LEC # | TOPICS |
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1 | Example Problems and Basic Equations (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Luca Daniel, Shihhsien Kuo, and Karen Veroy.) |

2 | Equation Formulation Methods - Stamping Techniques, Nodal versus Node-Branch Form (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

3 | Linear System Solution - Dense GE, Conditioning, Stability (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

4 | Direct Methods for Sparse Linear Systems - Data Structures, Fill-in, Ordering, Graph Interpretations (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Luca Daniel, and Karen Veroy.) |

5 | Linear System Solution - Orthogonalization Methods, QR, Singular Matrices (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

6 | QR and Krylov Iterative Methods. Brief Convergence Analysis (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

7 | Krylov Methods (cont.) (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

8 | Nonlinear System Solution - 1D Newton Methods, Convergence Analysis (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.) |

9 | Nonlinear System Solution-Multi-D Newton, Forming Jacobian by Stamping Approach, Singularity (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.) |

10 | Nonlinear System Solution - Damping, Optimization and Continuation Schemes (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.) |

11 | Nonlinear System Solution - Matrix-Implicit Methods and Methods for Singular Problems (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, Jaime Peraire, and Andrew Lumsdaine.) |

12 | ODE Solution Methods - BE, FE, Trap Examples, Convergence (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.) |

13 | ODE Solution Methods - Multistep Methods and Stability, Runga-Kutta Methods (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

14 | ODE Solution Methods - Stiffly Stable and Conservative Schemes (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

15 | Time-Periodic Solution Methods - Finite-Difference and Shooting Methods (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

16 | Time-Periodic Solution Methods - Matrix-Implicit Algorithms and Preconditioning (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

17 | Molecular Dynamics - Basic Numerical Issues (PDF)(Courtesy of Nicolas Hadjiconstantinou.) |

18 | Molecular Dynamics (cont.) (PDF) (Courtesy of Nicolas Hadjiconstantinou.) |

19 | 3-D Elliptic Problems - F-D Methods, Error Estimation (PDF) (Courtesy of Jaime Peraire, Anthony Patera, Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Dimitrios Rovas.) |

20 | 3-D Elliptic Problems - Finite-Element and Spectral Methods (PDF) (Courtesy of Jaime Peraire.) |

21 | 3-D Elliptic Problems - FFT and Multigrid Methods (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

22 | 3-D Elliptic Problems - Boundary-Element Approach (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Xin Wang.) |

23 | 3-D Elliptic Problems - FFT and Multipole Methods (PDF - 4.0 MB) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.) |

24 | Model Order Reduction I |

25 | Model Order Reduction II |