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Introduction to Numerical Simulation (SMA 5211) >> Content Detail



Lecture Notes



Lecture Notes

LEC #TOPICS
1Example Problems and Basic Equations (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, Luca Daniel, Shihhsien Kuo, and Karen Veroy.
2Equation Formulation Methods - Stamping Techniques, Nodal versus Node-Branch Form (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
3Linear System Solution - Dense GE, Conditioning, Stability (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
4Direct Methods for Sparse Linear Systems - Data Structures, Fill-in, Ordering, Graph Interpretations (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, Luca Daniel, and Karen Veroy.
5Linear System Solution - Orthogonalization Methods, QR, Singular Matrices (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
6QR and Krylov Iterative Methods. Brief Convergence Analysis (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
7Krylov Methods (cont.) (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
8Nonlinear System Solution - 1D Newton Methods, Convergence Analysis (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.
9Nonlinear System Solution-Multi-D Newton, Forming Jacobian by Stamping Approach, Singularity (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.
10Nonlinear System Solution - Damping, Optimization and Continuation Schemes (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.
11Nonlinear System Solution - Matrix-Implicit Methods and Methods for Singular Problems (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, Jaime Peraire, and Andrew Lumsdaine.
12ODE Solution Methods - BE, FE, Trap Examples, Convergence (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.
13ODE Solution Methods - Multistep Methods and Stability, Runga-Kutta Methods (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
14ODE Solution Methods - Stiffly Stable and Conservative Schemes (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
15Time-Periodic Solution Methods - Finite-Difference and Shooting Methods (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
16Time-Periodic Solution Methods - Matrix-Implicit Algorithms and Preconditioning (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
17Molecular Dynamics - Basic Numerical Issues (PDFCourtesy of Nicolas Hadjiconstantinou.
18Molecular Dynamics (cont.) (PDFCourtesy of Nicolas Hadjiconstantinou.
193-D Elliptic Problems - F-D Methods, Error Estimation (PDF) Courtesy of Jaime Peraire, Anthony Patera, Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Dimitrios Rovas.
203-D Elliptic Problems - Finite-Element and Spectral Methods (PDFCourtesy of Jaime Peraire.
213-D Elliptic Problems - FFT and Multigrid Methods (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
223-D Elliptic Problems - Boundary-Element Approach (PDFCourtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Xin Wang.
233-D Elliptic Problems - FFT and Multipole Methods (PDF - 4.0 MB) Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.
24Model Order Reduction I
25Model Order Reduction II

 








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