Numerical Simulation of Dynamic Systems

Beamer Presentations

  1. Tuesday, February 26, 2013 Introduction, Scope, Definitions (Friday, February 22, 2013)
  2. Tuesday, February 26, 2013 Principles of Numerical Integration: Forward Euler, Backward Euler, Truncation Error, Roundoff Error, Accumulation Error, Order of Approximation Accuracy, Numerical Stability Domain (Friday, February 22, 2013)
  3. Tuesday, March 5, 2013 Single-step Integration Methods I: Explicit Runge-Kutta Algorithms (Monday, March 4, 2013)
  4. Tuesday, March 5, 2013 Single-step Integration Methods II: Stiff Systems, Richardson Extrapolation, Marginally Stable Systems, Backinterpolation Techniques, Tustin's Method, Padé Approximations, Numerical Stability Properties (Wednesday, March 6, 2013)
  5. Tuesday, March 12, 2013 Single-step Integration Methods III: Accuracy Domain, Damping Plot, Damping Order Star, Frequency Plot, Frequency Order Star, Asymptotic Region, Step-size Control (Monday, March 11, 2013)
  6. Tuesday, March 12, 2013 Multi-step Integration Methods I: Newton-Gregory Polynomials, Adams-Bashforth Methods, Adams-Moulton Methods, Backward Difference Formulae, Nyström Methods, Milne Methods (Monday, March 11, 2013)
  7. Tuesday, March 19, 2013 Multi-step Integration Methods II: Searching for Stiffly-stable Methods, Performance Parameters, Error Coefficient, Asymptotic Region, Stable BDF Algorithms of Orders 7..9 (Wednesday, March 13, 2013)
  8. Tuesday, March 19, 2013 Multi-step Integration Methods III: Symbolic Coefficients, Newton iteration, Order Control, Step-size Control, Nordsieck Vector, Startup Problem, Dense Output (Wednesday, March 13, 2013)
  9. Tuesday, March 26, 2013 Second Derivative Systems I: Conservative Mechanical Systems, Velocity-free Models, Godunov's explicit 3rd-Order Algorithm, Linear Velocity Models (Sunday, March 24, 2013)
  10. Tuesday, March 26, 2013 Second Derivative Systems II: Non-linear Velocity Models, 3rd-Order Godunov/Adams Algorithm, Classes of Explicit and Implicit Godunov Algorithms, 4th-Order Godunov/Adams Algorithm, Newmark Algorithms (Sunday, March 24, 2013)
  11. Tuesday, April 9, 2013 Partial Differential Equations I: Method of Lines, Differentiation in Space, Boundary Conditions, Classification of PDEs, Parabolic PDEs, Consistency Error, Richardson Extrapolation, Order and Grid-width Control, Startup Problem (Thursday, April 4, 2013)
  12. Tuesday, April 9, 2013 Partial Differential Equations II: Hyperbolic PDEs, Consistency Error, Simulation of Hyperbolic PDEs, Shock Waves, Upwind Discretization, Grid-width Control (Thursday, April 4, 2013)
  13. Tuesday, April 9, 2013 Partial Differential Equations III: PDEs in Multiple Space Dimensions, Elliptic PDEs, Invariant Embedding, Finite Element Approximations, Simulation of Elliptic PDEs (Thursday, April 4, 2013)
  14. Tuesday, April 16, 2013 Differential Algebraic Equations: Causalization of Equations, Structure Incidence Matrix, Structure Digraph, Horizontal Sorting, Vertical Sorting (Wednesday, April 10, 2013)
  15. Tuesday, April 16, 2013 Differential Algebraic Equations II: Algebraic Loops, Tearing Algorithm, Relaxation Algorithm (Wednesday, April 10, 2013)
  16. Tuesday, April 23, 2013 Differential Algebraic Equations III: Structural Singularities, Index Reduction, Pantelides Algorithm (Wednesday, April 17, 2013)
  17. Tuesday, April 23, 2013 Differential Algebraic Equations IV: Solvability, State Selection, Dynamic Singularities (Wednesday, April 17, 2013)
  18. Tuesday, April 23, 2013 Differential Algebraic Equation Solvers: Simulation by Newton Iteration, DAE Solvers Based on BDF Algorithms, Higher Index Models, DAE Solvers Based on Adams Methods, Accuracy Properties (Wednesday, April 17, 2013)
  19. Tuesday, April 30, 2013 Differential Algebraic Equation Solvers II: DAE Solvers Based on Implicit Runge-Kutta Algorithms, Radau IIA, Lobatto IIIC, DASSL, Inline Integration (Wednesday, April 24, 2013)
  20. Tuesday, April 30, 2013 Differential Algebraic Equation Solvers III: Inlining IRK Algorithms, Stiffly-stable Step-size Control of IRK Algorithms, Inlining PDEs, Over-determined DAEs (Wednesday, April 24, 2013)
  21. Tuesday, May 7, 2013 Simulation of Discontinuous Systems: Abusing Step-size Control, Time Events, Sampled-data Systems, State Events, Zero-crossing Functions, Regula Falsi, Golden Section, Cubic Interpolation, Multiple Zero-crossings, Event Localization, Non-essential State Events (Thursday, May 2, 2013)
  22. Tuesday, May 7, 2013 Simulation of Discontinuous Systems II: Event Descriptions of Discontinuous Functions, Object-oriented Description of Discontinuities, Multi-valued Functions, Switch Equations, Ideal Diodes, Parameterized Curve Descriptions (Thursday, May 2, 2013)
  23. Tuesday, May 14, 2013 Simulation of Discontinuous Systems III: Variable Structure Models, Conditional Index Change, Leaky Diodes, Mixed-mode Integration, Mechanical Friction, State Transition Diagram, Deterministic Finite State Machine, Petri Nets, Normal Priority Petri Nets, Illegitimate Models (Thursday, May 9, 2013)
  24. Tuesday, May 14, 2013 Real-time Simulation: Synchronization With Real-time Clock, Race Against Time, Linearly Implicit Algorithms, Multi-rate Integration, Inline Integration, Mixed-mode Integration, Discontinuous Systems, Simulation Architecture, Overruns (Thursday, May 9, 2013)
  25. Tuesday, May 21, 2013 Discrete Event Simulation: Space Discretization, Discrete Event Systems, DEVS, Continuous-system Simulation in DEVS, DEVS Models of Quantized State Systems, PowerDEVS, Hysteretic Quantization Function, QSS Algorithm, DEVS Representation of a QSS, Simulation with QSS (Wednesday, May 15, 2013)
  26. Tuesday, May 21, 2013 Quantization-based Integration: Perturbation Analysis, Convergence Accuracy and Stability in QSS, QSS Simulation of Linear Time-invariant Systems, Choosing Quantum and Hysteresis Width, Cost vs. Precision in QSS, First-order Quantizer, Higher-order QSS Methods, Stability and Accuracy of QSS2, DAE Simulation with QSS Methods, Discontinuity Handling in QSS Methods, Time Events, State Events (Wednesday, May 15, 2013)
  27. Tuesday, May 28, 2013 Quantization-based Integration II: Logarithmic Quantization, QSS Methods and Stiff Systems, Backward QSS (BQSS) Method, Quantization Functions in BQSS, Stability and Error Bound of BQSS, Linearly Implicit QSS Methods (LIQSS), Stability and Error Bound in LIQSS, Higher-order LIQSS Methods, Marginally Stable Systems, Centered QSS (CQSS) Method, Delay Differential Equations (DDEs), QSS Methods for DDEs (DQSS), The Delay Algorithm, Theoretical Properties of DQSS, QSS Methods for Real-time Simulation (Sunday, May 26, 2013)

Versión reducida en Castellano (11 presentaciones de 50 minutos cada una)
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Last modified: May 26, 2013 -- © François Cellier