Cover
Half-title
Title
Copyright
Dedication
Contents
Preface
Acknowledgments
1 Introduction
1.1 Historical and modern role of modeling and simulation
1.1.1 Historical role of modeling and simulation
1.1.2 Changing role of scientific computing in engineering
1.1.2.1 Changing role of scientific computing in design, performance and safety of engineering systems
1.1.2.2 Interaction of scientific computing and experimental investigations
1.1.3 Changing role of scientific computing in various fields of science
1.2 Credibility of scientific computing
1.2.1 Computer speed and maturity of scientific computing
1.2.2 Perspectives on credibility of scientific computing
1.2.3 How is credibility built in scientific computing?
1.2.3.1 Quality of the analysts conducting the scientific computing
1.2.3.2 Quality of the physics modeling
1.2.3.3 Verification and validation activities
1.2.3.4 Uncertainty quantification and sensitivity analyses
1.3 Outline and use of the book
1.3.1 Structure of the book
1.3.2 Use of the book in undergraduate and graduate courses
1.3.3 Use of the book by professionals
1.4 References
Part I Fundamental concepts
2 Fundamental concepts and terminology
2.1 Development of concepts and terminology
2.1.1 Early efforts of the operations research community
2.1.2 IEEE and related communities
2.1.3 US Department of Defense community
2.1.4 AIAA and ASME communities
2.1.4.1 AIAA Guide
2.1.4.2 ASME Guide
2.1.5 Hydrology community
2.2 Primary terms and concepts
2.2.1 Code verification
2.2.2 Solution verification
2.2.3 Model validation
2.2.4 Predictive capability
2.2.5 Calibration
2.2.6 Certification and accreditation
2.3 Types and sources of uncertainties
2.3.1 Aleatory uncertainty
2.3.2 Epistemic uncertainty
2.3.2.1 Recognized uncertainty
2.3.2.2 Blind Uncertainty
2.4 Error in a quantity
2.5 Integration of verification, validation, and prediction
2.5.1 Specification of the application of interest
2.5.2 Planning and prioritization of activities
2.5.3 Code verification and software quality assurance activities
2.5.4 Design and execution of validation experiments
2.5.5 Computation of the system response quantities and solution verification
2.5.6 Computation of validation metric results
2.5.7 Prediction and uncertainty estimation for the application of interest
2.5.8 Assessment of model adequacy
2.5.9 Documentation of M&S activities
2.6 References
3 Modeling and computational simulation
3.1 Fundamentals of system specifications
3.1.1 Systems and surroundings
Example 1: Orbiting spacecraft
Example 2: Beam deflection
Example 3: Electronic circuit
3.1.2 Environments and scenarios
3.2 Fundamentals of models and simulations
3.2.1 Goals of scientific computing
3.2.2 Models and simulations
3.2.3 Importance of nondeterministic simulations
3.2.4 Analysis of nondeterministic systems
3.2.5 Example problem: mechanical oscillation
3.2.5.1 Aleatory uncertainty
3.2.5.2 Epistemic uncertainty
3.3 Risk and failure
3.4 Phases of computational simulation
3.4.1 Conceptual modeling phase
3.4.2 Mathematical modeling phase
3.4.3 Discretization and algorithm selection phase
3.4.4 Computer programming phase
3.4.5 Numerical solution phase
3.4.6 Solution representation phase
3.5 Example problem: missile flight dynamics
3.5.1 Conceptual modeling phase
3.5.2 Mathematical modeling phase
3.5.3 Discretization and algorithm selection phase
3.5.4 Computer programming phase
3.5.5 Numerical solution phase
3.5.6 Solution representation phase
3.6 References
Part II Code verification
4 Software engineering
4.1 Software development
4.1.1 Software process models
4.1.2 Architectural design
4.1.3 Programming languages
4.1.4 Agile programming
4.1.5 Software reuse
4.1.6 Refactoring
4.2 Version control
4.3 Software verification and validation
4.3.1 Definitions
4.3.2 Static analysis
4.3.2.1 Software inspection
4.3.2.2 Compiling the code
4.3.2.3 Automatic static analyzers
4.3.3 Dynamic testing
4.3.3.1 Defect testing
Unit testing
Component testing
System testing
4.3.3.2 Regression testing
4.3.3.3 Software validation testing
4.3.4 Test harness and test suites
4.3.5 Code coverage
4.3.6 Formal methods
4.4 Software quality and reliability
4.4.1 Reliability metrics
4.4.1.1 Defect density analysis
4.4.1.2 Complexity analysis
Lines of source code
NPATH metric
Cyclomatic complexity
Depth of conditional nesting
Depth of inheritance tree
4.5 Case study in reliability: the T experiments
4.6 Software engineering for large software projects
4.6.1 Software requirements
4.6.1.1 Types of software requirements
4.6.1.2 Requirements engineering process
4.6.1.3 Requirements management
4.6.2 Software management
4.6.2.1 Project management
4.6.2.2 Cost estimation
4.6.2.3 Configuration management
4.6.2.4 Quality management
4.6.2.5 Process improvement
4.7 References
5 Code verification
5.1 Code verification criteria
5.1.1 Simple tests
5.1.1.1 Symmetry tests
5.1.1.2 Conservation tests
5.1.1.3 Galilean invariance tests
5.1.2 Code-to-code comparisons
5.1.3 Discretization error evaluation
5.1.4 Convergence tests
5.1.5 Order-of-accuracy tests
5.2 Definitions
5.2.1 Truncation error
5.2.1.1 Example: truncation error analysis
5.2.1.2 Generalized truncation error expression (GTEE)
5.2.2 Discretization error
5.2.3 Consistency
5.2.4 Stability
5.2.5 Convergence
5.3 Order of accuracy
5.3.1 Formal order of accuracy
5.3.2 Observed order of accuracy
5.3.2.1 Asymptotic range
5.3.2.2 Effects of iterative and round-off error
5.4 Systematic mesh refinement
5.4.1 Uniform mesh refinement
5.4.2 Consistent mesh refinement
5.4.3 Mesh transformations
5.4.4 Mesh topology issues
5.5 Order verification procedures
5.5.1 Spatial discretization
1 Define mathematical model
2 Choose numerical algorithm
3 Establish formal order of accuracy
4 Obtain exact solution to mathematical model
5 Obtain numerical solutions on at least four meshes
6 Compute observed order of accuracy
7 Fix test implementation
8 Debug the code
9 Document results
5.5.2 Temporal discretization
5.5.3 Spatial and temporal discretization
5.5.3.1 Separate order analysis
5.5.3.2 Combined order analysis
5.5.4 Recommendations for debugging
5.5.5 Limitations of order verification
5.5.6 Alternative approaches for order verification
5.5.6.1 Residual method
5.5.6.2 Statistical method
5.5.6.3 Downscaling method
5.5.6.4 Summary of order verification approaches
5.6 Responsibility for code verification
5.7 References
6 Exact solutions
6.1 Introduction to differential equations
6.2 Traditional exact solutions
6.2.1 Procedures
6.2.1.1 Separation of variables
6.2.1.2 Transformations
6.2.1.3 Method of characteristics
6.2.1.4 Advanced approaches
6.2.2 Example exact solution: 1-D unsteady heat conduction
6.2.3 Example with order verification: steady Burgersโ equation
6.2.4 Example with order verification: linear elasticity
6.3 Method of manufactured solutions (MMS)
6.3.1 Procedure
6.3.1.1 Manufactured solution guidelines for code verification
6.3.1.2 Boundary and initial conditions
6.3.2 Benefits of MMS for code verification
6.3.3 Limitations of MMS for code verification
6.3.4 Examples of MMS with order verification
6.3.4.1 2-D steady heat conduction
6.3.4.2 2D Steady Euler equations
6.4 Physically realistic manufactured solutions
6.4.1 Theory-based solutions
6.4.2 Method of nearby problems (MNP)
6.4.2.1 Procedure
6.4.2.2 Example exact solution: 2-D steady NavierโStokes equations
6.5 Approximate solution methods
6.5.1 Infinite series solutions
6.5.2 Reduction to ordinary differential equations
6.5.3 Benchmark numerical solutions
6.5.4 Example series solution: 2-D steady heat conduction
6.5.5 Example benchmark convergence test: 2-D hypersonic flow
6.6 References
Part III Solution verification
7 Solution verification
7.1 Elements of solution verification
7.2 Round-off error
7.2.1 Floating point representation
7.2.2 Specifying precision in a code
7.2.2.1 C/C++ programming languages
7.2.2.2 Fortran 95/2003 programming languages
7.2.2.3 MATLABยฎ Programming Language
7.2.3 Practical guidelines for estimating round-off error
7.3 Statistical sampling error
7.3.1 Estimation of statistical sampling error
7.4 Iterative error
7.4.1 Iterative methods
7.4.1.1 Equations with a single unknown
7.4.1.2 Systems of equations
Direct solution methods
Stationary iterative methods
Krylov subspace methods
Hybrid methods
Examples of iterative methods in scientific computing
7.4.2 Iterative convergence
7.4.2.1 Types of iterative convergence
Monotone convergence
Oscillatory convergence
General convergence
7.4.2.2 Iterative convergence criteria
Difference between iterates
Iterative residuals
7.4.3 Iterative error estimation
7.4.3.1 Machine zero method
7.4.3.2 Local convergence rate
Monotone iterative convergence
Oscillatory iterative convergence
7.4.4 Relation between iterative residuals and iterative error
7.4.5 Practical approach for estimating iterative error
7.5 Numerical error versus numerical uncertainty
7.6 References
8 Discretization error
8.1 Elements of the discretization process
8.1.1 Discretization of the mathematical model
8.1.1.1 The finite difference method
8.1.1.2 The finite volume method
8.1.1.3 The finite element method
8.1.2 Discretization of the domain
8.1.2.1 Structured meshes
8.1.2.2 Unstructured meshes
8.1.2.3 Cartesian meshes
8.1.2.4 Mesh-free methods
8.2 Approaches for estimating discretization error
8.2.1 Type I: Higher-order estimates
8.2.1.1 Mesh refinement methods
8.2.1.2 Order refinement methods
8.2.1.3 Finite element recovery methods
8.2.2 Type II: Residual-based methods
8.2.2.1 Error transport equations
Continuous discretization error transport equation
Discrete discretization error transport equation
Approximating the truncation error
System response quantities
8.2.2.2 Finite element residual methods
Explicit residual methods
Implicit residual methods
8.2.2.3 Adjoint methods for system response quantities
Adjoint methods in the finite element method
Adjoint methods in the finite volume method
8.3 Richardson extrapolation
8.3.1 Standard Richardson extrapolation
8.3.2 Generalized Richardson extrapolation
8.3.3 Assumptions
8.3.3.1 Asymptotic range
8.3.3.2 Uniform mesh spacing
8.3.3.3 Systematic mesh refinement
8.3.3.4 Smooth solutions
8.3.3.5 Other numerical errors sources
8.3.4 Extensions
8.3.4.1 Completed Richardson extrapolation in space
8.3.4.2 Completed Richardson extrapolation in space and time
8.3.4.3 Least squares extrapolation
8.3.5 Discretization error estimation
8.3.5.1 Example: Richardson extrapolation-based error estimation
8.3.6 Advantages and disadvantages
8.4 Reliability of discretization error estimators
8.4.1 Asymptotic range
8.4.2 Observed order of accuracy
8.4.2.1 Constant grid refinement factor
8.4.2.2 Non-constant grid refinement factor
8.4.2.3 Application to system response quantities
8.4.2.4 Application to local quantities
8.5 Discretization error and uncertainty
8.6 Roacheโs grid convergence index (GCI)
8.6.1 Definition
8.6.2 Implementation
8.6.3 Variants of the GCI
8.6.3.1 Least squares method
8.6.3.2 Global averaging method
8.6.3.3 Factor of safety method
8.6.4 Reliability of the GCI
8.7 Mesh refinement issues
8.7.1 Measuring systematic mesh refinement
8.7.2 Grid refinement factor
8.7.3 Fractional uniform refinement
8.7.4 Refinement vs. coarsening
8.7.5 Unidirectional refinement
8.8 Open research issues
8.8.1 Singularities and discontinuities
8.8.2 Oscillatory convergence with mesh refinement
8.8.3 Multi-scale models
8.8.4 Coarse grid error estimators
8.9 References
9 Solution adaptation
9.1 Factors affecting the discretization error
9.1.1 Relating discretization error to truncation error
9.1.2 1-D truncation error analysis on uniform meshes
9.1.3 1-D truncation error analysis on nonuniform meshes
9.1.4 Isotropic versus anisotropic mesh adaptation
9.2 Adaptation criteria
9.2.1 Solution features
9.2.2 Discretization error
9.2.3 Recovery methods
9.2.4 Truncation errorresiduals
9.2.4.1 General truncation errorresidual-based methods
9.2.4.2 Finite element residual-based methods
9.2.5 Adjoint-based adaptation
9.3 Adaptation approaches
9.3.1 Adaptive remeshing
9.3.2 Mesh adaptation
9.3.2.1 Local mesh refinementcoarsening (h-adaptation)
9.3.2.2 Mesh movement (r-adaptation)
9.3.2.3 Mixed mesh refinement (r- and h-adaptation)
9.3.3 Order refinement (p-adaptation)
9.4 Comparison of methods for driving mesh adaptation
9.4.1 Mathematical model
9.4.2 Exact solution
9.4.3 Discretization approach
9.4.4 Results
9.5 References
Part IV Model validation and prediction
10 Model validation fundamentals
10.1 Philosophy of validation experiments
10.1.1 Validation experiments vs. traditional experiments
10.1.2 Goals and strategy of validation
10.1.2.1 Scientific validation
10.1.2.2 Project-oriented validation
10.1.3 Sources of error in experiments and simulations
10.1.4 Validation using data from traditional experiments
10.2 Validation experiment hierarchy
10.2.1 Characteristics of the complete system tier
10.2.2 Characteristics of the subsystem tier
10.2.3 Characteristics of the benchmark tier
10.2.4 Characteristics of the unit problem tier
10.2.5 Construction of a validation hierarchy
10.3 Example problem: hypersonic cruise missile
10.3.1 System tier
10.3.2 Subsystem tier
10.3.3 Benchmark tier
10.3.4 Unit-problem tier
10.3.5 Validation pyramid
10.3.6 Final comments
10.4 Conceptual, technical, and practical difficulties of validation
10.4.1 Conceptual difficulties
10.4.2 Technical and practical difficulties
10.5 References
11 Design and execution of validation experiments
11.1 Guidelines for validation experiments
11.1.1 Joint effort between analysts and experimentalists
11.1.2 Measurement of all needed input data
11.1.3 Synergism between computation and experiment
11.1.4 Independence and dependence between computation and experiment
11.1.5 Hierarchy of experimental measurements
11.1.6 Estimation of experimental uncertainty
11.2 Validation experiment example: Joint Computational/Experimental Aerodynamics Program (JCEAP)
11.2.1 Basic goals and description of JCEAP
11.2.2 Joint planning and design of the experiment
11.2.2.1 Wind tunnel conditions
11.2.2.2 Model geometry
11.2.2.3 Model fabrication and instrumentation
11.2.3 Characterize boundary conditions and system data
11.2.4 Synergism between computation and experiment
11.2.5 Independence and dependence between computation and experiment
11.2.6 Hierarchy of experimental measurements
11.3 Example of estimation of experimental measurement uncertainties in JCEAP
11.3.1 Random and systematic uncertainties
11.3.2 Example of DOE procedure for JCEAP force and moment experiment
11.3.2.1 DOE principles
11.3.2.2 DOE analysis and results
11.3.3 Example of DOE procedure for JCEAP surface pressure experiment
11.3.3.1 DOE principles
11.3.3.2 DOE analysis and results
11.4 Example of further computationalโexperimental synergism in JCEAP
11.4.1 Assessment of computational submodels
11.4.1.1 Transport property submodels
11.4.1.2 Equation of state submodel
11.4.1.3 Thermodynamic submodel
11.4.1.4 Continuum flow assumption
11.4.1.5 Outflow boundary condition assumption
11.4.1.6 Axisymmetric flow assumption
11.4.1.7 Re-evaluation of the experimental data
11.4.2 Simulation of the flowfield nonuniformities
11.4.2.1 Use of the flowfield calibration data
11.4.2.2 Simulation using the nonuniform flowfield
11.4.3 Lessons learned for validation experiments
11.5 References
12 Model accuracy assessment
12.1 Elements of model accuracy assessment
12.1.1 Methods of comparing simulations and experiments
12.1.2 Uncertainty and error in model accuracy assessment
12.1.3 Relationship between model accuracy assessment, calibration, and prediction
12.2 Approaches to parameter estimation and validation metrics
12.2.1 Parameter estimation
12.2.2 Hypothesis testing
12.2.3 Bayesian updating
12.2.4 Comparison of mean values
12.2.5 Comparison of probability distributions and p-boxes
12.3 Recommended features for validation metrics
12.3.1 Influence of numerical solution error
12.3.2 Assessment of the physics-modeling assumptions
12.3.3 Inclusion of experimental data post-processing
12.3.4 Inclusion of experimental uncertainty estimation
12.3.5 Inclusion of aleatory and epistemic uncertainties
12.3.6 Exclusion of any type of adequacy implication
12.3.7 Properties of a mathematical metric
12.4 Introduction to the approach for comparing means
12.4.1 Perspectives of the present approach
12.4.2 Development of the fundamental equations
12.4.3 Construction of the validation metric for one condition
12.4.4 Example problem: thermal decomposition of foam
12.5 Comparison of means using interpolation of experimental data
12.5.1 Construction of the validation metric over the range of the data
12.5.2 Global metrics
12.5.3 Example problem: turbulent buoyant plume
12.6 Comparison of means requiring linear regression of the experimental data
12.6.1 Construction of the validation metric over the range of the data
12.6.2 Global metrics
12.6.3 Example problem: thermal decomposition of foam
12.7 Comparison of means requiring nonlinear regression of the experimental data
12.7.1 Construction of the nonlinear regression equation
12.7.2 Computation of simultaneous confidence intervals for the metric
12.7.3 Global metrics
12.7.4 Example problem: compressible turbulent mixing
12.7.4.1 Problem description
12.7.4.2 Experimental data
12.7.4.3 Mathematical model
12.7.4.4 Validation metric results
12.7.5 Observations on the present approach
12.8 Validation metric for comparing p-boxes
12.8.1 Traditional methods for comparing distributions
12.8.2 Method for comparing p-boxes
12.8.2.1 Discussion of p-boxes
12.8.2.2 Validation metric for p-boxes
12.8.3 Pooling incomparable CDFs
12.8.3.1 u-pooling
12.8.3.2 Statistical significance of a metric
12.8.4 Inconsistency between experimental and simulation CDFs
12.8.5 Dealing with epistemic uncertainty in the comparisons
12.8.5.1 Epistemic uncertainty in the prediction and measurements
12.8.5.2 Epistemic and aleatory uncertainty in the metric
12.9 References
13 Predictive capability
13.1 Step 1: identify all relevant sources of uncertainty
13.1.1 Model inputs
13.1.2 Model uncertainty
13.1.3 Example problem: heat transfer through a plate
13.1.4 Final comments on step 1
13.2 Step 2: characterize each source of uncertainty
13.2.1 Model input uncertainty
13.2.2 Model uncertainty
13.2.3 Example problem: heat transfer through a solid
13.2.3.1 Model input uncertainty
13.2.3.2 Model uncertainty
13.3 Step 3: estimate numerical solution error
13.3.1 Iterative error
13.3.1.1 Iterative methods
13.3.1.2 Practical difficulties
13.3.2 Discretization error
13.3.2.1 Temporal discretization error
13.3.2.2 Finite-element-based methods for mesh convergence
13.3.2.3 Richardson extrapolation error estimators for mesh convergence
13.3.2.4 Practical difficulties
13.3.3 Estimate of total numerical solution error
13.3.4 Example problem: heat transfer through a solid
13.3.4.1 Iterative and discretization error estimation
13.3.4.2 Iterative and discretization error results
13.4 Step 4: estimate output uncertainty
13.4.1 Monte Carlo sampling of input uncertainties
13.4.1.1 Monte Carlo sampling for aleatory uncertainties
13.4.1.2 Monte Carlo sampling for combined aleatory and epistemic uncertainties
13.4.2 Combination of input, model, and numerical uncertainty
13.4.2.1 Combination of input and model uncertainty
13.4.2.2 Estimation of model uncertainty using alternative plausible models
13.4.2.3 Inclusion of numerical solution uncertainty
13.4.3 Example problem: heat transfer through a solid
13.4.3.1 Input uncertainties
13.4.3.2 Combination of input, model, and numerical uncertainties
13.5 Step 5: conduct model updating
13.5.1 Types of model parameter
13.5.2 Sources of new information
13.5.3 Approaches to parameter updating
13.5.4 Parameter updating, validation, and predictive uncertainty
13.5.4.1 Parameter updating
13.5.4.2 Validation after parameter updating
13.6 Step 6: conduct sensitivity analysis
13.6.1 Local sensitivity analysis
13.6.2 Global sensitivity analysis
13.7 Example problem: thermal heating of a safety component
13.7.1 Step 1: identify all relevant sources of uncertainty
13.7.2 Step 2: characterize each source of uncertainty
13.7.2.1 Model input uncertainty
13.7.2.2 Model uncertainty
Possible temperature dependence of material properties
Characterization of model uncertainty
13.7.3 Step 4: estimate output uncertainty
13.7.3.1 General discussion of combining input and model uncertainty
13.7.3.2 Combining input and model uncertainty for the thermal heating problem
13.7.3.3 Predicted probabilities for the regulatory condition
13.8 Bayesian approach as opposed to PBA
13.9 References
Part V Planning, management, and implementation issues
14 Planning and prioritization in modeling and simulation
14.1 Methodology for planning and prioritization
14.1.1 Planning for a modeling and simulation project
14.1.2 Value systems for prioritization
14.2 Phenomena identification and ranking table (PIRT)
14.2.1 Steps in the PIRT process for modeling and simulation
14.2.1.1 Assembly of the team
14.2.1.2 Definition of the objectives of the PIRT process
14.2.1.3 Specification of environments and scenarios
14.2.1.4 Identification of plausible physical phenomena
14.2.1.5 Construction of the PIRT
14.3 Gap analysis process
14.3.1 Construct the gap analysis table
14.3.2 Documenting the PIRT and gap analysis processes
14.3.3 Updating the PIRT and gap analysis
14.4 Planning and prioritization with commercial codes
14.5 Example problem: aircraft fire spread during crash landing
14.6 References
15 Maturity assessment of modeling and simulation
15.1 Survey of maturity assessment procedures
15.2 Predictive capability maturity model
15.2.1 Structure of the PCMM
15.2.1.1 Representation and geometric fidelity
15.2.1.2 Physics and material model fidelity
15.2.1.3 Maturity assessment
15.2.2 Purpose and uses of the PCMM
15.2.3 Characteristics of PCMM elements
15.2.3.1 Representation and geometric fidelity
15.2.3.2 Physics and material model fidelity
15.2.3.3 Code verification
15.2.3.4 Solution verification
15.2.3.5 Model validation
15.2.3.6 Uncertainty quantification and sensitivity analysis
15.3 Additional uses of the PCMM
15.3.1 Requirements for modeling and simulation maturity
15.3.2 Aggregation of PCMM scores
15.3.3 Use of the PCMM in risk-informed decision making
15.4 References
16 Development and responsibilities for verification, validation and uncertainty quantification
16.1 Needed technical developments
16.2 Staff responsibilities
16.2.1 Software quality assurance and code verification
16.2.1.1 Who should conduct SQA and code verification?
16.2.1.2 Who should require SQA and code verification?
16.2.2 Solution verification
16.2.2.1 Who should conduct solution verification?
16.2.2.2 Who should require solution verification?
16.2.3 Validation
16.2.3.1 Who should conduct validation?
16.2.3.2 Who should require validation?
16.2.4 Nondeterministic predictions
16.2.4.1 Who should conduct nondeterministic predictions?
16.2.4.2 Who should require nondeterministic predictions?
16.3 Management actions and responsibilities
16.3.1 Implementation issues
16.3.2 Personnel training
16.3.3 Incorporation into business goals
16.3.3.1 Intrinsic information quality
16.3.3.2 Contextual information quality
16.3.3.3 Representational information quality
16.3.4 Organizational structures
16.4 Development of databases
16.4.1 Existing databases
16.4.2 Recent activities
16.4.3 Implementation issues of Databases
16.5 Development of standards
16.6 References
Appendix: Programming practices
Recommended programming practices
Use strongly-typed programming languages
Use safe programming language subsets
Use static analyzers
Use long, descriptive identifiers
Write self-commenting code
Use private data
Use exception handling
Use indentation for readability
Use module procedures (Fortran only)
Error-prone programming constructs
Implicit type definitions
Mixed-mode arithmetic
Duplicate code
Equality checks for floating point numbers
Recursion
Pointers
Aliasing
Inheritance
GOTO statements
Parallelism
References
Index