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• Preface xi
• 1. Basic Concepts 1 1.1 Systems and Experiments, 2 1.1.1 Natural and Artificial Systems, 3 1.1.2 Experiments, 5 1.2 The Model Concept, 6 1.3 Simulation, 7 1.3.1 Reasons for Simulation, 8 1.3.2 Dangers of Simulation, 9 1.4 Building Models, 10 1.5 Analyzing Models, 12 1.5.1 Sensitivity Analysis, 12 1.5.2 Model-Based Diagnosis, 13 1.5.3 Model Verification and Validation, 13 1.6 Kinds of Mathematical Models, 14 1.6.1 Kinds of Equations, 15 1.6.2 Dynamic Versus Static Models, 16 1.6.3 Continuous-Time Versus Discrete-Time Dynamic Models, 17 1.6.4 Quantitative Versus Qualitative Models, 18 1.7 Using Modeling and Simulation in Product Design, 19 1.8 Examples of System Models, 21 1.9 Summary, 27 1.10 Literature, 27
• 2. A Quick Tour of Modelica 29 2.1 Getting Started with Modelica, 30 2.1.1 Variables and Predefined Types, 35 2.1.2 Comments, 37 2.1.3 Constants, 38 2.1.4 Variability, 38 2.1.5 Default start Values, 39 2.2 Object-Oriented Mathematical Modeling, 39 2.3 Classes and Instances, 41 2.3.1 Creating Instances, 42 2.3.2 Initialization, 43 2.3.3 Specialized Classes, 44 2.3.4 Reuse of Classes by Modifications, 45 2.3.5 Built-in Classes and Attributes, 46 2.4 Inheritance, 47 2.5 Generic Classes, 48 2.5.1 Class Parameters as Instances, 48 2.5.2 Class Parameters as Types, 50 2.6 Equations, 51 2.6.1 Repetitive Equation Structures, 53 2.6.2 Partial Differential Equations, 54 2.7 Acausal Physical Modeling, 54 2.7.1 Physical Modeling Versus Block-Oriented Modeling, 55 2.8 The Modelica Software Component Model, 57 2.8.1 Components, 58 2.8.2 Connection Diagrams, 58 2.8.3 Connectors and Connector Classes, 60 2.8.4 Connections, 61 2.8.5 Implicit Connections with Inner/Outer, 62 2.8.6 Expandable Connectors for Information Buses, 63 2.8.7 Stream Connectors, 64 2.9 Partial Classes, 65 2.9.1 Reuse of Partial Classes, 66 2.10 Component Library Design and Use, 67 2.11 Example: Electrical Component Library, 67 2.11.1 Resistor, 68 2.11.2 Capacitor, 68 2.11.3 Inductor, 68 2.11.4 Voltage Source, 69 2.11.5 Ground, 70 2.12 Simple Circuit Model, 70 2.13 Arrays, 72 2.14 Algorithmic Constructs, 74 2.14.1 Algorithm Sections and Assignment Statements, 75 2.14.2 Statements, 76 2.14.3 Functions, 77 2.14.4 Operator Overloading and Complex Numbers, 79 2.14.5 External Functions, 81 2.14.6 Algorithms Viewed as Functions, 82 2.15 Discrete Event and Hybrid Modeling, 83 2.16 Packages, 87 2.17 Annotations, 89 2.18 Naming Conventions, 91 2.19 Modelica Standard Libraries, 91 2.20 Implementation and Execution of Modelica, 94 2.20.1 Hand Translation of the Simple Circuit Model, 96 2.20.2 Transformation to State Space Form, 98 2.20.3 Solution Method, 99 2.21 History, 103 2.22 Summary, 107 2.23 Literature, 108 2.24 Exercises, 110
• 3. Classes and Inheritance 113 3.1 Contract Between Class Designer and User, 113 3.2 A Class Example, 114 3.3 Variables, 115 3.3.1 Duplicate Variable Names, 116 3.3.2 Identical Variable Names and Type Names, 116 3.3.3 Initialization of Variables, 117 3.4 Behavior as Equations, 117 3.5 Access Control, 119 3.6 Simulating the Moon Landing Example, 120 3.7 Inheritance, 123 3.7.1 Inheritance of Equations, 124 3.7.2 Multiple Inheritance, 124 3.7.3 Processing Declaration Elements and Use Before Declare, 126 3.7.4 Declaration Order of extends Clauses, 127 3.7.5 The MoonLanding Example Using Inheritance, 128 3.8 Summary, 130 3.9 Literature, 130
• 4. System Modeling Methodology 131 4.1 Building System Models, 131 4.1.1 Deductive Modeling Versus Inductive Modeling, 132 4.1.2 Traditional Approach, 133 4.1.3 Object-Oriented Component-Based Approach, 134 4.1.4 Top-Down Versus Bottom-Up Modeling, 136 4.1.5 Simplification of Models, 136 4.2 Modeling a Tank System, 138 4.2.1 Using the Traditional Approach, 138 4.2.2 Using the Object-Oriented Component-Based Approach, 139 4.2.3 Tank System with a Continuous PI Controller, 141 4.2.4 Tank with Continuous PID Controller, 144 4.2.5 Two Tanks Connected Together, 147 4.3 Top-Down Modeling of a DC Motor from Predefined Components, 148 4.3.1 Defining the System, 149 4.3.2 Decomposing into Subsystems and Sketching Communication, 149 4.3.3 Modeling the Subsystems, 150 4.3.4 Modeling Parts in the Subsystems, 151 4.3.5 Defining the Interfaces and Connections, 153 4.4 Designing Interfaces-Connector Classes, 153 4.5 Summary, 155 4.6 Literature, 155
• 5. The Modelica Standard Library 157 5.1 Summary, 168 5.2 Literature, 168 A. Glossary 169 Literature, 174 B. OpenModelica and OMNotebook Commands 175 B.1 OMNotebook Interactive Electronic Book, 175 B.2 Common Commands and Small Examples, 178 B.3 Complete List of Commands, 179 B.4 OMShell and Dymola, 185 OMShell, 185 Dymola Scripting, 185 Literature, 186 C. Textual Modeling with OMNotebook and DrModelica 187 C.1 HelloWorld, 188 C.2 Try DrModelica with VanDerPol and DAEExample Models, 189 C.3 Simple Equation System, 189 C.4 Hybrid Modeling with BouncingBall, 189 C.5 Hybrid Modeling with Sample, 190 C.6 Functions and Algorithm Sections, 190 C.7 Adding a Connected Component to an Existing Circuit, 190 C.8 Detailed Modeling of an Electric Circuit, 191 C.8.1 Equations, 191 C.8.2 Implementation, 192 C.8.3 Putting the Circuit Together, 195 C.8.4 Simulation of the Circuit, 195 D. Graphical Modeling Exercises 197 D.1 Simple DC Motor, 197 D.2 DC Motor with Spring and Inertia, 198 D.3 DC Motor with Controller, 198 D.4 DC Motor as a Generator, 199 References 201 Index 207.
• (source: Nielsen Book Data)

Using the versatile Modelica language and its associated technology, this book presents an object-oriented, component-based approach that makes it possible for readers to quickly master the basics of computer-supported equation-based object-oriented (EOO) mathematical modeling and simulation. Readers will find plenty of examples of models that simulate distinct application domains and that combine several domains. Written by the Director of the Open Source Modelica Consortium, this book is recommended for engineers and students interested in computer-aided design, modeling, simulation, and analysis of technical and natural systems.
(source: Nielsen Book Data)

• 1 Brief Review of Cyber Incidents 1 1.1 Cyber's Emergence as an Issue 3 1.2 Estonia and Georgia - Militarization of Cyber 4 1.3 Conclusions 6
• 2 Cyber Security - An Introduction to Assessment and Maturity Frameworks 9 2.1 Assessment Frameworks 9 2.2 NIST 800 Risk Framework 9 2.2.1 Maturity Models 12 2.2.2 Use Cases/Scenarios 13 2.3 Cyber Insurance Approaches 14 2.3.1 An Introduction to Loss Estimate and Rate Evaluation for Cyber 17 2.4 Conclusions 17 2.5 Future Work 18 2.6 Questions 18
• 3 Introduction to Cyber Modeling and Simulation (M&S) 19 3.1 One Approach to the Science of Cyber Security 19 3.2 Cyber Mission System Development Framework 21 3.3 Cyber Risk Bow-Tie: Likelihood to Consequence Model 21 3.4 Semantic Network Model of Cyberattack 22 3.5 Taxonomy of Cyber M&S 24 3.6 Cyber Security as a Linear System - Model Example 25 3.7 Conclusions 26 3.8 Questions 27
• 4 Technical and Operational Scenarios 29 4.1 Scenario Development 30 4.1.1 Technical Scenarios and Critical Security Controls (CSCs) 31 4.1.2 ARMOUR Operational Scenarios (Canada) 32 4.2 Cyber System Description for M&S 34 4.2.1 State Diagram Models/Scenarios of Cyberattacks 34 4.2.2 McCumber Model 35 4.2.3 Military Activity and Cyber Effects (MACE) Taxonomy 36 4.2.4 Cyber Operational Architecture Training System (COATS) Scenarios 37 4.3 Modeling and Simulation Hierarchy - Strategic Decision Making and Procurement Risk Evaluation 39 4.4 Conclusions 42 4.5 Questions 43
• 5 Cyber Standards for Modeling and Simulation 45 5.1 Cyber Modeling and Simulation Standards Background 46 5.2 An Introduction to Cyber Standards for Modeling and Simulation 47 5.2.1 MITRE's (MITRE) Cyber Threat Information Standards 47 5.2.2 Cyber Operational Architecture Training System 49 5.2.3 Levels of Conceptual Interoperability 50 5.3 Standards Overview - Cyber vs. Simulation 51 5.3.1 Simulation Interoperability Standards Organization (SISO) Standards 52 5.3.2 Cyber Standards 54 5.4 Conclusions 56 5.5 Questions 57
• 6 Cyber Course of Action (COA) Strategies 59 6.1 Cyber Course of Action (COA) Background 59 6.1.1 Effects-Based Cyber-COA Optimization Technology and Experiments (EBCOTE) Project 59 6.1.2 Crown Jewels Analysis 60 6.1.3 Cyber Mission Impact Assessment (CMIA) Tool 61 6.1.4 Analyzing Mission Impacts of Cyber Actions 63 6.2 Cyber Defense Measurables - Decision Support System (DSS) Evaluation Criteria 64 6.2.1 Visual Analytics 65 6.2.2 Managing Cyber Events 67 6.2.3 DSS COA and VV&A 68 6.3 Cyber Situational Awareness (SA) 68 6.3.1 Active and Passive Situational Awareness for Cyber 69 6.3.2 Cyber System Monitoring and Example Approaches 69 6.4 Cyber COAs and Decision Types 70 6.5 Conclusions 71 6.6 Further Considerations 72 6.7 Questions 72
• 7 Cyber Computer-Assisted Exercise (CAX) and Situational Awareness (SA) via Cyber M&S 75 7.1 Training Type and Current Cyber Capabilities 77 7.2 Situational Awareness (SA) Background and Measures 78 7.3 Operational Cyber Domain and Training Considerations 79 7.4 Cyber Combined Arms Exercise (CAX) Environment Architecture 81 7.4.1 CAX Environment Architecture with Cyber Layer 82 7.4.2 Cyber Injections into Traditional CAX - Leveraging Constructive Simulation 84 7.4.3 Cyber CAX - Individual and Group Training 85 7.5 Conclusions 86 7.6 Future Work 87 7.7 Questions 87
• 8 Cyber Model-Based Evaluation Background 89 8.1 Emulators, Simulators, and Verification/Validation for Cyber System Description 89 8.2 Modeling Background 90 8.2.1 Cyber Simulators 91 8.2.2 Cyber Emulators 93 8.2.3 Emulator/Simulator Combinations for Cyber Systems 94 8.2.4 Verification, Validation, and Accreditation (VV&A) 96 8.3 Conclusions 99 8.4 Questions 100
• 9 Cyber Modeling and Simulation and System Risk Analysis 101 9.1 Background on Cyber System Risk Analysis 101 9.2 Introduction to using Modeling and Simulation for System Risk Analysis with Cyber Effects 104 9.3 General Business Enterprise Description Model 105 9.3.1 Translate Data to Knowledge 107 9.3.2 Understand the Enterprise 114 9.3.3 Sampling and Cyber Attack Rate Estimation 114 9.3.4 Finding Unknown Knowns - Success in Finding Improvised Explosive Device Example 116 9.4 Cyber Exploit Estimation 116 9.4.1 Enterprise Failure Estimation due to Cyber Effects 118 9.5 Countermeasures and Work Package Construction 120 9.6 Conclusions and Future Work 122 9.7 Questions 124
• 10 Cyber Modeling & Simulation (M&S) for Test and Evaluation (T&E) 125 10.1 Background 125 10.2 Cyber Range Interoperability Standards (CRIS) 126 10.3 Cyber Range Event Process and Logical Range 127 10.4 Live, Virtual, and Constructive (LVC) for Cyber 130 10.4.1 Role of LVC in Capability Development 132 10.4.2 Use of LVC Simulations in Cyber Range Events 133 10.5 Applying the Logical Range Construct to System under Test (SUT) Interaction 134 10.6 Conclusions 135 10.7 Questions 136
• 11 Developing Model-Based Cyber Modeling and Simulation Frameworks 137 11.1 Background 137 11.2 Model- Based Systems Engineering (MBSE) and System of Systems Description (Data Centric) 137 11.3 Knowledge- Based Systems Engineering (KBSE) for Cyber Simulation 138 11.3.1 DHS and SysML Modeling for Buildings (CEPHEID VARIABLE) 139 11.3.2 The Cyber Security Modeling Language (CySeMoL) 140 11.3.3 Cyber Attack Modeling and Impact Assessment Component (CAMIAC) 140 11.4 Architecture- Based Cyber System Optimization Framework 141 11.5 Conclusions 141 11.6 Questions 142
• 12 Appendix: Cyber M&S Supporting Data, Tools, and Techniques 143 12.1 Cyber Modeling Considerations 143 12.1.1 Factors to Consider for Cyber Modeling 143 12.1.2 Lessons Learned from Physical Security 144 12.1.3 Cyber Threat Data Providers 146 12.1.4 Critical Security Controls (CSCs) 147 12.1.5 Situational Awareness Measures 147 12.2 Cyber Training Systems 148 12.2.1 Scalable Network Defense Trainer (NDT) 153 12.2.2 SELEX ES NetComm Simulation Environment (NCSE) 153 12.2.3 Example Cyber Tool Companies 154 12.3 Cyber- Related Patents and Applications 154 12.4 Conclusions 160 Bibliography 161 Index 175.
• (source: Nielsen Book Data)

Introduces readers to the field of cyber modeling and simulation and examines current developments in the US and internationally This book provides an overview of cyber modeling and simulation (M&S) developments. Using scenarios, courses of action (COAs), and current M&S and simulation environments, the author presents the overall information assurance process, incorporating the people, policies, processes, and technologies currently available in the field. The author ties up the various threads that currently compose cyber M&S into a coherent view of what is measurable, simulative, and usable in order to evaluate systems for assured operation. An Introduction to Cyber Modeling and Simulation provides the reader with examples of tools and technologies currently available for performing cyber modeling and simulation. It examines how decision-making processes may benefit from M&S in cyber defense. It also examines example emulators, simulators and their potential combination. The book also takes a look at corresponding verification and validation (V&V) processes, which provide the operational community with confidence in knowing that cyber models represent the real world. This book: Explores the role of cyber M&S in decision making Provides a method for contextualizing and understanding cyber risk Shows how concepts such the Risk Management Framework (RMF) leverage multiple processes and policies into a coherent whole Evaluates standards for pure IT operations, "cyber for cyber, " and operational/mission cyber evaluations-"cyber for others" Develops a method for estimating both the vulnerability of the system (i.e., time to exploit) and provides an approach for mitigating risk via policy, training, and technology alternatives Uses a model-based approach An Introduction to Cyber Modeling and Simulation is a must read for all technical professionals and students wishing to expand their knowledge of cyber M&S for future professional work. .
(source: Nielsen Book Data)

Now in a fully revised second edition, this work introduces dynamic-system simulation with a main emphasis on OPEN DESIRE and DESIRE software. Offering a complete update of all material, the new edition boasts two completely new chapters on fast simulation of neural networks as well as three appendices on radial-basis-function, fuzzy-basis-function networks, and CLEARN algorithm. A companion CD contains complete binary OPEN DESIRE modeling/simulation program packages for personal-computer LINUX and MS Windows, DESIRE examples, source code, and a comprehensive, indexed reference manual.
(source: Nielsen Book Data)

• Preface
• Abbreviations
• Nomenclature
• Superscript
• Subscript
• 1. Introduction
• 2. Combustion basis of internal combustion engines
• 3. Mathematical description of reactive flow with sprays
• 4. In-cylinder turbulence
• 5. Fuel sprays
• 6. Combustion and pollutant emissions
• 7. Optimization of direct-injection gasoline engines
• 8. Optimization of diesel and alternative fuel engines
• Index
• About the author.

• 4.2.1 RANS Methodology
• 4.2.2 The Classical k-ε Model
• 4.3 RNG k-ε Models
• 4.3.1 RNG Methodology
• 4.3.2 The RNG k-ε Model for Variable-Density Flows
• 4.3.3 Other RNG k-ε Model Variants
• 4.4 Large-Eddy Simulation
• 4.4.1 LES Methodology and Sub-Grid Models
• 4.4.1.1 Smagorinsky Model
• 4.4.1.2 Dynamic Smagorinsky Model
• 4.4.1.3 k-Equation Model
• 4.4.1.4 Dynamic Structure Model
• 4.4.2 Engine Simulation Examples
• 4.4.2.1 Intake and In-Cylinder Flows
• 4.4.2.2. Cycle-to-Cycle Combustion Variation
• 4.4.2.3 Low-Temperature Spray Combustion

Simulation and Optimization of Internal Combustion Engines provides the fundamentals and up-to-date progress in multidimensional simulation and optimization of internal combustion engines. While it is impossible to include all the models in a single book, this book intends to introduce the pioneer and/or the often-used models and the physics behind them providing readers with ready-to-use knowledge. Key issues, useful modeling methodology and techniques, as well as instructive results, are discussed through examples. Readers will understand the fundamentals of these examples and be inspired to explore new ideas and means for better solutions in their studies and work. Topics include combustion basis of IC engines, mathematical descriptions of reactive flow with sprays, engine in-cylinder turbulence, fuel sprays, combustions and pollutant emissions, optimization of direct-injection gasoline engines, and optimization of diesel and alternative fuel engines.
(source: Nielsen Book Data)

• Elementary C programming
• Parallel computing using OpenMP
• Distributed programming and MPI
• GPU programming and CUDA
• GPU programming and OpenCL
• Applications

Based on a course developed by the author, Introduction to High Performance Scientific Computing introduces methods for adding parallelism to numerical methods for solving differential equations. It contains exercises and programming projects that facilitate learning as well as examples and discussions based on the C programming language, with additional comments for those already familiar with C++. The text provides an overview of concepts and algorithmic techniques for modern scientific computing and is divided into six self-contained parts that can be assembled in any order to create an introductory course using available computer hardware. Part I introduces the C programming language for those not already familiar with programming in a compiled language. Part II describes parallelism on shared memory architectures using OpenMP. Part III details parallelism on computer clusters using MPI for coordinating a computation. Part IV demonstrates the use of graphical programming units (GPUs) to solve problems using the CUDA language for NVIDIA graphics cards. Part V addresses programming on GPUs for non-NVIDIA graphics cards using the OpenCL framework. Finally, Part VI contains a brief discussion of numerical methods and applications, giving the reader an opportunity to test the methods on typical computing problems

• Theory of classical sliding mode control
• Introduction to higher order sliding mode control
• Constrained SMC
• Optimization SMC
• SMC for networked systems
• Adaptive SMC algorithms
• Advanced SMC of robots
• Advanced SMC of microgrids

A compendium of the authors' recently published results, this book discusses sliding mode control of uncertain nonlinear systems, with a particular emphasis on advanced and optimization based algorithms. The authors survey classical sliding mode control theory and introduce four new methods of advanced sliding mode control. They analyze classical theory and advanced algorithms, with numerical results complementing the theoretical treatment. Case studies examine applications of the algorithms to complex robotics and power grid problems. Advanced and Optimization Based Sliding Mode Control: Theory and Applications is the first book to systematize the theory of optimization based higher order sliding mode control and illustrate advanced algorithms and their applications to real problems. It presents systematic treatment of event-triggered and model based event-triggered sliding mode control schemes, including schemes in combination with model predictive control, and presents adaptive algorithms as well as algorithms capable of dealing with state and input constraints. Additionally, the book includes simulations and experimental results obtained by applying the presented control strategies to real complex systems.
(source: Nielsen Book Data)

• Multiscale problems and numerical homogenization
• Numerical analyst's review of elliptic homogenization
• Decomposition of scales in elliptic problems
• Localization of numerical correctors
• Localized orthogonal decomposition method
• Effective coefficients and periodic homogenization
• Implementation aspects
• Eigenvalue problems
• Parabolic problems
• Further applications and generalizations

This book presents the first survey of the Localized Orthogonal Decomposition (LOD) method, a pioneering approach for the numerical homogenization of partial differential equations with multiscale data beyond periodicity and scale separation. The authors provide a careful error analysis, including previously unpublished results, and a complete implementation of the method in MATLAB. They also reveal how the LOD method relates to classical homogenization and domain decomposition. Illustrated with numerical experiments that demonstrate the significance of the method, the book is enhanced by a survey of applications including eigenvalue problems and evolution problems. Numerical Homogenization by Localized Orthogonal Decomposition is appropriate for graduate students in applied mathematics, numerical analysis, and scientific computing. Researchers in the field of computational partial differential equations will find this self-contained book of interest, as will applied scientists and engineers interested in multiscale simulation.
(source: Nielsen Book Data)

• The model reduction enterprise
• Systems theory sundries
• Interpolatory model reduction
• Data-driven model reduction and the Loewner modeling framework
• Optimal H2 approximation via interpolation
• Interpolatory model reduction of parameter-dependent systems
• Interpolatory model reduction of nonlinear systems
• Model reduction in related norms
• Interpolatory reduction of differential algebraic systems
• Iterative solves in interpolatory projections

Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.
(source: Nielsen Book Data)

• I. Mathematics foundation. 1. Vector spaces
• 1.1. Introduction
• 1.2. Vector spaces
• 1.3. Functions on vector spaces
• 1.4. Geometric properties of vector spaces
• 1.5. The p norms
• 1.6. Subspace and basis
• 1.7. Orthogonality
• 1.8. Outlook : Banach and Hilbert spaces
• 1.9. Notes

• 2. Linear transformations
• 2.1. Introduction
• 2.2. Four fundamental vector spaces
• 2.3. Vector spaces of matrices
• 2.4. Square matrices as linear operators
• 2.5. Matrix norms
• 2.6. Orthogonal matrices
• 2.7. Projectors
• 2.8. Outlook : bivectors and tensors
• 2.9. Notes

• II. Computer science foundation. 3. Algorithms and data structures
• 3.1. Introduction
• 3.2. Correctness and complexity of algorithms
• 3.3. Accuracy and stability of floating point arithmetic
• 3.4. Data and memory
• 3.5. Data structures
• 3.6. Graph algorithms
• 3.7. Computer graphics and the convolution algorithm
• 3.8. Outlook : simulation and time stepping
• 3.9. Notes

• 4. High performance computing
• 4.1. Introduction
• 4.2. Parallel computing
• 4.3. Parallel programming models
• 4.4. Accelerators
• 4.5. Data centric computing
• 4.6. Parallel performance
• 4.7. Emerging computing platforms
• 4.8. Outlook : quantum computing
• 4.9. Notes

• III. Matrix factorization. 5. Direct methods for systems of linear equations
• 5.1. Introduction
• 5.2. Systems of linear equations
• 5.3. Gram-Schmidt QR factorization
• 5.4. Householder QR factorization
• 5.5. LU factorization
• 5.6. Cholesky factorization
• 5.7. Block matrix algorithms
• 5.8. Sparse matrix algorithms
• 5.9. Outlook : differential and integral operators
• 5.10. Notes

• 6. Eigenvalue and singular value decompositions
• 6.1. Introduction
• 6.2. Complex vector spaces
• 6.3. Eigenvalues and eigenvectors
• 6.4. Similarity transformations and spectral theorems
• 6.5. Generalized eigenvalues
• 6.6. Singular value decomposition
• 6.7. The QR algorithm
• 6.8. The implicit QR algorithm
• 6.9. Outlook : continuum mechanics
• 6.10. Notes

• IV. Iterative methods. 7. Iterative methods for linear equations
• 7.1. Introduction
• 7.2. Convergence of iterative methods
• 7.3. Error estimation
• 7.4. Conditioning and stability
• 7.5. Fixed point iteration
• 7.6. Richardson iteration and preconditioning
• 7.7. Iterative methods based on matrix splitting
• 7.8. GMRES and Arnoldi iteration
• 7.9. The conjugate gradient method
• 7.10. Low rank matrix approximations
• 7.11. Outlook : linear dynamical systems
• 7.12. Notes

• 8. Iterative methods for nonlinear equations
• 8.1. Introduction
• 8.2. Continuous and differentiable functions
• 8.3. Nonlinear scalar equations
• 8.4. Systems of nonlinear equations
• 8.5. Recurrence relations, fractals, and chaos
• 8.6. Outlook : nonlinear dynamical systems
• 8.7. Notes

• V. Approximation. 9. Function approximation
• 9.1. Introduction
• 9.2. Optimal polynomial approximation
• 9.3. Polynomial interpolation
• 9.4. Regression
• 9.5. Projection methods
• 9.6. Transforms
• 9.7. Outlook : finite element methods
• 9.8. Notes

• 10. Function approximation for multidimensional domains
• 10.1. Introduction
• 10.2. Approximation for multidimensional domains
• 10.3. Structured grids
• 10.4. Unstructured meshes
• 10.5. Mesh refinement and coarsening
• 10.6. Polynomial approximation on simplicial meshes
• 10.7. The reference element
• 10.8. Barycentric coordinates
• 10.9. Domain decomposition methods
• 10.10. Multigrid methods
• 10.11. Outlook : spline approximation
• 10.12. Notes

• VI. Integration. 11. Integration methods
• 11.1. Introduction
• 11.2. Newton-Cotes quadrature
• 11.3. Gauss quadrature
• 11.4. The fundamental theorem of calculus
• 11.5. Measures and the Lebesgue integral
• 11.6. Lp spaces
• 11.7. The divergence theorem
• 11.8. Outlook : integral operators and kernels
• 11.9. Notes

• 12. Stochastic methods
• 12.1. Introduction
• 12.2. A very brief review of probability theory
• 12.3. Stochastic processes
• 12.4. Random samples
• 12.5. Monte Carlo integration
• 12.6. Emergence and agent-based modeling
• 12.7. Outlook : model order reduction
• 12.8. Notes

• VII. Differential equations. 13. Scalar initial value problems
• 13.1. Introduction
• 13.2. The scalar initial value problem
• 13.3. Stability of the initial value problem
• 13.4. Stability of time stepping methods
• 13.5. A priori error analysis
• 13.6. Adjoint based a posteriori error analysis
• 13.7. Outlook : stochastic differential equations
• 13.8. Notes

• 14. Systems of initial value problems
• 14.1. Introduction
• 14.2. Systems of initial value problems
• 14.3. Harmonic oscillators
• 14.4. Energy analysis of harmonic oscillators
• 14.5. Particle models
• 14.6. Compartment models
• 14.7. Lumped parameter models and bond graphs
• 14.8. Adaptive time stepping algorithms
• 14.9. Parallel time stepping algorithms
• 14.10. Outlook : partial differential equations
• 14.11. Notes

• VIII. Optimization and learning. 15. Optimization
• 15.1. Introduction
• 15.2. Convex minimization
• 15.3. Gradient descent minimization
• 15.4. Multi-objective and global minimization
• 15.5. Constrained minimization
• 15.6. Lagrange multipliers
• 15.7. Design optimization
• 15.8. Outlook : optimal control
• 15.9. Notes

• 16. Learning from data
• 16.1. Introduction
• 16.2. Geometric methods
• 16.3. Statistical decision theory
• 16.4. Deep learning
• 16.5. Backpropagation
• 16.6. Generative adversarial networks
• 16.7. Graph neural networks
• 16.8. Outlook : data-driven dynamical systems
• 16.9. Notes

• IX. Epilogue.
• 17. Closing remarks

Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms with the aim of familiarizing the reader with the field's theoretical foundations and providing the practical skills to use and develop computational methods. Methods in Computational Science extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing, is centered around a set of fundamental algorithms presented in the form of pseudocode, presents theoretical material alongside several examples and exercises, and provides Python implementations of many key algorithms. Methods in Computational Science is a textbook for computer science and data science students at the advanced undergraduate and graduate level. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Because the text is self-contained, it can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science.
(source: Nielsen Book Data)

• Overview and motivation / Martin W. Hess, Marco Tezzele, Gianluigi Rozza
• Finite element-based reduced basis method in computational fluid dynamics / Federico Pichi, Maria Strazzullo, Francesco Ballarin, Gianluigi Rozza
• Certified Smagorinsky reduced basis turbulence model / Enrique Delgado Ávila, Francesco Ballarin, Gianluigi Rozza
• Finite element-based reduced basis method for optimal flow control / Maria Strazzullo, Francesco Ballarin, Gianluigi Rozza
• Reduced basis approaches to bifurcating nonlinear parametrized partial differential equations / Federico Pichi, Francesco Ballarin, Gianluigi Rozza
• Reduced basis stabilization for convection-dominated problems / Enrique Delgado Ávila, Francesco Ballarin, Gianluigi Rozza
• Finite volume-based reduced order models for laminar flows / Matteo Zancanaro, Saddam Hijazi, Umberto Morelli, Giovanni Stabile, Gianluigi Rozza
• Finite volume-based reduced order models for turbulent flows / Matteo Zancanaro, Saddam Hijazi, Michele Girfoglio, Andrea Mola, Giovanni Stabile, Gianluigi Rozza
• Nonintrusive data-driven reduced order models in computational fluid dynamics / Marco Tezzele, Nicola Demo, Giovanni Stabile, Gianluigi Rozza
• Spectral element method-based model order reduction / Martin W. Hess, Gianluigi Rozza
• Discontinuous Galerkin-based reduced order models / Andrea Lario, Francesco Romor, Gianluigi Rozza
• Weighted reduced order methods for uncertainty quantification / Davide Torlo, Maria Strazzullo, Francesco Ballarin, Gianluigi Rozza
• Reduced basis, embedded methods, and parametrized level-set geometry / Efthymios N. Karatzas, Giovanni Stabile, Francesco Ballarin, Gianluigi Rozza
• Reduced order methods for fluid-structure interaction problems / Monica Nonino, Francesco Ballarin, Gianluigi Rozza
• Reduced order models for bifurcating phenomena in fluid-structure interaction problems / Moaad Khamlich, Federico Pichi, Gianluigi Rozza
• Reduction in parameter space / Marco Tezzele, Francesco Romor, Gianluigi Rozza
• Geometrical parametrization and morphing techniques with applications / Andrea Mola, Nicola Demo, Marco Tezzele, Gianluigi Rozza
• Reduced order methods for hemodynamics applications / Zakia Zainib, Pierfrancesco Siena, Michele Girfoglio, Martin W. Hess, Francesco Ballarin, Gianluigi Rozza
• Scientific software development and packages for reduced order models in computational fluid dynamics / Nicola Demo, Marco Tezzele, Giovanni Stabile, Gianluigi Rozza
• A deep learning approach to improving reduced order models / Laura Meneghetti, Nirav Shah, Michele Girfoglio, Nicola Demo, Marco Tezzele, Andrea Lario, Giovanni Stabile, Gianluigi Rozza

Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their optimization and includes recent developments in advanced topics such as turbulence, stability of flows, inverse problems, optimization, and flow control, as well as applications

• A first look at screening using R
• Variance-based sensitivity measures
• Spectral and metamodel-based estimation
• Variance-based sensitivity measures with dependent inputs
• Beyond variance-based indices
• A case study in R : COVID-19 epidemic model

This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their usage and usefulness in practice. Basics and Trends in Sensitivity Analysis: Theory and Practice in R covers a lot of material, including theoretical aspects of Sobol' indices as well as sampling-based formulas, spectral methods, and metamodel-based approaches for estimation purposes; screening techniques devoted to identifying influential and noninfluential inputs; variance-based measures when model inputs are statistically dependent (and several other approaches that go beyond variance-based sensitivity measures); and a case study in R related to a COVID-19 epidemic model where the full workflow of sensitivity analysis combining several techniques is presented. This book is intended for engineers, researchers, and undergraduate students who use complex numerical models and have an interest in sensitivity analysis techniques and is appropriate for anyone with a solid mathematical background in basic statistical and probability theories who develops and uses numerical models in all scientific and engineering domains.
(source: Nielsen Book Data)

One of the physics goals for ITER is to achieve high fusion power PDT at a high gain QDT. This goal is important for studying the physics of reactor-relevant burning plasmas. Simulations of plasma performance in ITER can help achieve this goal by aiding in the design of systems such as diagnostics and in planning ITER plasma regimes. Simulations can indicate areas where further research in theory and experiments is needed. To have credible simulations integrated modeling is necessary since plasma profiles and applied heating, torque, and current drive are strongly coupled.

Newcomb's Lagrangian for ideal MHD in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.

The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles.

Recent H-mode experiments on Alcator C-Mod [I.H. Hutchinson, et al., Phys. Plasmas 1 (1994) 1511] which exhibit an internal transport barrier (ITB), have been examined with flux tube geometry gyrokinetic simulations, using the massively parallel code GS2 [M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comput. Phys. Commun. 88 (1995) 128]. The simulations support the picture of ion/electron temperature gradient (ITG/ETG) microturbulence driving high xi/ xe and that suppressed ITG causes reduced particle transport and improved ci on C-Mod. Nonlinear calculations for C-Mod confirm initial linear simulations, which predicted ITG stability in the barrier region just before ITB formation, without invoking E x B shear suppression of turbulence. Nonlinear fluxes are compared to experiment, which both show low heat transport in the ITB and higher transport within and outside of the barrier region.

We have developed a threaded parallel data streaming approach using Globus to transfer multi-terabyte simulation data from a remote supercomputer to the scientist's home analysis/visualization cluster, as the simulation executes, with negligible overhead. Data transfer experiments show that this concurrent data transfer approach is more favorable compared with writing to local disk and then transferring this data to be post-processed. The present approach is conducive to using the grid to pipeline the simulation with post-processing and visualization. We have applied this method to the Gyrokinetic Toroidal Code (GTC), a 3-dimensional particle-in-cell code used to study microturbulence in magnetic confinement fusion from first principles plasma theory.

Implicit algorithms are essential for predicting the slow growth and saturation of global instabilities in today’s magnetically confined fusion plasma experiments. Present day algorithms for obtaining implicit solutions to the magnetohydrodynamic (MHD) equations for highly magnetized plasma have their roots in algorithms used in the 1960s and 1970s. However, today’s computers and modern linear and non‐linear solver techniques make practical much more comprehensive implicit algorithms than were previously possible. Combining these advanced implicit algorithms with highly accurate spatial representations of the vector fields describing the plasma flow and magnetic fields and with improved methods of calculating anisotropic thermal conduction now makes possible simulations of fusion experiments using realistic values of plasma parameters and actual configuration geometry.

Scientific simulation, which provides a natural bridge between theory and experiment, is an essential tool for understanding complex plasma behavior. Recent advances in simulations of magnetically-confined plasmas are reviewed in this paper with illustrative examples chosen from associated research areas such as microturbulence, magnetohydrodynamics, and other topics. Progress has been stimulated in particular by the exponential growth of computer speed along with significant improvements in computer technology.