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