| 1 |
Example Problems and Basic Equations |
| 2 |
Equation Formulation Methods - Stamping Techniques, Nodal versus Node-Branch Form |
| 3 |
Linear System Solution - Dense GE, Conditioning, Stability |
| 4 |
Direct Methods for Sparse Linear Systems - Data Structures, Fill-in, Ordering, Graph Interpretations |
| 5 |
Linear System Solution - Orthogonalization Methods, QR, Singular Matrices |
| 6 |
QR and Krylov Iterative Methods. Brief Convergence Analysis. |
| 7 |
Krylov Methods (cont.) |
| 8 |
Nonlinear System Solution - 1D Newton Methods, Convergence Analysis |
| 9 |
Nonlinear System Solution-Multi-D Newton, Forming Jacobian by Stamping Approach, Singularity |
| 10 |
Nonlinear System Solution - Damping, Optimization and Continuation Schemes |
| 11 |
Nonlinear System Solution - Matrix-Implicit Methods and Methods for Singular Problems |
| 12 |
ODE Solution Methods - BE, FE, Trap Examples, Convergence |
| 13 |
ODE Solution Methods - Multistep Methods and Stability, Runga-Kutta Methods |
| 14 |
ODE Solution Methods - Stiffly Stable and Conservative Schemes |
| 15 |
Time-Periodic Solution Methods - Finite-Difference and Shooting Methods |
| 16 |
Time-Periodic Solution Methods - Matrix-Implicit Algorithms and Preconditioning |
| 17 |
Molecular Dynamics - Basic Numerical Issues |
| 18 |
Molecular Dynamics (cont.) |
| 19 |
3-D Elliptic Problems - F-D Methods, Error Estimation |
| 20 |
3-D Elliptic Problems - Finite-Element and Spectral Methods |
| 21 |
3-D Elliptic Problems - FFT and Multigrid Methods |
| 22 |
3-D Elliptic Problems - Boundary-Element Approach |
| 23 |
3-D Elliptic Problems - FFT and Multipole Methods |
| 24 |
Model Order Reduction I |
| 25 |
Model Order Reduction II |
| 26 |
Class Choice |
