Lecture Notes

LEC # TOPICS
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