| 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 |
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