Introduction to Numerical Simulation (SMA 5211)

Calendar

LEC #	TOPICS
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