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Example Problems and Basic Equations (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, Luca Daniel, Shihhsien Kuo, and Karen Veroy.
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| 2 |
Equation Formulation Methods - Stamping Techniques, Nodal versus Node-Branch Form (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 3 |
Linear System Solution - Dense GE, Conditioning, Stability (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 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.
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| 5 |
Linear System Solution - Orthogonalization Methods, QR, Singular Matrices (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 6 |
QR and Krylov Iterative Methods. Brief Convergence Analysis (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 7 |
Krylov Methods (cont.) (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 8 |
Nonlinear System Solution - 1D Newton Methods, Convergence Analysis (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.
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| 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.
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| 10 |
Nonlinear System Solution - Damping, Optimization and Continuation Schemes (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.
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| 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.
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| 12 |
ODE Solution Methods - BE, FE, Trap Examples, Convergence (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.
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| 13 |
ODE Solution Methods - Multistep Methods and Stability, Runga-Kutta Methods (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 14 |
ODE Solution Methods - Stiffly Stable and Conservative Schemes (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 15 |
Time-Periodic Solution Methods - Finite-Difference and Shooting Methods (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 16 |
Time-Periodic Solution Methods - Matrix-Implicit Algorithms and Preconditioning (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 17 |
Molecular Dynamics - Basic Numerical Issues (PDF) Courtesy of Nicolas Hadjiconstantinou.
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| 18 |
Molecular Dynamics (cont.) (PDF) Courtesy of Nicolas Hadjiconstantinou.
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| 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.
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| 21 |
3-D Elliptic Problems - FFT and Multigrid Methods (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 22 |
3-D Elliptic Problems - Boundary-Element Approach (PDF) Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Xin Wang.
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| 23 |
3-D Elliptic Problems - FFT and Multipole Methods (PDF - 4.0 MB) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
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| 24 |
Model Order Reduction I |
| 25 |
Model Order Reduction II |
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