPPDE.” (Robert C. Kirby, SIAM Review, Vol. 65 (1), March, 2023)Table of ContentsFor Example: Modelling Processes in Porous Media with Differential Equations.- For the Beginning: The Finite Difference Method for the Poisson Equation.- The Finite Element Method for the Poisson Equation.- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order.- Grid Generation and A Posteriori Error Estimation.- Iterative Methods for Systems of Linear Equations.- Beyond Coercivity, Consistency and Conformity.- Mixed and Nonconforming Discretization Methods.- The Finite Volume Method.- Discretization Methods for Parabolic Initial Boundary Value Problems.- Discretization Methods for Convection-Dominated Problems.- An Outlook to Nonlinear Partial Differential Equations.- Appendices.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Book SynopsisThis book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.Table of ContentsSpace-time approximations for linear acoustic, elastic, and electro-magnetic wave equations.- Local wellposedness and long-time behavior of quasilinear Maxwell equations.- Error analysis of second-order time integration methods for discontinuous Galerkin discretizations of Friedrichs’ systems.- An abstract framework for inverse wave problems with applications.

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Book SynopsisThe use of difference matrices and high-level MATLAB® commands to implement finite difference algorithms is pedagogically novel. This unique and concise textbook gives the reader easy access and a general ability to use first and second difference matrices to set up and solve linear and nonlinear systems in MATLAB which approximate ordinary and partial differential equations. Prerequisites include a knowledge of basic calculus, linear algebra, and ordinary differential equations. Some knowledge of partial differential equations is a plus though the text may easily serve as a supplement for the student currently working through an introductory PDEs course. Familiarity with MATLAB is not required though a little prior experience with programming would be helpful. In addition to its special focus on solving in MATLAB, the abundance of examples and exercises make this text versatile in use. It would serve well in a graduate course in introductory scientific computing for partial differential equations. With prerequisites mentioned above plus some elementary numerical analysis, most of the material can be covered and many of the exercises assigned in a single semester course. Some of the more challenging exercises make substantial projects and relate to topics from other typical graduate mathematics courses, e.g., linear algebra, differential equations, or topics in nonlinear functional analysis. A selection of the exercises may be assigned as projects throughout the semester. The student will develop the skills to run simulations corresponding to the primarily theoretical course material covered by the instructor. The book can serve as a supplement for the instructor teaching any course in differential equations. Many of the examples can be easily implemented and the resulting simulation demonstrated by the instructor. If the course has a numerical component, a few of the more difficult exercises may be assigned as student projects. Established researchers in theoretical partial differential equations may find this book useful as well, particularly as an introductory guide for their research students. Those unfamiliar with MATLAB can use the material as a reference to quickly develop their own applications in that language. Practical assistance in implementing algorithms in MATLAB can be found in these pages. A mathematician who is new to the practical implementation of methods for scientific computation in general can learn how to implement and execute numerical simulations of differential equations in MATLAB with relative ease by working through a selection of exercises. Additionally, the book can serve as a practical guide in independent study, undergraduate or graduate research experiences, or for reference in simulating solutions to specific thesis or dissertation-related experiments.Table of Contents1. Introduction.- 2. Review of elementary numerical methods and MATLAB(R).- 3. Ordinary Differential Equations.- 4. Partial Differential Equations.- 5. Advanced topics in semilinear elliptic BVP.- References.

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Book SynopsisThis book provides an introduction to modern topics in scientific computing and machine learning, using JULIA to illustrate the efficient implementation of algorithms. In addition to covering fundamental topics, such as optimization and solving systems of equations, it adds to the usual canon of computational science by including more advanced topics of practical importance. In particular, there is a focus on partial differential equations and systems thereof, which form the basis of many engineering applications. Several chapters also include material on machine learning (artificial neural networks and Bayesian estimation).JULIA is a relatively new programming language which has been developed with scientific and technical computing in mind. Its syntax is similar to other languages in this area, but it has been designed to embrace modern programming concepts. It is open source, and it comes with a compiler and an easy-to-use package system. Aimed at students of applied mathematics, computer science, engineering and bioinformatics, the book assumes only a basic knowledge of linear algebra and programming.Trade Review“The author’s writing style is clear and concise, making the book easy to follow and understand. The book also includes useful code snippets and diagrams that help illustrate the concepts and algorithms discussed. … the book is well-written and an excellent resource for all those interested in learning the Julia language along with its applications. The extensive discussion of algorithms covering a variety of topics makes it a beneficial book for students, teachers, and researchers alike.” (Syed Inayatullah, zbMATH 1512.90003, 2023)Table of ContentsAn Introduction to the Julia Language.- Functions.- Variables, Constants, Scopes, and Modules.- Built-in Data Structures.- User Defined Data Structures and the Type System.- Control Flow.- Macros.- Arrays and Linear Algebra.- Ordinary Differential Equations.- Partial-Differential Equations.- Global Optimization.- Local Optimization.- Neural Networks.- Bayesian Estimation.

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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.

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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.

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Book SynopsisThis book constitutes the proceedings of the 4th Iberoamerican Conference and third Indo-American Conference on Knowledge Graphs and Semantic Web, KGSWC 2022, which took place in Madrid, Spain, in November 2022.The 22 full and 3 short research papers presented in this volume were carefully reviewed and selected from 63 submissions. The papers cover topics related to software and its engineering, software creation and management, Emerging technologies, Analysis and design of emerging devices and systems, Emerging tools and methodologies and others.Table of ContentsDBkWik++ - Multi Source Matching of Knowledge Graphs.- A Survey on Knowledge Graph-based Methods for Automated Driving.- Physicians’ Brain Digital Twin: Holistic Clinical & Biomedical Knowledge Graphs for Patient Safety and Value-Based Care to Prevent The Post-pandemic Healthcare Ecosystem Crisis.- Combining Ontology and Natural Language Processing methods for Prevention of Falls from Height.- Learning to Automatically Generating Genre-Specific Song Lyrics: A Comparative Study.- DLIME-Graphs: A DLIME Extension based on Triple Embedding for Graphs.- Edge-labelled graphs and property graphs - to the user, more similar than different.- Knowledge Graph supported machine parameterization for the injection moulding industry.- IPR: Integrative Policy Recommendation Framework based on Hybrid Semantics.- Convolutional Neural Networks applied to emotion analysis in texts: Experimentation from the Mexican context.- Proficient Annotation Recommendation in a Biomedical Content Authoring Environment.- DKMI: Diversification of Web Image Search using Knowledge Centric Machine Intelligence.- Does Wikidata Support Analogical Reasoning?.- Flexible Queries over Knowledge Graphs.- Knowledge Graphs for Community Detection in Textual Data.- Framework for Author Name Disambiguation in Scientific Papers Using an Ontological Approach and Deep Learning.- On contrasting and completing YAGO with GPT language models: an experiment for person-related attributes.- Easy and complex: new perspectives for metadata modeling using RDF-star and Named Graphs.- Multi-Aspect Sentiment Analysis using Domain Ontologies.- Popularity Driven Data Integration.- Methodology for Creating a Community Corpus using a Wikibase Knowledge Graph.- Understanding Human Activity Patterns in Smart Homes with Process Mining.- String Matching based Framework for Online Hindi Question Answering System.- Towards an ontological approach to business continuity assessment.- From Ontology to Knowledge Graph Trend: Ontology As Foundation Layer For Knowledge Graph.

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Book SynopsisThis book constitutes the refereed proceedings of the 5th International Conference on Optimization and Learning, OLA 2022, which took place in Syracuse, Sicilia, Italy, in July 2022. The 19 full papers presented in this volume were carefully reviewed and selected from 52 submissions. The papers are organized in the following topical sections: Optimization and Learning; Novel Optimization Techniques; Logistics; and Applications.Table of ContentsOptimization and Learning.- Evolutionary-Based Co-Optimization of DNN and Hardware Configurations on Edge GPU.- Maximum Information Coverage and Monitoring Path Planning With Unmanned Surface Vehicles Using Deep Reinforcement Learning.- Tuning ForestDisc hyperparameters: A sensitivity analysis.- Multi-objective hyperparameter optimization with performance uncertainty.- Novel Optimization Techniques.- A new algorithm for bi-objective problems based on gradient information.- Adaptive Continuous Multi-Objective Optimization using Cooperative Agents.- Integer Linear Programming reformulations for the linear ordering problem.- SHAMan: a versatile auto-tuning framework for costly and noisy HPC systems.- Cooperation-based search of global optima.- Date-driven Simulation-Optimization (DSO): An Efficient Approach to Optimize Simulation Models with Databases.- Logistics.- Sweep Algorithms for the Vehicle Routing Problem with TimeWindows.- Improving the accuracy of vehicle routing problem approximation using the formula for the average distance between a point and a rectangular area.- Optimal Delivery Area Assignment for the Capital Vehicle Routing Problem Based on a Maximum Likelihood Approach.- Neural Order-First Split-Second Algorithm for the Capacitated Vehicle Routing Problem.- Applications.- GRASP-based hybrid search to solve the multi-objective requirements selection problem.- Comparing Parallel Surrogate-based and Surrogate-free Multi-Objective Optimization of COVID-19 vaccines allocation.- Decentralizing and Optimizing Nation-Wide Employee Allocation while Simultaneously Maximizing Employee Satisfaction.- Categorical-Continuous Bayesian optimization applied to chemical reactions.- Assessing Similarity-Based Grammar-Guided Genetic Programming Approaches for Program Synthesis.

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Book SynopsisThis book constitutes the conference proceedings of the 48th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2023, held in Nový Smokovec, Slovakia, during January 15–18, 2023.The 22 full papers presented together with 2 best papers and 2 best students papers in this book were carefully reviewed and selected from 43 submissions.This workshop focuses on graphs problems and optimization; graph drawing and visualization; NP-hardness and fixed parameter tractability; communication and temporal graphs; complexity and learning; and robots and strings. Table of ContentsThe Complexity of Finding Tangles.- A spectral algorithm for finding maximum cliques in dense random intersection graphs.- Solving Cut-Problems in Quadratic Time for Graphs With Bounded Treewidth.- More Effort Towards Multiagent Knapsack.- Dominance Drawings for DAGs with Bounded Modular Width.- Morphing Planar Graph Drawings Through 3D.- Visualizing Multispecies Coalescent Trees: Drawing Gene Trees Inside Species Trees.- Parameterized Approaches to Orthogonal Compaction.- Hardness of bounding influence via graph modification.- On the Parameterized Complexity of $s$-club Cluster Deletion Problems.- Balanced Substructures in Bicolored Graphs.- On the Complexity of Scheduling Problems With a Fixed Number of Parallel Identical Machines.- On the 2-Layer Window Width Minimization Problem.- Sequentially Swapping Tokens: Further on Graph Classes.- On the Preservation of Properties when Changing Communication Models.- Introduction to Routing Problems with Mandatory Transitions .- Multi-Parameter Analysis of Finding Minors and Subgraphs in Edge-Periodic Temporal Graphs.- Lower Bounds for Monotone $q$-Multilinear Boolean Circuits.- A faster algorithm for determining the linear feasibility of systems of BTVPI constraints.- Quantum complexity for vector domination problem.- Learning through Imitation by using Formal Verification.- Delivery to Safety with Two Cooperating Robots.- Space-Efficient STR-IC-LCS Computation.- The k-center Problem for Classes of Cyclic Words.

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Book SynopsisThe once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider’s view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas.Table of ContentsInverse problems and subjective computing.- Linear algebra.- Continuous and discrete multivariate distributions.- Introduction to sampling.- The praise of ignorance: randomness as lack of certainty.- Enter subject: Construction of priors.- Posterior densities, ill-conditioning, and classical regularization.- Conditional Gaussian densities.- Iterative linear solvers and priorconditioners.- Hierarchical models and Bayesian sparsity.- Sampling: the real thing.- Dynamic methods and learning from the past.- Bayesian filtering and Gaussian densities.-

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