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Description
6.336J is an introduction to computational techniques for the simulation of a large variety of engineering and physical systems.
Applications are drawn from aerospace, mechanical, electrical, chemical and biological engineering, and materials science. Topics include: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations, fast methods for partial differential and integral equations, techniques for dynamical system model reduction and approaches for molecular dynamics.
This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5211 (Introduction to Numerical Simulation).
Course Curriculum
- Example Problems and Basic Equations Unlimited
- Equation Formulation Methods – Stamping Techniques, Nodal versus Node-Branch Form Unlimited
- Linear System Solution – Dense GE, Conditioning, Stability Unlimited
- Direct Methods for Sparse Linear Systems – Data Structures, Fill-in, Ordering, Graph Interpretations Unlimited
- Linear System Solution – Orthogonalization Methods, QR, Singular Matrices Unlimited
- QR and Krylov Iterative Methods. Brief Convergence Analysis Unlimited
- Krylov Methods (cont.) Unlimited
- Nonlinear System Solution – 1D Newton Methods, Convergence Analysis Unlimited
- Nonlinear System Solution-Multi-D Newton, Forming Jacobian by Stamping Approach, Singularity Unlimited
- Nonlinear System Solution – Damping, Optimization and Continuation Schemes Unlimited
- Nonlinear System Solution – Matrix-Implicit Methods and Methods for Singular Problems Unlimited
- ODE Solution Methods – BE, FE, Trap Examples, Convergence Unlimited
- ODE Solution Methods – Multistep Methods and Stability, Runga-Kutta Methods Unlimited
- ODE Solution Methods – Stiffly Stable and Conservative Schemes Unlimited
- Time-Periodic Solution Methods – Finite-Difference and Shooting Methods Unlimited
- Time-Periodic Solution Methods – Matrix-Implicit Algorithms and Preconditioning Unlimited
- Molecular Dynamics – Basic Numerical Issues Unlimited
- Molecular Dynamics (cont.) Unlimited
- 3-D Elliptic Problems – F-D Methods, Error Estimation Unlimited
- 3-D Elliptic Problems – Finite-Element and Spectral Methods Unlimited
- 3-D Elliptic Problems – FFT and Multigrid Methods Unlimited
- 3-D Elliptic Problems – Boundary-Element Approach Unlimited
- 3-D Elliptic Problems – FFT and Multipole Methods Unlimited
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