Introduction to Numerical Simulation (SMA 5211)

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