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



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

 








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